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ANALYSIS AND PREDICTION OF INDIVIDUAL VEHICLE ACTIVITY FOR MICROSCOPIC TRAFFIC MODELING
A Thesis Presented to
The Academic Faculty
By
Shauna L. Hallmark
In Partial Fulfillment of the Requirements
for the Degree Doctor of Philosophy in
Civil and Environmental Engineering
Georgia Institute of Technology December 1999
iii
TABLE OF CONTENTS
THESIS APPROVAL …………………………………………………………………ii
TABLE OF CONTENTS………..…………………………………………….……...iii
LIST OF FIGURES.……………...…………………………………………...………ix
LIST OF TABLES…………………………………………………………………....xi
GLOSSARY / ACRONYMS……………………………………………………..…xiv
SUMMARY ………………………………..……………………………………….xvii
1. INTRODUCTION…...…………………………………………………………….1
2. BACKGROUND………………………..………………………………………….6
2.1 Automobile Exhaust Emission…..………………………………………. 7 2.1.1 Ozone.…………..……………………………………………… 8
2.1.2 Carbon Monoxide.………………………………...…………… 9 2.1.3 Oxides of Nitrogen…………………..…………………………10
2.1.4 Pm10…………………………………………………………… 11 2.1.5 Hydrocarbons…………………………..………………………12
2.2 Drawbacks to Traditional Emission Modeling..………………………. 13
2.2.1 Vehicle Activity…………………………………………….. 15 2.2.1.1 Speed Estimates………………………….. ………...16 2.2.1.2 Volume Estimates……….…………………………..19
2.2.2 Emission Rates….……………………………………………...19
3. TOWARDS A MODAL APPROACH FOR TRANSPORTATION- RELATED EMISSION MODELING………………………………………..23
3.1 Evidence of a Mode Specific Emission Relationship………………….24
3.1.1 Tunnel Studies…………………………………..…………..….24 3.1.2 Activity Outside the FTP………………………………………25
iv
3.1.3 Enrichment.………….…………………………………………26
v
3.1.3.1 Acceleration………...…………………..……………28 3.1.3.2 Grade……………….…………………...……………30 3.1.3.3 Air Conditioner Use……….....………………………31 3.1.3.4 Rapid Load Reduction…….…………………………32
3.2 Towards a Modal Approach……….……………..………………………32
3.2.1 Improved Emission Factor Estimates..………………………34 3.2.2 Improved Vehicle Activity Estimates……...……...…………...37
3.2.2.1 On-Road Vehicle Activity Modeling.…...….………..38 3.2.2.2 Simulation..…………………………..………………39
3.2.3 MEASURE………………………………….….………………43
3.3 Fundamentals of Vehicle Activity in Traffic Engineering.…………….. 46 3.3.1 Acceleration Performance of Passenger Cars...…..……………46 3.3.2 Acceleration Performance of Heavy Trucks...…………………52
3.3.3 Deceleration Performance……………………..……………….54
3.4 Discussion…………………………………………….……………….…54
4. RESEARCH APPROACH………………………………………………………..56
4.1 Statement of Problem……………………….……………………………56
4.2 Hypothesis to be Tested …………………………………………………59
4.3 Objectives ………..……..………………….…………………….………59
4.4 Scope of Work…………..………………….……………………………61
4.5 Statistical Modeling…….….…………….….………………...…………65 4.5.1 Chi-Square Test.………………….……………………………66 4.5.2 Kolmogorv-Smirnov Two-Sample..……………………………68 4.5.3 Linear Regression…………………………………………...…70 4.5.4 Hierachiacal Based Regression Tree Analysis…...…………….72
4.5.4.1 Description of Test…..………….……………………74 4.5.4.2 Applicability of Test to Research…..………….….….76
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4.6 Research Scope and Presentation of Statistical Approach………………77
4.7 Response Variables………………………………………………………78 4.7.1 Carbon Monoxide Model………………………………………80
4.7.2 Hydrocarbon Model………………….………..…………….…85 4.7.3 Oxides of Nitrogen..………….……………….………………. 87 4.7.4 Final Response Variables………………………………………88
4.8 Independent Variables for Vehicle Activity Data..………………………89
4.8.1 Driver Variables..………………………………………………90 4.8.1.1 Trip Purpose…………………………………………91 4.8.1.2 Demographics.….……………………………………91
4.8.2 Vehicle Variables………………………………………………91 4.8.3 Roadway Variables…………………………….………………91
4.8.3.1 Horizontal and Vertical Curvature.……..……………92 4.8.3.2 Grade…………………………………………………93
4.8.3.3 Distance Between Adjacent Intersections……………94 4.8.3.4 Number of Lanes…………………………..…………94 4.8.3.5 Lane Width.….…………………………………….…95 4.8.3.6 Speed Limit.….………………………………………95
4.8.4 Environmental Factors.…..….…………………………………95 4.8.4.1 Pavement Condition …………………………………... 95
4.8.4.2 Weather …………………………………………….… 96 4.8.5 Other Factors..…………………………………………………96
4.8.5.1 Pedestrian Activity …………..…………………… 96 4.8.5.2 Location Along Segment .…….…………………… 97 4.8.5.3 Physical Location of Site .………………………… 97 4.8.5.4 Queue Position …………………………………… 98
4.8.6 Operational Characteristics..………………………………...…99 4.8.6.1 Level of Service……………………………...………99 4.8.6.2 Volume to Capacity ..……………………………… 99
4.8.6.3 Volume..………………………………………….…101 4.8.6.4 Density…..…………………………………….……101 4.8.6.5 Fleet Mix……………………………………………102
5. DATA PROTOCOLS.…………………………………………………………103
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5.1 Data Collection..………………………………………………………103 5.1.1 Selection of Sampling Locations.……………………………104
5.1.2 Advantage Laser Rangefinder…..……………………………106 5.1.3 JAMAR Boards..……………….……………………………107 5.1.4 Vehicle Attribute Data………….……………………………108 5.1.5 Site Attributes…..……………………………………………109 5.1.6 Data Collection Protocol.…………………………………….110
5.2 Data Handling….………………………………………………………110 5.2.1 Laser Rangefinder .…….……………………………….....… 112
5.2.2 RANGE.C Program ………………………………………..…113 5.2.3 ATTACH.C ………………………………………………..…117
5.2.4 Stopline Distances.……………………………………………117 5.2.5 Volume Calculations………………………………………….119 5.2.6 Percent Heavy Vehicle Calculations…………………….……119
5.2.7 LOS and V/C Ratio.……………….…………………….……120
5.3 Data Collection Sites..……………………….…………………………120
6. PRESENTATION OF DATA..……………………….…………………………128
6.1 Data Preparation….………………………….…………………………128
6.2 Data Analysis..……………………………….…………………………133 6.2.1 Identification of Microscopic Activity Distribution
Dependent Variables……….….……………………………137 6.2.2 Identification of Microscopic Activity Distribution
Independent Variables……………………………..…….…138
6.3 Results of Statistical Analysis for Passenger Cars……….………....…143 6.3.1 Activity for Queue Vehicles From Stopping Point to
200 Feet Downstream ACCEL Model………….….………..143 6.3.1.1 Percent Activity >= 6.0 mph/s
(ACCEL.6)……………………………….………….144 6.3.1.2 Percent Activity >= 3.0 mph/s (ACC.3) ………..… 149
6.3.1.3 Percent Activity <= -2.0 mph/s
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(DEC.2)…….……………………………………...149 6.3.1.4 Average Vehicle Speed (AVGSPD) ..…..………… 151
6.3.1.5 Inertial Power Surrogate >= 120 mph2/s (IPS120) ….………..……………………………… 152
6.3.1.6 Summarization of Results for ACCEL....……..……154 6.3.1.7 Final Predictor Model for ACCEL….………………155 6.3.1.8 Model Validation for ACCEL……….………………156
6.3.1.9 Final Model for Queued Vehicles for ACCEL………...…………………….………………158
6.3.2 Activity for Queued Vehicles From 200 to 400 Feet Downstream of Initial Stopping Point
(ACCELPLUS200….……………………………..…..……159 6.3.3 Activity for Queued Vehicles From 400 to 600 Feet
Downstream of Initial Stopping Point (ACCELPLUS400)………………………………………….160
6.3.4 Activity for Queued Vehicles From 600 to 1,000 Feet Downstream of Initial Stopping Point
(ACCELPLUS600 and ACCELPLUS800)………….…..….161 6.3.5 Activity for Queued Vehicles From Initial Stopping
Point Upstream 200 Feet (DECEL)..……………….………162 6.3.5 Activity for Queued Vehicles From 200 Feet Upstream
of the Initial Stopping Point to a Point 400 Feet Upstream (DECELNEG200)……………………….……….163
6.3.6 Activity for Queued Vehicles From 400 Feet Upstream of the Initial Stopping Point to 600 Feet Upstream (DECELNEG400)………………………………….………..164
6.3.7 Activity for “THRU” Vehicles at all Locations……....………164
6.4 Heavy Trucks……………………………………….………………..…166 6.4.1 Activity for Queued Vehicles From Initial Stopping
Point to 200 Feet Downstream (ACCEL)……….…………..166 6.4.2 Activity for Queued Vehicles From 200 Feet
Downstream to 800 Feet Downstream (ACCELPLUS200 to ACCELPLUS600)..………………….167
6.4.3 Activity for Queued Vehicles From 200 Feet Upstream to Stopping Point (DECEL)…………………………………167
6.4.4 Activity for Queued Vehicles From 600 to 200 Feet
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Upstream of Initial Stopping Point.…………………………168 6.4.5 Activity for “THRU”
Vehicles………………………………….……………..……169
6.5 Comparison of Research to Existing Simulation Modeling…………….169 6.5.1 Ranges of Field Data………………………………………….170
6.5.2 Comparison of Research to Existing Simulation Modeling ..………………………….………………….……174
6.5.3 Comparison of Research to Traffic Engineering Rates………182 6.5.4 Comparison of Research to NCHRP 185…..…………………183
6.5.5 Comparison of Research to FTP Range of Activity…..……185
7. DISCUSSION AND CONCLUSIONS….………………………………….……189
7.1 Model Limitations………………………………………………………190
7.2 Future Research Needs…………………………………………………193
7.3 Conclusions…………………………………………………..…………194
REFERENCES ……………………...………………………………………………196
APPENDIX A1…………………………………………………………………… 204
APPENDIX A2 ……………………………………………………………………219
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LIST OF FIGURES Figure 2-1, Traditional Emission Modeling……………………………………….…14 Figure 2-2, MOBILE Emissions Versus Speed Range for Carbon Monoxide………17 Figure 3-1, Modal Elements of a Vehicle Trip………………………………………34 Figure 3-2, Linear Speed-Acceleration Curve …………………………………..…. 48 Figure 3-3, Maximum Acceleration on Upgrades for Passenger Cars by Speed...…..52 Figure 4-1, Sample Vehicle Trace ………………………………………………… 62 Figure 4-2, Joint Acceleration-Speed Probability Density Function...………………64 Figure 4-3, Comparison of Empirical cdfs for Acceleration on a 9% Grade (x) and -9% Grade (z)………………………………………………….…69
Figure 4-5, Graduated Relationship Between Percent Hard Accelerations and
Queue Position……………………………………………………….…72
Figure 5-1, Data Collection and Reduction Methodology………………………….111
Figure 5-2, LRF Geometry Accounted for in RANGE70.C………………………..115
Figure 6-1, Schematic of Data Partions…………………………………………….132 Figure 6-2, Correlation Between V/C and Upstream Per
Lane Volume (R2 = 0.64)……………………………………………142
Figure 6-3, Original Untrimmed Regression Tree Model for ACC6……………….146 Figure 6-4, Reduction in Deviance with the Addition of Nodes………………...…146
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Figure 6-5, Normal Probability Plot of the Residuals for the Original Untrimmed Tree………………………………………………………….….147
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Figure 6-6, Trimmed ACC6 Model…………………………………………………148
Figure 6-7, Trimmed ACC3 Model………………………………………………...150
Figure 6-8, Trimmed DECEL2 Model…………………………………………...…151
Figure 6-9, Trimmed AVG_SPD Model……………………………………………153
Figure 6-10, Trimmed IPS120 Model………………………………………………154
Figure 6-11, Comparison of CDFs for Dataset Out1 and Out10………………...…157
Figure 6-12, Acceleration Distributions (mph/s) by Speed Ranges (mph)…………173 Figure 6-13, Comparison of Time Spent in Each Acceleration Range for Field
Data and NETSIM (-250 to 250 feet from the stopbar)……………176 Figure 6-14, Comparison of Time Spent in Each Speed Range for Field Data
and NETSIM (-250 to 250 feet from the stopbar)…………………176 Figure 6-15, Comparison of Time Spent in Each Acceleration Range for Field
Data and NETSIM (-250 to 250 feet from the stopbar) (Midblock) ……………178
Figure 6-16, Comparison of Time Spent in Each Speed Range for Field Data
and NETSIM (-250 to 250 feet from the stopbar) (Midblock) …………………178
Figure 6-17, Comparison of Field Data for First Vehicle in Queue with Linear
Speed-Acceleration Relationship……………………………………182
Figure 6-18, Acceleration Distribution (mph/s) by Speed Ranges (mph)………….178
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LIST OF TABLES
Table 3-1, Maximum Acceleration From Rest by Vehicle Type and Weight-to- Power Ratio……………………………………………………………..50
Table 3-2, Maximum Acceleration by Speed Range by Vehicle Type and
Weight-to-Power Ratio…………………………………………………50
Table 3-3, Maximum Acceleration on Upgrades by Speed Range ……………… 51
Table 4-1, Joint Acceleration-Speed Probability Density Function …...………… 65 Table 4-2, Modal Predictor Variables for Emission Rate Analysis for
Passenger Cars ……………………………………………………….88 Table 4-3, Operational and Geometric Factors Hypothesized to Affect Modal
Activity……………………………………………………………….90
Table 5-1, Example Data Collection Attribute Sheet …………………………… 109
Table 5-2, Example Output from RANGE……………………………………... 116
Table 5-3, Final Dataset Format ………………………………………………… 118
Table 5-4, Data Collection Sites …...…………………………………………… 122
Table 6-1, Data Partioning…………………………………………………………131
Table 6-2, Full Untrimmed Regression Tree Results for ACC6…..………………145
Table 6-3, Trimmed ACC6 Model Results………………………..………………148
Table 6-4, Trimmed ACC3 Model Results………………………..………………149
Table 6-5, Trimmed DECEL2 Model Results……………………………………..150
xiv
Table 6-6, Trimmed AVG_SPD Model Results…………………...………………152
xv
Table 6-7, Trimmed IPS120 Model Results……………………………………….153
Table 6-8, Breakpoints for Data Stratification from Initial Queue Position Downstream 200 Feet……………………………………...………155
Table 6-9, K-S Test Statistic for Comparison of Datasets 1 and 10 for
Acceleration Distributions…….………………………………………157 Table 6-10, K-S Test Statistic for Comparison of Datasets 1 and 10 for
Speed Distributions……………………………………………………157 Table 6-11, Breakpoints for Data Stratification From the Initial Queue Position
Downstream 200 Feet….……………………………………………159 Table 6-12, Breakpoints for Data Stratification From 200 to 400 Feet
Downstream of the Initial Queue Position…………………………159 Table 6-13, Breakpoints for Data Stratification from 400 to 600 Feet
Downstream of the Initial Queue Position…………………………160 Table 6-14, Breakpoints for Data Stratification from 600 to 1000 Feet
Downstream of the Initial Queue Position…………………………162 Table 6-15, Breakpoints for Data Stratification from Initial Stopping Point
Upstream 200 Feet…………………………………………………163 Table 6-16, Breakpoints for Data Stratification from 200 to 400 Feet Upstream of the
Initial Queue Position………………………………………………163 Table 6-17, Breakpoint for Data Stratification for “THRU” Vehicles for All
Distances Upstream and Downstream of the Data Collection Site…165 Table 6-18, Breakpoints for Queued Heavy Vehicles from Initial Queue
Position Downstream 200 Feet…..……………………………166 Table 6-19, Breakpoints for Queued Heavy Vehicles from 200 to 600 Feet
Downstream of the Initial Queue Position..…………………………167
xvi
Table 6-20, Breakpoints for Queued Heavy Vehicles from the Initial Queue
Position Upstream 200 Feet……………………………………………168 Table 6-21, Breakpoints for Queued Heavy Vehicles from the Initial Queue
Position from Upstream 200 to 600 Feet……………………………168 Table 6-22, Breakpoints for “THRU” Heavy Vehicles for All Distances
Upstream and Downstream of the Data Collection Site………………169 Table 6-23, Field Data Acceleration Observations by Speed Range………………171 Table 6-24, Comparison of Field Data and Traffic Engineering Handbook
Maximum Acceleration by Speed Range………………………………183 Table 6-25, Percent of Activity by Speed-Acceleration Ranges Outside the
FTP…………………………………………………………………187
Table 7-1, Limits of Prediction for Independent Variables……………………..…193
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ACRONYMS CAAA: Clean Air Act Amendments CARB: California Air Resource Board CART: Classification and Regression Tree Analysis CBD: Central Business District CO: Carbon Monoxide CO2: Carbon Dioxide DMI: Distance Measuring Devices FHWA: Federal Highway Administration FTP: Federal Test Procedure GIS: Geographic Information System HC: Hydrocarbons HCS: Highway Capacity Software HPMS: Highway Performance Monitoring System HTBR: Hierchiacal Based Regression Tree ITS: Intelligent Transportation Systems JASPROD: Joint Acceleration-Speed Probability Density Function K/S: Kolmogorv-Smirnov
xviii
LDV: Light Duty Vehicle LOS: Level of Service LRF: Laser Rangefinders MEASURE: Mobile Emission Assessment System for Urban and Regional Evaluation NAAQS: National Ambient Air Quality Standards NCHRP: National Highway Cooperative Program NO: Nitrogen Oxide NOx: Oxides of Nitrogen NO2: Nitrogen Dioxide O3: Ozone PPM: Parts Per Million Pb: Lead RMD: Residual Mean Deviance ROG: Reactive Organic Gas SO2: Sulfur Dioxide TCM: Transportation Control Measure TSP: Total Suspended Particulate VOC: Volatile Organic Compounds VMT: Vehicle Miles Traveled
xix
V/C: Volume to Capacity USEPA: United States Environmental Protection Agency UTPS: Urban Transportation Planning Software
xx
SUMMARY
Current research suggests that vehicle emission rates are highly correlated with
modal vehicle activity and that specific instances of load induced enrichment may contribute a
disproportionate share of motor vehicle emissions. Consequently, a modal approach to
transportation-related air quality modeling is becoming widely accepted as more accurate in
making realistic estimates of mobile source contribution to local and regional air quality.
New vehicle modal emission rate models will assess emissions as a function of specific
operating mode or engine load surrogates. These new models require that vehicle activity be
input by fraction of time spent in different operating modes. However, the ability to
realistically model microscopic on-road modal vehicle activity currently limits the
implementation of these models.
To provide better estimates of microscopic vehicle activity, field studies using laser
rangefinding devices were undertaken to quantify actual vehicle behavior along signalized
arterials and at signal-controlled intersections in Atlanta, Georgia. Data were analyzed to
determine the fractions of vehicle activity spent in different operating modes, especially those
that may lead to high engine load and elevated emissions. Statistical analysis of the data
yields a model for prediction of microscopic vehicle
xxi
activity based on geometric and operational characteristics of the roadway. Research results
will provide the ability to estimate microscopic vehicle activity as
input to both local and regional transportation-related air quality models. Findings may also
enhance current methods for estimating capacity and modeling traffic flow and may have
applications for intelligent transportation systems (ITS).
1
CHAPTER I
1. INTRODUCTION
For at least ten years, the technical, scientific, and administrative community
has expressed concerns about the current certification cycle for automotive emissions
being representative of actual driving behavior (Cicero-Fernandez and Long, 1994). A
major shortcoming of current emission modeling is the aggregated representation of
on-road vehicle activity, which inaccurately characterizes on-road driving behavior.
The current modeling philosophy is built on the assumption that drivers behave
similarly, rather than being based on individual or actual driver behavior. Average
behavior assumes that all drivers engage in driving patterns similar to those over
which vehicle emissions have been tested, such as the Federal Test Procedure (FTP)
Certification Cycle. Likewise, corresponding emission factors were developed from
procedures based on the assumption that vehicles pollute similarly under an average
range of speeds and vehicle miles traveled (VMT). This traditional approach neglects
variations in driving behavior, especially extremes such as hard accelerations or stop-
and-go driving under congested conditions.
2
A large body of evidence suggests that under most on-road operating
conditions, actual vehicle emissions can differ dramatically from those predicted by
current mobile source emission models (Pierson et al., 1990; LeBlanc, 1994; Barth et
al., 1997). Current research indicates that vehicle emissions rates are highly correlated
with engine operating mode. In particular, vehicle operation leading to engine loading
and elevated emissions are hard accelerations, air conditioner use, vehicle operation on
a grade, and hard decelerations.
Because recent research has indicated that various shortcomings exist in the
data input, modeling, and output of traditional mobile source air quality models,
current research activities are focusing on a modal approach to mobile source emission
modeling. Modal or activity-specific models attempt to estimate emissions as a
function of specific operating mode or engine load surrogates. To implement modal
models, statistical distributions of vehicle activity corresponding to the amount of time
that vehicles spend in different ranges of speeds and corresponding accelerations must
be developed. Once vehicle activity is disaggregated into speed and acceleration
distributions, activity-specific emission rates may be applied to estimate emissions.
Modal emissions modeling is becoming widely accepted as a more theoretically
accurate approach that will provide more realistic estimates of mobile source
emissions contributions to local and regional air quality analysis.
3
Although a modal approach to emissions modeling offers promising benefits in
terms of accuracy, a weak link is the ability to realistically model on-road modal
vehicle activity. Currently, little data exists relative to how vehicles operate in a real
world setting. Various activity estimation methods are in-use or proposed, such as
simulation models. None of these methods have been validated as to whether the
output realistically models the wide range of vehicle activity encountered on the
roadway. Additionally, the ability does not exist to relate activity to external variables
such as roadway grade or traffic volumes.
This research was conducted as part of a study underway at Georgia Institute
of Technology. Research was conducted under a cooperative grant from the U.S.
Environmental Protection Agency (USEPA) and the Federal Highway Administration
(FHWA).
The principal goal of this research was to develop a model that can predict
modal vehicle activity at signalized intersections and along signalized segments.
Individual vehicle traces were collected on-road at signalized intersections with laser
rangefinders (LRF) in the Atlanta, Georgia metropolitan area. With collection and
analysis of field data, statistical distributions of vehicle activity were generated and
tested using regression tree analysis to relate speed-acceleration profiles of vehicles to
roadway characteristics such as grade, location along the study link, queue position, or
4
volume of roadway to physical capacity. Data were analyzed with Hierachical Based
Regression Tree (HBTR) analysis and relevant predictor variables identified. The
final model predicts microscopic vehicle activity based on those operational and
geometric characteristics of the roadway, which were shown to influence vehicle
activity such as grade, location along link, queue position, or volume of roadway to
physical capacity. Model development ensured that final distributions of vehicle
activity can be linked with the modal emission rates from Georgia Tech’s MEASURE
model to provide input to both regional and microscale air quality models.
Chapter 2 of this work provides a background on air quality in general and
discusses some of the inadequacies of traditional transportation-related air quality
models. Chapter 3 overviews research that evidences a relationship between rate of
emission output and engine operating mode and provides explanatory information on
current research efforts for modal modeling.
In Chapter 4, the various statistical models considered for data analysis are
discussed and the final statistical model presented. The response variables based on
emission factor models from MEASURE are explained and a list of all independent
variables hypothesized to influence vehicle activity is presented. Chapter 5 covers
data collection and handling. The methodology for calculating variables, such as level
of service, is also covered. In Chapter 6, research results are presented along with the
5
final microscopic activity prediction models. A comparison of field data with various
traffic engineering relationships and with simulation modeling is also provided.
Finally, Chapter 7 presents a discussion and conclusion on research results.
The significance of this research work is development of a model capable of
predicting microscopic vehicle activity at signalized intersection based on roadway or
operational characteristics that influence behavior. Because the results have described
microscopic vehicle activity, research findings may also enhance current methods for
estimating capacity and modeling traffic flow and may have applications for
intelligent transportation systems (ITS).
6
CHAPTER II
2. BACKGROUND
Degraded air quality continues to be a major concern in most major cities in the
United States. Unhealthy levels of air pollution continue; posing health concerns, choking
economic development, and threatening federal transportation dollars, despite advances in
emissions control for both mobile and stationary sources. A significant share of blame for
urban air problems can be directly attributed to increasing development and urban sprawl,
which has resulted in a rapid increase VMT with the resulting emissions.
The Clean Air Act Amendments of 1990 (CAAA) were issued as a legislative mandate
to improve air quality in designated metropolitan areas. To regulate air pollution, National
Ambient Air Quality Standards (NAAQS) were established, setting acceptable levels for
specific airborne pollutants, including particulate matter, carbon monoxide (CO), oxides of
nitrogen (NOx), sulfur dioxide (S02), ozone (O3), and lead (Pb). NAAQs set the maximum
air pollution concentrations allowable in any one area based on the minimum dose of the
pollutant required to cause adverse health effects in the most sensitive members of the
population (Kaliski, 1991).
7
Air pollution comes from a variety of sources, which can be divided into three main
categories:
• Stationary sources: factories, power plants, smelters, etc.;
• Mobile sources: automobiles, trucks, buses, trains, and planes; and
• Natural sources: pollution from wildfires, windblown, dust, volcanic eruptions, etc.
(USEPA, 1995a).
This chapter provides background information on transportation-related air pollutants
including the National Ambient Air Quality Standards. An introduction on traditional
transportation-related air quality modeling along with a discussion on the drawbacks of the
modeling process in terms of both emission factors and vehicle
activity are presented.
2.1 Automobile Exhaust Emissions
The transportation sector is directly responsible for a significant proportion of harmful
ambient emissions (Anderson et al., 1996). Estimates for the amount of pollutants produced
by motor vehicles vary from 33 to 50% of NOx, 33 to 97% of CO, 40 to 50% of HC, 50%
of ozone precursors, and at least one-fourth of volatile organic compounds (VOC ) (Mullen
et al., 1997; SCAQMD, 1996; EPA, 1995a; USDOT, 1993; CARB 1994; Chatterjee et
al., 1997). Although not included in the NAAQs, particulate matter with aerodynamic size
less than or equal to 10 microns (PM-10) is also released by motor vehicles from diesel
8
engines and tire wear. Hydrocarbons (HC) are also not included in the NAAQs but are
included in mobile source emission modeling since they contribute to ozone formation. CO,
NOx, and HC are a by-product of combustion and are found directly in automobile exhaust.
Fuel evaporation also contributes emissions of VOC.
2.1.1 Ozone
The NAAQS for ozone are 0.23 parts per million (ppm) for a one-hour period.
This standard may not be exceeded more than 3 times over a continuous 3-year period
(Chatterjee et al., 1997). This pollutant is a highly reactive form of oxygen. It is a colorless
gas, characterized by a sharp odor. Ozone occurs naturally in the stratosphere but normally
only in low doses (0.03 to 0.05 ppm) near the surface of the earth. Ozone is not emitted
directly from mobile sources; rather it is produced by a complicated series of chemical and
photochemical reactions between reactive organic compounds, oxides of nitrogen, and
naturally occurring oxygen. Photochemical reactions require solar radiation to act as a
catalyst; consequently peak concentrations of ozone are found around the middle of the day
and climax during the summer months.
The associated health effects of ozone include decreased breathing capacity,
increased airway resistance, impaired host defenses, acute inflammation of the lung tissue,
and respiratory cell damage. A correlation is hypothesized between an increasing number of
9
hospital admissions for all respiratory causes, including asthma, and an increase in ambient
ozone, sulfates, or sulfur dioxide levels (SCAQMD, 1996; Mullholland, 1998).
2.1.2 Carbon Monoxide
The pollutant, carbon monoxide is a colorless, odorless, relatively inert gas
introduced by both human and natural sources, such as forest fires. In urban areas, the
primary source of CO is incomplete combustion of carbon-containing fuels, mostly gasoline.
During optimum combustion, each carbon atom has affinity to bond with two oxygen atoms
forming carbon dioxide (CO2). When an oxygen deficiency is present in the engine, some
carbon atoms are only able to bond with a single oxygen atom and the result is CO.
Consequently, an overly rich air-fuel ratio is the primary cause of CO formation (King,
1995). Colder temperatures are more conducive to the formation of CO, consequently CO
exceedances are more common in the winter (CARB 1995).
Ambient concentration of CO are spatially and temporally correlated to the rate at
which CO is emitted and prevailing meteorological conditions, with peak concentrations
occurring in the fall and winter months. Because automobile exhaust is the major source of
CO, high concentrations can result in urban areas with heavy traffic congestion (EPA,
1995a). NAAQS for CO are 35 ppm for a one-hour averaging period and 9 ppm for an 8-
hour period, which is not to be exceeded more than once per year.
10
Carbon monoxide enters the bloodstream and displaces oxygen, binding with
hemoglobin in the blood. This reduces the blood’s ability to carry oxygen to the body’s
organs and tissues. Therefore, most of the toxic effects of CO are caused by reduced
oxygen supply. Those at the highest risk from carbon monoxide are heart patients, smokers,
and people who engage in heavy exercise (SCAQMD, 1996). Other health effects due to
exposure to elevated CO levels include visual impairment, reduced work capacity, reduced
manual dexterity, poor learning ability, and difficulty in performing complex tasks (EPA,
1995a).
2.1.3 Oxides of Nitrogen
The nitrogen content of both gasoline and diesel fuels is negligible. Oxides of
nitrogen, a colorless gas, is actually formed from the destruction of atmospheric nitrogen
(N2), which makes up 80% of air, during the combustion process. Although ambient
nitrogen and oxygen do not normally react, in the presence of sufficiently high temperatures,
a chemical reaction occurs catalyzing oxygen and nitrogen to form nitrogen oxide (NO)
(King, 1995). Formation of oxides of nitrogen is exacerbated by high temperature and high
concentrations of oxygen. Once formed, oxides of nitrogen quickly react with oxygen and
form nitrogen dioxide (NO2), a reddish-brown gas with a bleach-like odor, which is
primarily responsible for the brownish tinge characteristic of polluted air. Nitrogen dioxide
also plays a major role in atmospheric reactions, which produce ground-level ozone (EPA,
1995). Critical engine variables that determine the amount of oxides of nitrogen produced
11
are the fuel/air equivalence ratio (Ø), the burned gas fraction of the in-cylinder unburned
mixture, and spark timing.
Once oxides of nitrogen are released into the atmosphere, a reaction occurs with
reactive organic gas (ROG) to form ozone. This reaction is catalyzed by sunlight and
therefore occurs more often in the summer corresponding to higher temperatures and greater
amounts of sunlight (CARB, 1995). Besides ozone formation, nitrogen oxides in the air are
a potentially significant contributor to a number of environmental effects such as acid rain and
eutrophication in coastal waters. Eutrophication is an increase in nutrients that reduce the
amount of oxygen in a body of water creating an environment that is destructive to fish and
other animal life (EPA, 1995a).
Children and adults with respiratory illnesses are most susceptible to oxides of
nitrogen, which is a respiratory irritant and reduces resistance to respiratory infection such as
influenza (SCAQMD, 1996).
2.1.4 PM 10
PM10 is a category of total suspended particulate (TSP), which is made up of a
complex mixture of solid material suspended in the atmosphere. Finer fractions of TSP have
greater effects on health and visibility than coarse fractions. PM10 is particulate matter with
diameter less than approximately 10 micrometers. The mobile source contribution to
12
particulate matter is a product of combustion, machinery, and tire wear (Chatterjee et al.,
1997).
The main health effects associated with PM10 include increased mortality,
exacerbation of preexisting respiratory and cardiovascular disease, changes in lung function
and structure, altered defense mechanisms, and increased risks of developing cancer
(SCAQMD, 1996). Children, the elderly, and persons with chronic lung disease, influenza,
or asthma tend to be especially sensitive to the effects of particulate matter. In an acid form,
PM-10 is destructive to manmade materials and is a major cause of reduced visibility in
many parts of the United States (EPA, 1995a).
2.1.5 Hydrocarbons
Hydrocarbons are one of the three commonly modeled transportation-related
pollutants (CO, NOx, and HC). Hydrocarbon emissions result from incomplete combustion
of hydrocarbon-based fuel, such as gasoline. Fuel composition can significantly affect the
types and amounts of hydrocarbons released. Hydrocarbons are released as part of the
combustion process and from piston blow-by gases. Unburned hydrocarbons are released
during fuel evaporation and through vents in the fuel tank and carburetor after engine shut-
down (Heywood, 1988).
Gasoline itself is a hydrocarbon compound and when burned properly, the hydrogen
and carbon atoms split apart and then bond with oxygen to form water,
13
(H20), or carbon dioxide, CO2 (King, 1995).
2.2 Drawbacks to Traditional Emissions Modeling
In order to meet CAAA goals and demonstrate progress towards conformity, the
traditional mobile source emission modeling approach was developed. A flowchart of the
general process is presented in Figure 2-1. In its most basic form, this approach simply
multiplies an estimate of vehicle activity by an emission factor to determine the total quantity
of pollution released by a roadway, group of roadways, or region. The most common
emission factor models are the MOBILE family of models, widely used throughout the
United States, and the EMFAC models used in California.
Although emission estimates play an important role in determining a region’s progress
towards meeting air quality goals and influence transportation investment decisions, numerous
inadequacies exist in both the data input and modeling methodology of traditional mobile
source emission modeling. These inadequacies extend to both the vehicle activity side of the
equation as well as to emission factor estimates. One of the main flaws is that the data used
to support modeling often come from sources not intended to support air quality analysis and
consequently may produce inaccuracy in the air quality analysis and the conclusions they
present.
14
15
Figure 2-1: Traditional Emission Modeling (source: Roberts, 1999)
14
16
Another major flaw is the aggregate representation of on-road vehicle activity to
estimate emissions, resulting in inaccurate characterization of actual driving behavior. The
current modeling philosophy assumes that all drivers engage in driving patterns similar to
those over which vehicle emissions have been tested. Likewise, corresponding emission
factors were developed from aggregate representations of vehicles based on the assumption
that vehicles pollute similarly under an average range of speeds and vehicle miles traveled
(Guensler and Sperling, 1994).
2.2.1 Vehicle Activity
One of the main shortcomings of the traditional modeling approach is that it is unable
to capture actual on-road vehicle behavior. Instead, activity estimates are frequently based
on output from regional transportation modeling systems, which were developed to forecast
the need for new highway facilities, rather than air quality modeling. Consequently, these
models are not sensitive to the inputs and parameters required for air quality modeling, such
as accurate estimates of vehicle speeds. Inaccuracies in vehicle estimates are related to data
input, mathematical algorithms, and the calibration procedures of regional transportation
models. Data input to regional models are often based on databases that are incomplete or
outdated. Information about the number of trips, geographic distribution of those trips, and
timing of tripmaking is often estimated from household surveys done years previously
(USDOT, 1993).
17
2.2.1.1 Speed Estimates One of the major shortcomings of vehicle activity
estimates is the use of average speed estimates derived from regional models. Historically,
the MOBILE or EMFAC series of motor vehicle emission rate models estimated emissions
as a function of average speed, consequently the modeled relationship between emissions
and vehicle activity is highly speed dependent. Emission rates vary greatly across different
speed ranges as shown in Figure 2-2 for CO in grams per mile. For CO, MOBILE5A
emission rates are highest in the lower speed ranges and then reach their lowest rates in the
middle speed ranges from 30 to 45 mph. Emission rates increase again after 55 mph.
Locations on the emission curve where the slope is the steepest, indicate areas where
emission rates are the most sensitive to changes in speeds. Inspection of Figure 2-2
indicates that an increase in average speed, from approximately 3 to 20 mph, reduces the
emission rate from 130 to 20 g/mile. Logically, areas on the chart where emission rates are
the most sensitive to changes in average speed are also locations where errors in estimating
average speed would have the greatest impact to over or underestimate emissions. Around
60 mph, an error of only 1.2 mph will cause a 10% error in the CO emissions factor. At 20
mph, an error of 2.3 mph in average speed would be required to create that same 10% error
in CO emissions (Chatterjee, et al., 1997).
Although emissions are speed dependent in traditional modeling, the main data
sources for both traffic volume and speed data are output from the traffic assignment
18
Figure 2-2: MOBILE Emissions Versus Speed Range for Carbon Monoxide
17
18
stage of travel demand modeling, whose main purpose is to forecast roadway volumes, not
accurately replicate link speeds. Link speeds are used to calibrate the model for realistic
volume output (Chatterjee et al 1997). Speeds input to four-step modeling are often the
posted speed limit or default values, such as 45 mph for arterials, 35 mph for collectors, etc.,
instead of observed freeflow speeds. In some cases the use of speed limits or defaults may
lead to underestimation of actual speeds since motorists frequently exceed speed limits. The
use of average speeds also fails to accurately describe the wide ranges of vehicle activity
actually found in normal driving. A group of vehicles at high speed coupled with a group of
low speed vehicles, both of whom are operating in the higher emission factor ranges, could
average out somewhere in the mid-speed ranges where emission factors are lowest for HC
and CO (DeCarlo-Souza et al., 1995). Comparisons of modeled versus actual speeds have
demonstrated that speeds modeled by travel demand forecasting models may exceed on-
road speeds by 35%. Discrepancies in modeled and actual speeds may result from the fact
that the capacity-restraint formula often used in travel demand models does not degrade for
speed appropriately with considerable congestion. Speeds are used to calibrate travel
demand models so that when modeled volumes replicate actual volumes, such as a screen
line counts, match within a reasonable range of accuracy (commonly 10%), the model is
considered to be calibrated. Rarely are model speeds compared against on-road speeds.
Volume and speed estimates from regional models are also likely to become increasing
19
unreliable under congested conditions, which are a common occurrence in urban areas
(USDOT, 1993).
2.2.1.2 Volume Estimates A regional estimate for VMT, usually from the regional
travel demand forecasting models, is often multiplied by emission factors in grams per mile to
calculate total emissions produced. However, VMT output from regional models has several
inherent inaccuracies. First, the road network used in travel demand models is not detailed
enough for air quality modeling. Travel demand models use stick representation of the
surface street system, which typically include only major roads such as arterials, freeways,
and collectors. Consequently, VMT is available only for representative roadways in the
network. Volume data is not available from travel demand modeling for all links in the
network. Second, local street systems are not adequately accounted for in regional modeling
(Chatterjee et al 1997). Local streets, themselves are not highly significant in the four-step
modeling process since their purpose is only to provide access to the major street network.
Consequently they are usually represented as centroid connectors. The lack of available
data is particularly a problem as no accepted technique exists for VMT calculations for local
roads. Local roads are typically low volume facilities, however they may make up a
significant proportion of total miles of roadway in urban areas (Chatterjee et al., 1997).
Consequently, lack of representation of both VMT and speeds on local roads presents a
major deficiency in urban activity modeling.
20
2.2.2 Emission Rates
A major shortcoming in traditional emission factor modeling is that a complete range of
vehicle activity is not represented in the Federal Test Procedure on which MOBILE is
based. The main algorithms in the MOBILE model were developed for the following default
assumptions:
• average vehicle speed of 19.6 mph;
• ambient temperature of 75° F; and
• start mode fractions of 20.6% cold and 27.3% hot starts.
Emission factor are based on the default assumptions and then adjusted by
dimensionless correction factors to represent region-specific conditions, such as average
speed, ambient temperature, percent cold starts, gasoline volatility, implementation of
inspection/maintenance programs, and use of oxygenated fuels (Keenan and Escarpeta,
1995). In the development of the FTP, acceleration rates were artificially reduced to
accommodate testing equipment capabilities. Additionally, the original objective of the FTP
was to capture average driving not variations in speed, consequently more aggressive driving
behavior such as high speed and high accelerations are not captured (USEPA, 1995b).
The Federal Test Procedure, on which MOBILE is based, was established over two
decades ago and was intended to replicate the operation of a typical in-use urban vehicle.
21
The FTP uses the average driving conditions, which are embodied in a pre-determined
driving cycle, to determine emission factors (Barth et al., 1996). The FTP was developed to
represent a typical driving pattern in primarily urban areas and was created to simulate a trip
route in Los Angeles representative of a typical home based work trip. The original route
was selected to match the engine operating mode distribution obtained in central Los
Angeles using a variety of drivers and routes. The driving cycle is a particular pattern of idle,
acceleration, cruise, and deceleration over which a vehicle is tested. Then emission factors
specific to each cycle are produced (CARB, 1995).
Emission factors were also developed using a small sample of vehicles, which may
not be representative of the actual on-road fleet. This is particularly significant since
emissions rates may vary even between vehicles of the same type based on miles
accumulated on the vehicle, driving behavior, inspection and maintenance history, etc.
(USDOT, 1993).
Another drawback to current practice is that vehicle activity and speed estimates are
link-based while emission factor models such as MOBILE are trip based. MOBILE
estimates emissions over an entire trip, about 20 minutes, rather than for a particular link.
Travel demand forecasting models are based on a street network represented by nodes
(intersections) and links and as a result link-specific speed and traffic volumes are
22
generated. This trip-based emission factor modeling is therefore inconsistent with link-
based modeling (DeCorla-Souza et al., 1995).
Inaccuracies in vehicle emissions models can also occur from errors in basic emission
rates, as well as in correction factors, such as speed correction factors, which are used to
adjust basic emissions rates. Basic emission rates are measured from a simulated pattern
intended to be representative of "typical" city driving. This approach does not accurately
reflect differing road facilities, vehicle types, and operational activity common to urban
driving. Additionally, the overall average speed of 19.6 mph does not reflect actual speeds
on urban collectors, arterials or freeways (USDOT, 1993).
23
CHAPTER III
3. TOWARDS A MODAL APPROACH FOR TRANSPORTATION-
RELATED AIR QUALITY MODELING
As explained in Chapter 2, various shortcomings exist in the traditional mobile source
emission-modeling regime. The most significant drawback for both activity and emission
factor modeling is the inability to model actual on-road vehicle behavior, especially activity
outside the range of the FTP, and to correlate emission production specifically to operating
mode. This chapter first outlines current research indicating that operating mode is related to
emission output rates. Next, an overview is provided of research efforts focused on mode
specific activity and emission factor estimates. Finally, an overview of current
representations of speed/acceleration relationships common to traffic engineering are
presented, to provide the reader with necessary background information. These
relationships are often the basis for simulation models and other methods in use to create
modal activity estimates. Later, in the data analysis chapter, Chapter 6, field data are
compared with these traffic-engineering relationships. An overview of vehicle dynamics as
they relate to speed and acceleration is also provided in Appendix A for more background
information.
24
25
3.1 Evidence of a Mode Specific Emission Relationship
An overview of contemporary research which has demonstrated inadequacies in the
current average speed based approach and has indicated that emissions are related to engine
operating mode are presented in the following sections.
3.1.1 Tunnel Studies
Initial evidence that traditional modeling may not adequately represent actual on-road
emissions was evidenced by studies in several traffic tunnels. An initial study was conducted
in the Van Nuys Tunnel in California in 1987, which measured vehicle emissions with a mass
flow study. The pollutant levels collected from the tunnel were three times higher for CO and
four times higher for HC than predicted by EMFAC7C (Pierson et al., 1990).
Additional studies were conducted in other tunnels. Emissions from motor vehicles
for CO, NO, NOx, gas-phase speciated nonmethane hydrocarbons, and carbon
compounds were measured in 1992 in the Fort McHenry Tunnel under Baltimore Harbor
and the Tuscararoa Mountain Tunnel of the Pennsylvania Turnpike. The tunnels were
characterized by high speeds with little acceleration. The vehicle fleet for both tunnels was
relatively new with the median vehicle age less than 4 years old. Consequently, cleaner
vehicles under steady speed conditions dominated the study. Results indicated that
MOBILE4.1 and MOBILE5 only gave predictions within +-50% of observation with the
MOBILE models tending to overpredict emissions (Pierson et al 1996).
26
3.1.2 Activity Outside the FTP
Various studies show that a significant amount of on-road driving activity occurs
outside the range of activity represented in the Federal Test Procedure (velocity >= 57 mph
and acceleration >= 3.3 mph/s).
The USEPA supported instrumentation of instrumented approximately 350 vehicles
in Spokane, Washington; Baltimore, Maryland; and Atlanta, Georgia and recorded vehicle
speed, engine speed, acceleration, and manifold absolute pressure (LeBlanc et al., 1995).
Statistically significant differences were noted in vehicle speeds and acceleration
characteristics across these cities. The three-city instrumented vehicle study also found
accelerations ranging from a minimum of -19.49 mph/s to a maximum of 16.69 mph/s.
Although these values, contrast sharply with the maximum acceleration in the FTP of 3.3
mph/s (USEPA, 1995b) they do appear to be extremely high.
Trip lengths were also recorded for the three-city study and an average trip length of
4.9 miles in length discovered as compared to the 7.5 mile average trip used for the FTP,
this suggests that that actual trip lengths may be much shorter than those modeled in the FTP
(Enns et al., 1994).
Another study using 1,100 miles of driving data from the Los Angeles area were
used to develop seven cycles of vehicle activity. The researchers found differences between
27
freeway and arterial driving. Cycles representing freeway activity were much smoother in
terms of speed and ranges of accelerations and decelerations as compared to arterial flow,
which was much rougher. The authors indicated that 18.7% of driving time was spent in
accelerations greater than 3 mph/s for arterials versus 2.3% for freeways and 32.9% of
arterial and 7.6% of freeway activity was spent in decelerations less than -3mph/s (Effa and
Larsen, 1994). This indicates that differences in modal activity may occur across roadway
types.
3.1.3 Enrichment
One of the extremes in vehicle activity that has been demonstrated to contribute a
disproportionate share of emissions is commanded enrichment. Commanded enrichment is
an engine-operating mode where the engine management feedback control system (which
ensures stoichiometric operation) is overriden to increase the fuel:air ratio (LeBlanc et al.,
1994; Ganesan, 1994). Commanded enrichment provides increased engine power output
to enhance performance and also reduces peak exhaust gas temperatures protecting engine
components and exhaust after-treatment systems from the high exhaust gas temperatures that
would result under high load conditions.
Commanded enrichment is typically called for whenever the engine operates under
high load conditions, such as undergoing a hard acceleration, action against a grade, or
pulling a load. The air-fuel ratios for commanded enrichment can be as rich as 11.7:1
28
compared to the normal stoichiometric air-fuel level of approximately 14.7:1 (Heywood,
1988).
Engine-out CO emissions increase as the air-fuel ratio is enriched from stoichiometric
levels. Emissions increase due to the lack of oxygen available to complete the combustion
process, which normally results in conversion of hydrocarbons to CO2 and water.
Hydrocarbon emissions also increase under fuel-rich conditions, since less fuel is burned.
The catalyst conversion efficiency levels for both HC and CO emissions are very sensitive to
air-fuel ratios. In a fuel-rich combustion environment, the lack of oxygen causes the normal
oxidation process that converts HC and CO into CO2 and water vapor to drop off very
quickly causing a reduction in catalyst conversion efficiency (Heywood, 1988).
St. Denis and Winer (1994) used an instrumented Ford Taurus (1991 model year)
to collect on-road driving data in California. The researcher found relevant differences
between actual collected emissions and the amount of emissions calculated using the FTP
procedure. The differences for CO were attributed to enrichment, which was estimated to be
responsible for two-thirds of the difference between modeled and FTP calculated emissions.
Study results also found that pollutants released during enrichment were two to three times
higher than for stoichiometric operation indicating that engine operating mode is an important
variable in determining emission output.
29
Other tests on individual vehicles reported that moderate to heavy engine loads lead
to enrichment conditions that can increase gram/second emission rates for carbon monoxide
by 2500 times and hydrocarbon emissions by 40 times compared to normal stoichiometric
operation (LeBlanc, 1994; Barth et al, 1996).
3.1.3.1 Acceleration Commanded enrichment is caused by engine loading. One factor
leading to engine loading is "hard" accelerations. Research has indicated that a single "hard"
acceleration event (enrichment event) may cause as much pollution as the remainder of the
trip (Guensler, 1993). Emissions tests conducted at the California Air Resources Board,
primarily on carbureted vehicles, showed a large increase of HC and CO during hard
acceleration events. Later studies indicate that a single hard acceleration (> 6mph/s) could
increase the total trip emission for carbon monoxide (CO) by a factor of two.
Cicero-Fernandez and Long (1994) evaluated ten current technology vehicles over
four testing cycles. One of cycles was a specially designed acceleration cycle, which
included various acceleration events. Comparison of the acceleration specific cycle
emissions to those from a comparable FTP cycle indicated that HC emissions were 3 times
higher for the acceleration cycle than the FTP cycle. For CO, it was 19 times higher than the
FTP cycle and for NOx the acceleration cycle was similar to the FTP cycle indicating a
stable release of NOx even under enrichment. They also indicated that accelerations at low
30
to medium speeds had less pronounced emission increases than accelerations at higher
speeds.
Le Blanc et al. (1995) also conducted research that estimated emissions as a
function of speed/acceleration ranges. The researchers found a correlation between
increased CO output in g/s and the following:
• high speeds with speeds greater than 57 mph and acceleration rates less 1 mph/s;
• high accelerations greater than 3.3 mph/s with speeds less than 57 mph; and
• high speeds/high accelerations with speeds greater than 57 mph and accelerations
greater than 1 mph/s.
Research by CARB also found that hard accelerations triggered increased emissions,
especially for CO. An increase in HC was also found to be significant under hard
accelerations. Accelerations at mid to high speeds emitted more emissions than low to mid-
range speeds. For NOx, speed was found to be a more influential variable in emission rates
than accelerations (CARB, 1997).
Finally, Yu (1998) also found a correlation between speed, acceleration, and
emission rates using remote sensing studies in Houston at five locations. From the data
collected, a model was developed which correlated on-road vehicle exhaust emission rates
31
with the vehicle's instantaneous speed profile. Study results were compared with existing
emission models. Results indicated that both the MOBILE and EMFAC emission models
underestimated emissions for all vehicle types as compared to on-road estimates.
3.1.3.2 Grade Roadway gradient has been investigated as a geometric effect that
may increase emissions. Acceleration against a grade results in additional load on the engine
beyond that which is associated with normal driving. The higher mass flow associated with
increased engine load is expected to produce higher emissions for all three pollutants (CO,
NOx, and HC). It may also increase the frequency or extend the duration of enrichment
which impacts CO emissions (USEPA, 1995b).
Cicero-Fernandez et al. (1997) studied the effect of road grade and found that for
each 1% increase in grade, the HC emission rate increased by 0.04 g/mile and the CO
emission rate increased by 3.0 g/m. The study consisted of controlled runs with speeds
between 35 and 55 mph and a maximum acceleration of 3.3 mph/s. Runs were conducted
on both flat terrain and road segments with grades from 0 to 7% in Los Angeles, California.
Both freeways and arterials were included in the study. Enns et al. (1994) tested 9 vehicles
for grade influences and found increases in CO of 3.2 grams/mile with much smaller
increases for HC and NOx.
32
The Fort McHenry tunnel study, discussed in section 3.1.1 collaborates the
correlation between grade and elevated emissions. The tunnel had +3.76 upgrade and -3.76
downgrade. The vehicle fleet was composed of relatively newer vehicles and vehicle activity
in the tunnel was composed of smooth flow. Comparison of emissions from the upgrade and
downgrade yielded an increase in emissions per mile by a factor of two. The authors
concluded that the effect of grade was significant and that is should be included in
transportation-related air quality modeling (Pierson et al., 1996).
3.1.3.3 Air Conditioner Use Evidence has shown that air conditioner use in a
vehicle results in elevated emissions. The effects of air conditioning use detailed in the
previously described study by Cicero-Fernandez et al. (1997), who conducted controlled
test vehicle runs with speeds between 35 and 55 mph and low acceleration on road
segments with grades from 0 to 7%. With the air conditioner running at full setting, emissions
increased by 0.07 g/mile for HC and 31.9 g/mile for CO. Enns et al. (1994) also described
the impact of air conditioning use as increasing NOx emissions by 0.21 grams/mile. Another
study found that air conditioning use (on max) in combination with roadway grades of up to
6.7% increased HC emissions up to 57% and CO up to 268% (CARB, 1997).
3.1.4 Rapid Load Reduction
Most research identified loading events, such as work against a grade or hard
accelerations, as the culprits for elevated emissions in otherwise normally emitting
33
vehicles. Elevated HC emissions have also been associated with rapid load reduction and
long deceleration events. During stoichiometric driving, the quantity of condensed fuel on the
intake manifold walls is in rough equilibrium, dependent to some degree on the recent history
of fuel injection (power level). With negative engine power, which often occurs in
coastdown and braking, air flow continues with little or no fuel injection causing an extremely
low ratio of fuel to air, which inhibits combustion. This allows the condensed fuel to be
removed by evaporation over a period of several seconds resulting in elevated unburned
hydrocarbons levels. A study by An et al. (1998a) tested 200 vehicles and found that this
phenomenon contributed 10 to 20% of the overall HC emissions under various test cycles.
3.2 Towards A Modal Approach For at least ten years, the technical, scientific, and regulatory community has
expressed concerns about the current certification cycle for automotive emissions being
representative of actual driving behavior (Cicero-Fernandez and Long, 1994). Because
recent research has indicated that various shortcomings exist in the data input, modeling, and
output of traditional mobile source air quality models, current research activities are focusing
on a modal approach to mobile source emission modeling.
To address shortcomings in current transportation-related air quality models and
provide agencies with enhanced tools for vehicle emission estimates, various modal modeling
approaches have been suggested. Modal models attempt to estimate pollutants as a function
of specific operating mode or engine load surrogates. To implement modal models,
34
statistical distributions of vehicle activity corresponding to the amount of time that vehicles
spend in different ranges of speeds and corresponding accelerations must be developed.
Once vehicle activity is disaggregated into speed and acceleration distributions, activity-
specific emission rates may be applied. Modal emission modeling is becoming widely
accepted as a more theoretically accurate approach that will provide more realistic estimates
of mobile source contributions to local and regional air quality (Guensler, 1993; Barth et al,
1996; Washington, 1996). Figure 3-1 shows a schematic of the modal elements of a
hypothetical trip, including idling, acceleration, cruise, and deceleration. This figure presents
a schematic of a typical trip when broken down into its modal elements.
Currently various research groups, both nationally and internationally, are working on
various facets of modal modeling. Research efforts include development of activity specific
emission factors, improved prediction of fleet mix, improved estimation of cold and hot start
fractions, development of methods to better predict on-road vehicle modal activity, etc.
Following is a summation of the major research efforts underway for emission factor and
vehicle activity modeling.
35
Figure 3-1: Modal Elements of a Vehicle Trip
3.2.1 Improved Emission Factor Estimates
One of the major flaws in traditional modeling is the use of emission factors, which
average emissions over a cycle, such as the FTP, and neglect extremes in vehicle activity. To
improve emission factor estimates, various research efforts have focused on developing
methods to relate emission output to specific vehicle activity such as a vehicle's instantaneous
speed and corresponding acceleration.
Post et al. (1985) tested 177 Australian light duty vehicles on a dynamometer and
created averaged vehicle maps of emissions. Data were mapped into matrix format showing
emission rates for specific speed/acceleration bins. The model was developed to make fuel
36
consumption predictions for any type of vehicle, engine capacity, and driving pattern.
Emission rates for carbon monoxide, carbon dioxide, oxides of nitrogen, and hydrocarbons
were output during the dynamometer testing and emission rates correlated to instantaneous
velocity and acceleration. The three-parameters (speed, acceleration, and emissions) were
used to develop a two-parameter (power and emissions) emission model. The power term
is the product of speed and acceleration. Elevated emissions were noted for higher
accelerations independent of the corresponding speed for both CO and HC. Increasing
speeds were also correlated to elevated emissions for the two pollutants.
Sierra Research has created driving cycles, based on chase car and instrumented
vehicle data from Baltimore, Spokane and Los Angeles, which was collected during the FTP
Revision Project. Cycles were constructed to match observed speed-acceleration and
specific power frequency distribution of chase car driving data. Facility-specific cycles were
constructed using randomly selected microtrips to match the speed-acceleration frequency
distribution of all vehicle operation occurring under conditions of interest such as a particular
facility type or level of service (LOS). Vehicle activity was collected using a specially
designed instrumented vehicle with a grill mounted laser rangefinder and distance measuring
instrument. This type of data collection allowed calculation of the instantaneous speed and
acceleration of the "followed" vehicle. Other variables were collected such as LOS. Vehicle
activity was categorized into six driving cycles defined by LOS of the freeway segments.
37
The level of service calculated, however, was a rough estimate based on data collector’s
perception of activity around the chase vehicle rather than a formal calculation (USEPA,
1997).
An et al. (1997) outlined on-going development of a comprehensive modal emissions
model capable of predicting emissions for a wide variety of light-duty cars and trucks based
on engine operating mode. At the highest resolution, the model will predict second by second
vehicle trajectories (location, speed, acceleration).
Approximately 320 in-use vehicles were recruited and tested on a dynamometer
over three different driving cycles. For each cycle, second-by-second emissions for CO2,
CO, NOx, and HC emissions were collected and analyzed for different driving conditions.
Ultimately, the model will be able to predict emissions for a variety of light duty vehicles
(LDVs) in different maintenance states (properly functioning, deteriorated, malfunctioning,
etc.). The model will predict emissions and fuel consumption second by second (Barth et al.
1999).
Another study described the use of SMOG DOG, a remote sensing technology that
is able to simultaneously measure emission concentration for CO, HC, NOx and CO2 in the
dispersing exhaust cloud of vehicles as well as the instantaneous speed and acceleration of
38
the vehicle. Analysis of the data derived a relationship between pollutant concentrations and
a vehicle's instantaneous speed profile. Data were collected for five highway locations for
parts per million (ppm) of CO, HC, and NOx. Emission factors were calculated using
regression equations for six independent variables. Of the six variables, speed, speed
squared, acceleration squared, ambient temperature, and humidity proved to be relevant in
predicting emission rates (Yu, 1999).
3.2.2 Improved Vehicle Activity Estimates
Accurate modal modeling requires two primary components; activity specific
emission factors and accurate estimates of on-road vehicle activity. Currently, few models
exist that accurately represent the range of activity that vehicles undergo as part of normal
driving operation on any type of roadway. To address this, a number of efforts have been
undertaken to more accurately model on-road vehicle activity. Various attempts have
focused on collection of actual on-road data. However, collection, analysis, and model
development of field data is extremely resource intensive. Consequently, many research
efforts have utilized some manner of simulation model to obtain vehicle profiles to be coupled
with mode specific emission production or fuel consumption factors. However, as will be
discussed later in this work, there are several inherent inaccuracies in simulation models in
terms of vehicle activity estimates, especially at signalized intersections where vehicle activity
is especially complicated. The following sections describe the various research efforts for
vehicle activity modeling.
39
3.2.2.1 On-Road Vehicle Activity Modeling Recent efforts undertaken by Grant
(1998) were aimed at statistically relating observed speed/acceleration characteristics on
freeways as a function of vehicle class, traffic flow, and geometric highway parameters using
laser rangefinders. This new approach used aggregate measures of flow and roadway
geometry to predict the important load-related measures of flow. While Grant’s methods
work for freeway segments in Atlanta, the general methods have yet to be applied to the
more complex traffic flow conditions that occur on non-freeway roads. In particular, Grant
derived a regression model that related the amount of activity where accelerations exceeded
3 mph/s. Final analysis indicated that percent of acceleration activity beyond the threshold of
3 mph/s for light duty vehicles was correlated with density of vehicles on the roadway,
horizontal curvature, and the percent of heavy-duty trucks in the traffic stream. For
decelerations less than 2 mph/s, a correlation was found between roadway density and
curvature.
Roberts et al. (1999) described development of a freeway modal activity model.
Activity data were collected on California freeways using chase vehicles with SnapOn
Scanners, Distance Measuring Devices (DMI), or Laser-tracking coupled with DMI
measurements. Percentage of significant activity (acceleration greater than 3mph/s, PKE >
60, etc.) were analyzed with regression tree analysis and significant variables determined.
40
Significant explanatory variables included density, flow, and fraction of mainline volume
merging or diverging in a weaving section.
3.2.2.2 Simulation Simulation offers an attractive method to easily create vehicle
activity profiles. Many packages model vehicles on a microscale so that second by second
parameters such as location, speed, or acceleration can be output. Following is a discussion
of various research projects that have or are using simulation for microscopic vehicle activity.
However, there are several inherent problems with each of the approaches that will affect
activity output and ultimately air quality estimates based on simulated vehicle activity. In
Chapter 6, results of this research are compared with simulation model output and the
various models presented here are critiqued.
As early as 1988, Al-Omishy and Al-Samarrai (1988) had developed a road traffic
simulation model that predicted emissions based on vehicle type, location along the roadway,
speed, and acceleration. The FORTRAN based traffic simulation model predicted both HC
and NOx and could be used for evaluation of various traffic and pollutant control strategies.
The simulation model estimated vehicle activity and location based on car-following theory.
Matzoros (1990) reported the development of a modal emission simulation model.
The model predicted air pollution concentrations for vehicles in urban areas. Modal activity
simulated by the model included the formation and dissipation of queues as well as cruise,
41
idle, acceleration, and deceleration at different positions along a street link. The model
included emission rates disaggregated by operating mode. Queue lengths were specifically
modeled. Emission factors were provided for cruise, idling, acceleration, deceleration, and
creeping. The highest emission rates for all pollutants (CO, HC, NOx, and lead)
corresponded to acceleration. The modal approach was based on earlier work, which had
observed that pollution concentrations were the highest near intersections, tailing off
midblock. Model results were compared with data from two actual locations and it was
found that, with the exception of NOx, an overall agreement exists between observed and
modeled values.
An analytical model to estimate intersection fuel consumption was created to
investigate the effects of signal timing on fuel consumption by Liao and Machemehl (1998).
The model attempted to identify inter-relationships between traffic characteristics, signal
control strategies, and roadway geometric conditions based on consideration of vehicle
operating conditions. The model used mathematical relationships to derive fuel consumption
estimates rather than using simulation.
A major research effort is currently in development by Los Alamos National Laboratory
to develop the TRANSIMS model, which is a simulation system for the analysis of
transportation options in metropolitan areas. The base of the system is a cellular automata
42
microsimulation model producing second-by-second vehicle positions defined by 7.5 meter
cell locations. TRANSIMS is a set of integrated analytical and simulation models and
supporting databases dealing with prediction and simulation of trips for individual households,
residents, and vehicles as well as movement of individual freight loads (Williams et al. 1999).
Many traffic simulation and optimization models such as TRANSYT-7F,
INTEGRATION, FREQ, NETSIM, and INTRAS also have incorporated modules for
estimating emissions. These modules are structured to be sensitive to modal model output
but none of the models were developed based on on-road emission or vehicle activity data
(Yu, 1999).
Rakha et al. (1999) likewise is in the process of developing a modal microscopic
simulation model, which combines a traffic simulation model with an emission module. The
model uses car-following and lane changing logic to simulate vehicle activity. Speeds and
headway are updated and calculated each tenth of a second. Acceleration is modeled as
speeds are updated every deci-second based on the distance headway and speed differential
between the subject vehicle and the vehicle immediately ahead of it, which can result in
unrealistically high accelerations. To compensate, the model uses a linear acceleration decay
function that decreases the vehicle's acceleration as a function of its speed, resulting in a
linear speed/acceleration relationship.
43
Fuel consumption and emissions were calculated from data collected on a
dynamometer at Oak Ridge National Lab. This provided fuel consumption and emission
rates for a range of speeds from 0 to 75 mph km/h and for a range of accelerations from -
1.5 m/s2 to 8.0 m/sec2. The model was developed to represent typical driving conditions
including idling, acceleration, and deceleration. Data were collected for eight vehicles and an
emission model for a composite vehicle created. The simulation model models acceleration
as a by-product of car-following logic and does not actually replicate realistic on-road
behavior.
In another study, the microsimulation model TRAF-NETSIM, used for urban
roadways, and the microsimulation model INTRAS, used for modeling freeways, were used
to develop a modeling framework for prediction of vehicle activity in regional areas for
improved emission estimates. Output from the simulation modules was used to develop
relationships between basic link characteristics and the time spent in each operating mode.
Field data using instrumented vehicles for a freeway segment were used to validate model
results. The relationships developed were then incorporated into a post processor from the
Urban Transportation Planning Software (UTPS) four-step planning model so that region-
wide estimates of vehicle activity can be applied with the existing state-of-practice in regional
modeling (Skabardonis, 1997).
44
3.2.3 MEASURE
To address the various problems with existing transportation-related emission
models and shortcomings in more contemporary vehicle activity modeling such as simulation,
a research-grade motor vehicle emissions model based in a geographic information system
(GIS) platform is underway at Georgia Institute of Technology. The Mobile Emission
Assessment System for Urban and Regional Evaluation (MEASURE) predicts emissions
based on operating mode. Operating modes represented include cruise, idle, deceleration,
acceleration, and other modes where power demand leads to enrichment. The model
applies both vehicle characteristics, such as model year, engine size, etc, and
speed/acceleration profiles to predict emissions.
Because MEASURE resides in a GIS, it is able to capture both spatial and temporal
characteristics of vehicle fleet and modal activity. It is also able to incorporate both existing
and real-time datasets such as Highway Performance Monitoring System (HPMS) traffic
counts. Many agencies already maintain traffic information in some form of a spatial
database so the GIS platform allows integration of various datasets. The model also allows
an enhanced approach to modeling emissions spatially (Guensler et al. 1998). The research
model is based in a GIS package, which allow storage of all spatial and temporal attributes
of the modeling regime and integration of a wide variety of data sources, spatial attributes,
45
and temporal distributions for use by external programs to estimate emissions. The GIS
actually contains the physical transportation network with accompanying topology and
attributes such as link length, number of lanes, grade, capacity, etc. Locations where
enrichment is more likely to occur such as freeway on-ramps or signalized intersections can
also be identified.
The model takes in spatial data (road segment and census block) about vehicle
activity and technology and outputs estimated, gridded, mobile exhaust emissions. It employs
modal emission rates developed in house as well as MOBILE based emission rates. It relies
on modal vehicle activity measures; starts, idle, cruise, acceleration, and deceleration.
Vehicle technology characteristics (model year, engine size, etc) and operating conditions
(road grade, traffic flow, etc) were also developed at a large scale (small zones and road
segments).
The scope of MEASURE is currently being expanded to include microscale air
quality estimation and estimates of all mobile source pollutants (CO, HC, NOx, CO2, and
toxics). As designed, MEASURE will be able to read spatial databases and estimates of
modal activity and then provide facility-level estimates as well as gridded estimates of the
various pollutants. From a research perspective, MEASURE will be able to make
comparisons of standard speed correction factor approaches versus activity-specific
46
approaches since both types will be embedded. From a practical perspective, it will provide
planners and engineers a toolkit to generate regulatory level reporting as well as a provide
flexible means of gaming various TCMs. Both of these capabilities make MEASURE an
attractive tool for the research discussed in this paper. One of the important facets of the
model are the modal emission rates generated during model development. These emission
rates provide the ability to explore the emission impacts of changes in acceleration profiles or
idling fractions.
Some of the major features of MEASURE are:
• the model includes modal emission rates as well as MOBILE emission rates;
• user-defined grid cells;
• an improved spatial aggregation technique; and
• the inclusion of local road emissions.
Modal emission rates are designed to estimate emissions for specific vehicle activities
(idle, cruise, acceleration, and deceleration) and vehicle technology combinations (cold and
warm engine starts, hot-stabilized, and enrichment). Over a region, engine start emissions
are estimated for census blocks, and hot-stabilized and enrichment emissions are estimated
for road segments (intersection to intersection). Emissions from the zones and lines are
aggregated into user defined grid cells directly by completing polygon-on-polygon and line-
47
on-polygon spatial summarization. The main advantage of MEASURE is that it allows users
to model a wide-range of strategies that may have an effect on emissions (i.e. signal timing
and high-occupancy vehicle lanes) (Sarasua et al. 1999).
3.3 Fundamentals of Vehicle Activity in Traffic Engineering
In the above sections, the evidence for moving towards a modal approach to
analyzing transportation-related air quality is presented as well as an overview of other
research efforts into modal modeling. Many research efforts focusing on the activity side of
the emission equation are using either simulation modeling or other activity estimation based
on speed/acceleration relationships commonly used in traffic engineering. Following is a
synopsis of the common representations of vehicle activity used in various traffic engineering
applications as well as description of several research efforts that attempt to better describe
vehicle activity relationships. In the data analysis chapter, Chapter 6, field data are
compared to the common traffic engineering relationships described below.
3.3.1 Acceleration Performance of Passenger Cars
The most common comprehensive early study on vehicle acceleration/speed
profiles was a research effort by St. John and Kobett (1978), reported in National Highway
Cooperative Research Program (NCHRP) 185. The report presents analysis of speed and
acceleration data points from a single passenger car (1970 Chevrolet Impala sedan) driven
over a test course. The study used an on-board light beam oscillograph recorder to record a
48
time trace of speed and acceleration. Test results indicated a linear relationship existed
between speed and acceleration for passenger cars. This relationship, for passenger cars on
zero grade, is given by:
a = ao [1-(V/Vm)] (3-1)
Where: a = acceleration capability at speed V;
ao = maximum acceleration for speeds ≈ 0;
V = vehicle speed;
Vm = a pseudo maximum speed indicated by the linear relation between
acceleration and speed when data are fitted in the normal operating
range.
Maximum acceleration was calculated from an earlier study and was not explained in detail. The mathematical representation of maximum acceleration (ao) is given by:
Ao = [131.2/(W/bhp)] + 5.093 (3-2) Maximum acceleration is achieved at zero speed and linearly decreases as speed increases.
Maximum acceleration is a linear function of the inverse of the weight/horsepower ratio.
Major drawbacks to the test study were that data were limited to one older model year
vehicle on a fixed test route and the relationship describes the upper bound of the
49
speed/acceleration curve rather than a distribution of speeds and accelerations expected
under normal vehicle operation. This upper-bound linear speed-acceleration relationship is
presented in Figure 3-2.
A correlation between acceleration performance and grade was noted in the St. John and Kobett study as well. The relationship is described in Equation (3-3).
aGV = aLV - Rg (3-3)
50
Figure 3-2: Linear Speed-Acceleration Curve
where: aGV = acceleration capability at speed V on grade;
aLV = acceleration capability at speed V on level terrain;
g = acceleration due to gravity; and
R = percent grade expressed as a decimal (for a 4% upgrade, R = 0.04).
The acceleration capability of vehicles has primarily been used for road design.
Acceleration capability influences passing zone lengths and acceleration lane lengths.
Acceleration capability is also a factor in signal timing design, calculation of fuel economy and
travel time values, and in estimating the return to normal traffic operation after a breakdown
in traffic flow patterns (ITE, 1992). Microscopic simulation models often employ maximum
on-road acceleration to generate individual vehicle activity profiles.
The Traffic Engineering Handbook (ITE, 1994) lists maximum acceleration rates for
both passenger cars and heavy trucks based on the vehicle's weight-to-power ratio. The
weight/power ratio is a measure of the vehicle's ability to accelerate and maintain speed on
upgrades. Weight-to-power ratio is the gross weight of the vehicle in pounds divided by the
power in horsepower. Weight is a rough indicator of resistance to motion so the higher the
51
weight/power ratio the lower the acceleration performance, while a low weight/power ratio
reflects higher performance capabilities
(ITE, 1994). Details are shown in Table 3-1. Acceleration rates for different speed ranges
are given in Table 3-2.
Table 3-1: Maximum Acceleration from Rest by Vehicle Type and Weight-to-Power Ratio (source: Traffic Engineering Handbook 4th Edition (ITE, 1994))
Typical Maximum Acceleration Rate on Level Road (mph/s)
Vehicle Type
Weight-to-Power Ratio (lb/hp)
0 to 10 mph
0 to 20 mph
0 to 30 mph
0 to 40 mph
0 to 50 mph
25 6.3 6.1 5.8 5.6 5.3 30 5.3 5.1 4.9 4.6 4.4
Passenger Car
35 4.6 4.4 4.2 4.0 3.8 100 2.0 1.6 1.5 1.4 1.0 200 1.2 1.1 1.0 0.8 0.7 300 0.9 0.9 0.8 0.8 0.4
Tractor-Semitrailer
400 0.9 0.8 0.8 0.5 --- Table 3-2: Maximum Acceleration by Speed Range by Vehicle Type and Weight-to-Power Ratio (source: Traffic Engineering Handbook 4th Edition (ITE, 1994))
Typical Maximum Acceleration Rate on Level Road (mph/s)
Vehicle Type
Weight-to-Power Ratio (lb/hp) 20 to 30
mph 30 to 40 mph
40 to 50 mph
50 to 60 mph
25 5.3 4.8 4.3 3.8 30 4.4 4.0 3.5 3.1
Passenger Car
35 3.8 3.4 3.0 2.6
52
100 1.4 1.0 0.7 0.4 200 0.9 0.5 0.3 0.3 300 0.7 0.4 0.2 --
Tractor-Semitrailer
400 0.6 0.3 -- --
Grade affects the maximum acceleration that can be achieved and according to
the Traffic Engineering Handbook (ITE, 1994) has the following relationship, which is similar to NCHRP 185:
aGV = aLV - Gg/100 (3-4)
where:
aGV = maximum acceleration rate at speed V on grade (ft/sec2);
aLV = maximum acceleration rate at Speed V in level terrain (ft/sec2);
G = Gradient (%); and
g = acceleration of gravity (32.2 ft/sec2).
Maximum acceleration on upgrades by speed range is provided in Table 3-3 for passenger
cars and heavy trucks. A graphical representation of maximum speed versus grade is shown
in Figure 3-3.
Table 3-3: Maximum Acceleration on Upgrades by Speed Range (source: Traffic Engineering Handbook 4th Edition (ITE, 1994))
Passenger Car (30 lb/hp) Tractor-Semitrailer (200lb/hp) Speed Change Level 2% 4% 6% 10% Level 2% 4% 6% 10% 0 to 20 mph 5.1 4.7 4.2 3.8 2.9 1.9 0.7 0.2 * *
53
20 to 30 mph 4.4 4.0 3.5 3.1 2.3 0.9 0.5 * * * 30 to 40 mph 4.0 3.5 3.1 2.7 1.8 0.5 0.1 * * * 40 to 50 mph 3.5 3.1 2.7 2.3 1.4 0.3 * * * * 50 to 60 mph 3.1 2.7 2.2 1.8 0.9 0.3 * * * *
*Truck unable to accelerate or maintain speed on grade
Figure 3-3: Maximum Acceleration on Upgrades for Passenger Cars by Speed
3.3.2 Acceleration Performance of Heavy Trucks
NCHRP 185 also describes acceleration performance of heavy trucks. A heavy
vehicle acceleration model was developed using a computer model to simulate vehicle
54
movement. Speed-acceleration traces were output and compared with heavy vehicle data
from the Western Highway Institute and the Road Research Laboratory. The following
formula was derived to describe the acceleration capabilities of large trucks (St. John and
Kobett, 1978):
Ae = [?V/(?V + Spts(Ap - Ac)]Ap V > V1 (3-5)
Where: Ae = effective acceleration (ft/sec2);
? = a parameter that depends on the range of engine speeds;
typical values range from 0.33 to 0.43 (0.4 is recommended);
V = vehicle speed (ft/sec);
Sp = one time the sign of Ap (which can be either + or -);
ts = actual time required to shift gears (sec);
Ap = power-limited acceleration (with the engine employed and vehicle at
speed (V) uses the average available net horsepower (ft/sec2);
Ac = acceleration in coasting at vehicle speed V (ft/sec2); uses an average gear
ratio for the coasting chassis losses; and
V1 = the maximum speed in lowest gear ratio (ft/sec).
55
The research acknowledged that the effect of grade was underestimated by applying
the simple addition of a gravity component to zero-grade performance. When a heavy truck
starts and accelerates on zero grade, the time to shift gears is about 1.5 seconds,
consequently a large portion of the time is spent coasting without power applied. If a truck
starts out on a positive grade, the acceleration in each gear ratio is lower and the time in each
ratio is longer so the engine is usefully employed a larger percent of the time. In equation 3-5
above, the terms Ac and Ap included the direct added effect of grade (St. John and Kobett,
1978).
3.3.3 Deceleration Performance
Deceleration occurs either when the accelerator pedal is released due to the
retarding effects of constant resistance to motion, an increase in resistance to motion, or
when vehicle brakes are used. Without brakes, deceleration rates are greater at high running
speeds since because of resistance to motion. At 70 mph, release of the accelerator pedal
results in a deceleration rate of 2.2 mph/s. Around horizontal curves or on a gradient, the
resistance to motion will increase and deceleration will occur without a corresponding
increase on the accelerator pedal. Maximum deceleration occurs with braking and is
determined by the retardation forces developed in brake drums or discs negating slip
between the pavement and tire. Roadway and tire friction also affect maximum deceleration
rates. Maximum deceleration is typically only applied in emergency situations. For traffic
56
engineering applications, such as determining vehicle clearance intervals at traffic signals, a
common deceleration rate of 6.8 mph/s is used (ITE, 1994).
3.4 Discussion
An overview of current literature which indicates a relationship between engine
operating mode and emissions and literature that outlines other efforts to develop more
realistic emission rates and activity estimates was presented in this chapter. The intent was to
provide a background on previous and ongoing research into modal emissions modeling and
to provide a sampling of the evidence suggesting that a modal approach is more accurate.
It was beyond the scope of this paper to critique the validity or accuracy of each
work. Several works employed questionable methods such as the level of service estimation
used by Sierra Research or the unusually high acceleration rates reported in the three-city
instrumented vehicle study. However, even with flaws, the bulk of research does point
towards a relationship between engine mode and emission output.
56
CHAPTER IV
4. RESEARCH APPROACH
This Chapter presents the research framework for this dissertation work. First
the problem is defined, followed by presentation of the research hypothesis and
research objectives. Statistical techniques considered for analysis of the data are
discussed. A final statistical model is presented including an overview of the response
variables. Following, the various predictor or independent variables hypothesized to
affect vehicle activity, which were considered as part of experiment design, are
outlined. Although presentation of the data collection protocol follows this chapter, a
note is made of whether each independent variable could be and was actually included
in the data collection phase of this research.
4.1 Statement of Problem
The previous chapters explained the need for a modal approach to
transportation-related air quality modeling. For a modal emission model to accurately
predict emissions, both activity-specific emission rates and accurate estimates of
vehicle activity are required. Much research activity has focused on the emission rate
side of the modal-based emission prediction equation to develop methods that relate
emissions specifically to a particular speed-acceleration combination or on identifying
specific vehicle operating modes where emissions are disproportionate compared to
58
other modes. Efforts to model on-road vehicle activity have been undertaken to a
much lesser extent. As discussed in Section 3.2.2, many emerging models are basing
vehicle activity on a limited sample of vehicle profiles or on algorithms that attempt to
simulate queuing, acceleration, and deceleration. None of these methods have been
validated as to whether the output realistically models the wide range of vehicle
activity encountered on the roadway. Additionally, current modeling efforts have not
yet been shown to relate vehicle activity to on-road conditions such as grade or traffic
volumes. Without accurate vehicle activity estimates, modal emission models are
handicapped in their ability to successfully relate activity-specific emission rates with
accurate estimates of vehicle activity. Consequently, the activity prediction side of the
equation may be the limiting factor in accurate deployment of modal models.
No modal model can be complete unless it addresses the air quality impacts of
signalized intersections. By their nature, signalized intersections encompass much of
the modal activity experienced by motor vehicles in an urban area. A significant
amount of modal vehicle activity occurs within a relatively short distance of the
intersection depending on queue length. Vehicles decelerate to a stop, idle, and then
accelerate from rest. Even for vehicles not stopped or slowed by the signal, a large
number of interactions with other vehicles occur leading to "rough" traffic flow.
Significant modal activity may also occur at other locations along signalized links
experiencing heavy congestion resulting in over-capacity stop and go conditions.
Other locations of significant modal vehicle activity include freeway ramps and along
59
freeway segments where vehicles undergo braking due to interference with other
vehicles and rapid accelerations when merging with existing traffic. Although,
freeway segments may be the source of most hard accelerations at high speed, non-
freeway roadway links make up the bulk of existing roadways and the majority of
vehicle activity. Consequently, the modal emissions impact of signalized intersections
is highly relevant.
4.2 Hypothesis to be Tested
This purpose of this work was to create a methodology to predict microscopic
vehicle profiles at signalized intersections that can be used as input to regional or
microscale transportation-related air quality models that use an activity-specific
(modal) approach. The research hypothesis can be encapsulated by the following:
Research Hypothesis: Modal activity on signalized roadways can be forecasted as a
function of macroscopic activity (traffic volume, percent heavy trucks, etc.) and
facility geometric properties (roadway grade, number of lanes, distance to
downstream intersection, etc.).
4.3 Objectives
To model activity at signalized intersections, this research had three main
objectives, which are detailed in the following sections.
60
Objective 1: Develop a method to sample representative modal activity on
signalized roadways to represent the widest range of geometric and operation
conditions possible.
The goal of this research was to develop a model that can predict modal
vehicle activity at signalized intersections and along signalized roadway segments
using actual field data. The model ideally should be able to predict vehicle activity
based on those operational and geometric characteristics of the roadway, shown to
influence vehicle activity. Consequently, data collection sites were selected to
represent as broad a range of different characteristics as was economically viable.
To forecast vehicle activity based on significant roadway and operational
conditions, all the variables that may affect vehicle operation were identified and then
those that could realistically be included were selected for the final experimental
design.
Objective 2: Develop a robust and repeatable methodology for forecasting modal
activity on signalized roadways.
This objective entails development of a statically valid methodology to analyze the
data. Included in this portion of the research was identification of the "best" statistical
procedure for analyzing the collected data. Various statistical methods that were
considered are covered in section 4-4. An overview of the final statistical method is
61
provided in section 4-5. Selection of relevant response and potential predictor
variables are discussed later.
Objective 3: Develop a model that will integrate with MEASURE for output of
vehicle activity given specific roadway, fleet mix, and operational characteristics.
The final objective was to develop the framework for integration of a
prediction model with the Georgia Tech MEASURE model discussed in Section 3.2.3.
4.4 Scope of Work
To meet the objectives outlined for this work, various tasks were undertaken.
First, an in-depth literature review was completed with relevant background
information to this work as presented in Chapters 2 and 3. Next, the experiment was
designed including a data collection plan and selection of appropriate statistical
analysis procedures. The data collection is discussed in Chapter 5 and the selection of
the appropriate statistical analysis procedure, including identification of response
variables and final selection of predictor variables is the subject of this chapter.
The defining feature of this research work was development of a method
capable of generating complete vehicle profiles along the path of a signalized link
through the intersection and onto the following link. An individual vehicle profile is
illustrated in Figure 4-1. All individual vehicle traces are summed to reflect the
number of vehicles on the link. The statistical analysis determined which of the
62
independent operational or geometric variables of the study locations were relevant in
influencing vehicle activity. The final output of the statistical model is a Joint
Acceleration-Speed Probability Density Function (JASPROD), which is a three-
dimensional (tri-variable) function of speed, acceleration, and the joint probability for
a given speed-acceleration bin. An empirical JASPROD is created by sampling the
Figure 4-1: Sample Vehicle Trace
63
simultaneous speed and acceleration trace of a vehicle along a specified path (or run),
such as a vehicle's trajectory from the point of queuing to some point downstream. For
the final model, data were divided by homogeneous zones of activity (distance from
the stopping point or from the intersection stopbar) and by homogenous predictor
variables determined by statistical analysis, as discussed in Chapter 6. Data were
collected in one-second intervals so the resulting JASPROD are for one second
intervals. JASPRODs are created by dividing vehicle traces into a matrix of speed and
associated accelerations bins. Each bin has a unique speed and acceleration range. A
JASPROD is shown in Figure 4-2 and Table 4-1. Once data are binned, the
probability of any bin can be calculated by dividing its frequency by the sum of the
frequencies of all bins. For each given geometric and operational condition that is
investigated, the frequency of activity in a specific speed-acceleration bin is the
number of seconds of operation in a given bin divided by the total number of seconds
of activity. The sum of all frequencies for the vehicle trace will equal 1.
The emission rate models, which will be described in Section 4.6, only require
the fraction of activity for the specific modal variable which was shown to be
correlated to emission rates (i.e. the percent of activity where acceleration >= 6.0
mph/s). Data could have been analyzed in this manner, however a method that
allowed a distribution of data as output was desirable, since response variables may
change in the future depending on results of on-going emission rate modeling. With
output in the form of a distribution of data, the model output can be used with any
64
emission rate model that identifies critical modal variables. For example, if a 3-
dimensional activity distribution is available and future research identifies acceleration
greater than 5 mph/s as significant, the total fraction of activity that falls within this
range can be selected from the JASPROD as shown in the shaded section in Table 4-1.
This research model ultimately will be used as input to the Georgia Tech
MEASURE model for regional air quality modeling and final data output designed for
Figure 4-2: Joint Acceleration-Speed Probability Density Function (graphical form)
65
Table 4-1: Joint Acceleration-Speed Probability Density Function (matrix form) (Range of Activity Where Acceleration >= 5.0 mph/s is Shaded)
Acceleration (mph/s) Speed (mph) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 1 3 12 20 31 39 72 221 36 10 0 0 0 0 0 0 0 0 5 0 2 5 2 13 32 40 39 11 7 2 5 26 52 28 15 0 0 0 0 0
10 1 2 4 7 24 33 37 32 5 2 1 5 11 21 39 44 25 2 3 3 0 15 1 4 3 9 30 45 46 20 9 7 7 20 37 40 64 40 13 10 0 0 0 20 1 1 8 16 22 31 49 22 11 8 14 33 69 84 46 25 9 3 1 0 0 25 1 2 5 11 19 26 35 28 9 15 31 57 82 89 32 12 2 1 1 0 0 30 1 3 2 7 17 18 31 23 18 17 36 77 82 57 28 10 3 1 0 0 0 35 1 0 0 8 12 13 20 19 19 16 29 61 59 25 12 6 0 0 0 0 0 40 0 1 1 2 4 9 6 18 20 7 18 37 33 24 6 0 2 1 0 0 0 45 0 0 0 2 1 2 2 4 4 6 19 25 7 3 2 0 0 0 0 0 0 50 0 0 0 0 1 1 1 1 1 0 0 1 0 2 1 0 0 0 0 0 0 55 0 0 0 0 0 0 0 0 1 0 0 1 4 0 0 0 0 0 0 0 0 60 0 0 0 0 0 0 0 0 0 1 3 1 2 0 0 0 0 0 0 0 0 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
compatibility with the model. The research model may also be used for microscopic
air quality modeling, evaluating the effectiveness of transportation control measures
(TCMs), or intelligent transportation system (ITS) alternatives.
4.5 Statistical Modeling
The purpose of the statistical modeling was to determine which predictor
variables influence vehicle activity behavior so that the data can be stratified by those
variables and 3-dimensional matrices of speed and acceleration created. To determine
which operational and geometric variables influence how vehicles operate, statistical
analysis can be used to compare whether two distributions of data, which were
disaggregated by the various variables, differ statistically. Unfortunately, no common
66
test existed, that allowed comparison of complex 3-dimensional distributions. The
speed-acceleration matrix produced from data preparation was a three dimensional
distribution (speed x acceleration x frequency). The three dimensional distribution
may have been reduced to two dimensions if a distribution of speed versus frequency
or acceleration versus frequency were used singularly or if a product of the two, a
surrogate for power (speed x acceleration) versus frequency were used. There are
various methods that may be used to test differences across two distributions.
Goodness-of-fit tests examine two random samples to test the hypothesis that two
unknown distributions are identical. Most methods are limited to 2-dimensional or
simple 3-dimensional distributions.
Regression uses a single response variable regressed against one or more
predictor variables. For example, the percent of activity where acceleration are >= 3.0
mph/s can be regressed against a number of variables such as per lane volume, percent
trucks, lane width, etc. A discussion of the various methods tested and the final
methodology used follows.
4.5.1 Chi-Square Tests
The chi-square test is the oldest and best known goodness-of-fit test. The test
assumes that the observations are independent and that the sample size is reasonably
large. This method can be used to test whether a sample fits a known distribution, or
whether two unknown distributions from different samples are the same. The test
67
assumptions are that the sample is random and that the measurement scale is at least
ordinal (Conover, 1980).
The chi-square provides a relatively easy to apply approach for analyzing two
dimensions of data (acceleration and frequency or speed and frequency). The main
problem with using the chi-square is the orders of magnitudes of separate tests that
would have to be conducted to test all possible combinations of variables in the
datasets. For example, to just test 5 queue positions, grades from -9 to 9, and level of
service, a total of 570 datasets would result, assuming data existed for each mutually
exclusive group of variables. To compare the distributions to determine where they
differ, a large share of the 570 datasets would have to be compared to the all the
others. This quickly becomes logistically infeasible. Additionally, since the test only
allows comparison across 2-dimensions, only distribution of accelerations from one
dataset could be compared to another or the speed distribution of two datasets could be
compared at a time. It does not allow comparison of the relationship between speed
and acceleration except as a two-dimensional product. Another problem is applying
the chi-square is that stratification of the data often resulted in cells with 0
observations, which presents difficulty for the chi-square test since it cannot handle
cells with no observations.
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4.5.2 Kolmogorv-Smirnov Two-Sample
The Kolmogorov-Smirnov (K/S) two-sample test compares the empirical
distibution functions of two samples, F1 and F2. The Kolmogorov-Smirnov test is a
non-parametric test, which can be used to test whether two or more samples are
governed by the same distribution by comparing their empirical distribution functions.
The Kolmogorov-Smirnov two-sample test is illustrated in Figure 4-3 for a
sample dataset using data for the first vehicle in the queue for an intersection with a
positive 9% grade and data for the first vehicle in the queue for an intersection with a
negative 9% grade. Calculations and graphs were made in SPLUS statistical software.
In the figure the cumulative distribution function (cdfs) for each distribution is plotted.
If the distributions are similar, the cdfs would also be similar. The wide variation
between the two indicates that the two datasets were from quite different distributions.
The test also provides a numerical solution as well as a visual plot.
The Kolmogorov-Smirnov two-sample test provides an improved
methodology over the chi-squared test since data does not have to be assigned
arbitrarily to bins. Further, it is a non-parametric test so a distribution does not have to
be assumed. However, the main disadvantage to the K/S is similar to the chi-square in
that the orders of magnitudes of separate tests that would have to be conducted to test
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Figure 4-3: Comparison of Empirical cdfs for Accelerations on a 9% Grade (x) and -9% Grade (z)
all the possible combinations of variables in the datasets become logistically
infeasible. The K/S also only allows comparison across 2-dimensions. The
distribution of accelerations from one dataset could be compared to another or the
speed distribution of two datasets could be compared. It does not allow comparison of
the relationship between speed and acceleration except as a two-dimensional product.
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4.5.3 Linear Regression
Regression analysis is a statistical method used to explain a dependent variable
as a mathematical function of one or more independent variables (Studenmund, 1985).
For example, regression may be used to estimate the number of accidents along
roadway segments as a function of pavement condition. Linear regression is a
commonly used and easily understood statistical method. Linear regression explores
relationships that can be described by straight lines or their generalization to many
dimensions. Regression allows a single response variable to be described by one or
more predictor variables.
Linear regression was a viable analysis tool for the research data. This type of
analysis would regress a single response variable based on relevant emission
producing modes of activity against various predictor variables. The response variable
would have to be a variable such as % of time spent in accelerations greater than 6.0
mph/s, which would be regressed against related variables such as LOS, distance to
downstream intersection, per-lane volume, etc. This method would necessitate
development and validation of a separate model for each response variable.
The largest problem with this statistical approach is that a linear relationship,
or a transformation form of a linear relationship, must exist between the response and
relevant predictor variables. Relationships may exist between vehicle activity and
certain ranges of a predictor variable but not others. For example, volume-to-capacity
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may not influence vehicle behavior in the lower ranges, (i.e 0 to 0.7) but may be
relevant at higher ranges (0.7 to 1.0+). Additionally, even at the higher range, a linear
relationship may not exist (i.e. V/C from 0.7 to 1.0+ may affect vehicle operation but
the effect is constant rather than linearly increasing or decreasing). Even with
transformations on the data, such as taking the log, a relationship may not show up or
a relationship may be forced between non-relevant ranges of the variable. Figure 4-5
shows this type of relationship between percent activity greater than or equal to 6
mph/s and queue position. As shown, an exact linear relationship does not exist
between queue position and hard accelerations. An ordinary least squares regression
of hard accelerations against queue positions only yields an R2 value of 0.27,
indicating that the model only explains 27% of the deviation.
Another disadvantage to this method is that only a single response variable can
be used. The relationship between speed and acceleration bins cannot be linked to
geometric and operational characteristics. Also, an individual model must be
developed for each response variable, rather than being able to derive a 3-dimensional
distribution of speed and acceleration activity.
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Figure 4-5: Graduated Non-Linear Relationship Between Percent Hard Accelerations and Queue Position.
4.5.4 Hierachiacal Based Regression Tree Analysis
Binary recursive partioning, more commonly referred to as hierachiacial tree-
based regression, is similar to forward stepwise variable selection methods. It is also
commonly referred to as classification and regression tree analysis (CART). One of
the advantages to HTBR or CART is that it assists in detecting the underlying
structure in data (Breiman et al., 1984). This technique generates a "tree" structure by
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dividing the sample data recursively into a number of groups. The groups are selected
to maximize some measure of difference in the response variable in the resulting
groups. One of the advantages of regression tree analysis over traditional regression
analysis is that it is a non-parametric method which by definition does not require any
distribution assumptions and is more resistant to the effects of outliers (Roberts,
1999).
The term CART is often used since it allows analysis of both classification and
regression analysis. Classification analysis are those where the endpoints (or terminal
nodes) are factors which are non-numeric. An example of a classification tree is rule-
based method for determining the chances of survival or non-survival for a heart
attack patient based on monitored variables, such as blood pressure, during the first 24
hours following the attack. Regression trees are those where the model endpoints end
in predicted numerical values.
Tree-based modeling is an exploratory technique that is increasingly being
used for:
§ devising prediction rules that can be rapidly and repeatedly evaluated;
§ screening variables;
§ assessing the adequacy of linear model; and
§ summarizing large multivariate datasets (Mathsoft, 1997).
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4.5.4.1 Description of Test
The model uses a set of classification or predictor variables (x), and a single
response variable (y). Regression tree rules are determined by a procedure known as
recursive partioning. The regression tree methodology proceeds by iteratively asking
and answering via a numerical search process: 1) Which variable of all of the
predictor variables offered should be selected to produce the maximum reduction in
variability of the response? and 2) Which value of the selected variable (discrete or
continuous) results in the maximum reduction in variability of the response? The
binary partioning algorithm recursively splits the data into increasingly homogenous
regions. The splitting continues until either a desirable end condition is met with a
homogeneous end node or too few observations exist to proceed further. Node
homogeneity is determined by deviance where a deviance of zero indicates a perfectly
homogenous node (Wolf et al 1997).
The partioning process can be explained mathematically by the following three
formulas:
Ds = Σm=1 to M (Yms - µs)2 (4-1) ∆(all x) = Ds - (Dl + Dr) (4-2) ∆(all x) = Σm=1 to M(Ym-µs)2 - (Σp=1 to P(Ypr - µr)2 + Σq=1 to Q(Yqr - µr)2) (4-3)
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Ds in equation 4-1 is the deviance of node S, which is to be split into two new nodes
(designated left and right). Each of the subnodes, left and right contain a portion of
the sample points in s. Ds is the sum of squared error (SSE) at node s, which is
summed over all observations m in node s. The squared error term at node s is
calculated by the difference of the mth observation of the dependent variable y and the
mean µ of M observations in node s (Roberts, 1999). A split occurs on a "parent"
node on a particular value of one of the independent variables specified. The deviance
reduction function as shown in Equation 4-2 evaluates deviance over all independent
variables where Dl and Dr are the residual mean deviances of the left and right nodes.
An optimal split is selected from among all possible independent variables, X.
Tree-based models have various advantages over linear and additive models.
One of the main strengths of regression tree analysis is that independent variables do
not have to be specified in advance. A regression tree picks only the most important
predictor variables that result in the maximum reduction in deviance. Another
advantage is that results are invariant with respect to monotone transformations of the
independent variables so that the "right" transformation does not have to be sought.
Regression trees are a nonparametric procedure, meaning that a functional form does
not have to be specified. They are able to work well with data that have multiple
structures rather than uncover a single dominant structure in data as many parametric
models do. Regression trees are also robust to the effect of outliers since splits usually
occur at non-outlier values (Roberts, 1999).
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4.5.4.2 Applicability of Test to Research Regression tree analysis appears to
offer the most feasible and appropriate approach to testing for differences in vehicle
activity based on geometric or operational characteristics. The single largest
advantage to regression tree is the ability to model non-linear relationships. The
model divides responses by ranges of predictor variables in the data where a
relationship is shown to exist and does not require a relationship to be derived between
all ranges. For example, if grade greater than 5% is relevant, regression tree analysis
can split the data at this point without forcing a relationship for other ranges of grade.
Regression tree analysis also inherently handles correlation between predictor
variables. For example, level of service may only be relevant if the intersections are
less than 1000 feet apart. Regression tree analysis can model this type of relationship
easily while regression analysis is unable to pick up this type of relationship. Chi-
square and K/S can also model this type of relationship. However, it would require an
immense number of modeling iterations to model all subsets of data.
The main disadvantage to regression tree analysis is that only a single response
variable can be used, as for linear regression. The relationship between speed and
acceleration bins cannot be linked to geometric and operational characteristics. Also,
an individual model must be developed for each response variable, rather than being
able to derive a 3-dimensional distribution of speed and acceleration activity.
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4.6 Research Scope and Presentation of Statistical Approach
Initially, this research was funded by the United States Environmental
Protection Agency and the Federal Highway Administration. The scope of research
extends existing research one step further and provides a methodology to predict
vehicle activity that can be reasonably applied. The research is not comprehensive nor
applicable to all signalized roadways under all operating and geometric conditions.
The research scope was limited by both resources and practical constraints. Ideally,
given enough time and an unlimited budget, data for all combinations of geometric
and operational conditions could be collected and analyzed. However this would be
an enormous undertaking. Consequently, the main constraint was resources. Practical
constraints also limited the research. Data were only observational and could only be
collected by observing situations over which the researcher had no control. It was
impossible to set up control groups and vary variables. Further, it was expected other
factors, such as trip purpose or engine horsepower, may significantly affect vehicle
activity. Although it was impossible to account for these types of factor, other
research efforts are underway to accomplish just that (Wolf et al, 1999).
The statistical approach used for data analysis for this research work involves a
two-step process. First, HTBR was used to reduce the create a best "fit" model for
each response variable which identified the predictor variables that most influence
vehicle activity ranges determined to be relevant by emission rate models. However,
since a representative range of response variables were used (deceleration, average
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speed, medium acceleration, and hard acceleration activity), it may be assumed that
these variables will affect all ranges of modal activity. For example, if grade
influences both accelerations >= 3 mph/s and >= 6 mph/s, the inference would be
drawn that it will also impact accelerations >= 5 mph/s. The second step is to validate
the results of regression tree model using the K/S test to compare distributions of
stratified data.
4.7 Response Variables
Part of the MEASURE model research was to create new emission rates that
are more representative of real-world modal activity. Emission rates are being
developed for hydrocarbons, oxides of nitrogen, and carbon monoxide. The
production of carbon monoxide at signalized intersections is of particular concern
because of the immediate health effects. Therefore, CO is usually analyzed on a
microscale, whereas HC and NOx are most often analyzed on a regional scale.
Frequency of specific modes of operation were the response variable in the
prediction process. The actual response variable were percent of activity within a
given joint range of speeds and accelerations. In order to compare different locations
with a differing number of observations for each speed-acceleration "cell", the cell
aggregation was based on the results of emission rate modeling, discussed in the next
section. Consequently, the response variable was prediction of frequency of activity
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for a given range of vehicle activity, such as percent of activity where acceleration >=
3.0 mph/s.
In the following sections, the development of emission rate models for carbon
monoxide, hydrocarbons, and oxides of nitrogen are presented. Each model predicts
pollutants based on relevant vehicle or operating mode variables. The relevant
operating mode variables from the emission rate models will serve as the response
variables for the statistical model. A major part of the MEASURE model research
effort has been development of more accurate emission rate models, which reflect the
influence of modal activity. A detailed description of how the carbon monoxide
model was derived is provided in Section 4.7.1. Since a similar process was used to
derive the final model for hydrocarbons and oxides of nitrogen, they are also presented
but without an in-depth description of the process.
It should be noted that emission rate modeling will always be in a state of flux.
Ongoing revisions to the model (addition of new test data, identification of previously-
undefined relationships due to improved explanatory power of the model as new
variables are added, will result in revisions to the emissions-related variables of
concern. Consequently, this research attempted to identify variables that influenced
overall vehicle activity, not just predict a relationship between a single response
variable such as accelerations >= 6.0 mph/s and predictor variables as explained in
Section 4.6.
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4.7.1 Carbon Monoxide Model
The CO model for passenger cars was developed by analyzing a data set of
more than 13,000 hot-stabilized laboratory treadmill tests on 19 driving cycles
(specific speed versus time testing conditions), and 114 variables describing vehicle,
engine and test cycle characteristics (Fomung, 1999). The data set represents almost
two decades of in-use driving tests conducted by the EPA and CARB and compiled by
the EPA’s Office of Mobile Sources for use in developing the MOBILE model.
The emission rate model for CO, presented here, was estimated with a
response variable as the logarithm of the emission rate ratio for carbon monoxide. The
ratio is the vehicle emission rate (in grams/second) driven on a given cycle (or across a
speed/acceleration matrix) divided by that vehicle’s emission rate while driving on the
FTP Bag 2. The model predicts the ratio of g/second emission rates for each vehicle
technology group. The following sequence of equations shows the method of
calculating the predicted emission rate for CO in units of either g/second or g/mile:
ΨCO (g/sec) = ΨCO (g/mile) * S / t (4-4)
ΨCOBag2 (g/sec) = ΨCOBag2 (g/mile) * 3.91/866 (4-5)
RCO (rate ratio) = PCO (g/sec) / ΨCOBag2 (g/sec) (4-6)
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Where ΨCO is the measured or observed CO, PCO is the predicted CO, ΨCOBag2 is the
FTP Bag2 rate of CO for a given vehicle, S is the driving cycle distance in miles, t is
the cycle duration in seconds, 3.91 is the hot stabilized FTP Bag 2 sub-cycle distance
in miles, and 866 is the FTP Bag2 sub-cycle duration in seconds.
On a vehicle by vehicle basis this implies that after calculating RCO from the
response variable, the predicted rate in g/second can be obtained by:
PCO (g/sec) = RCO * ΨCOBag2 (4-7)
Note that Equation 5-13 is similar in form to the embedded algorithm in MOBILE,
which gives emission rates as BER x Correction Factors. Where BER stands for base
emission rate, akin to ΨCOBag2; RCO is a composite representation of several variables
and can be thought of as speed, load, and technology correction factors. Equation 4-7
can be easily converted to g/mile by using;
PCO (g/mile) = RCO * ΨCOBag2 * 1/AVGSPD (4-8)
Where AVGSPD is the average speed of the speed - acceleration profile of the driving
schedule.
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The CO model is presented in both an estimation form, and a prediction form.
The estimation form is the regression equation 4-9:
LogRCO = 0.0809 + 0.002*AVGSPD + 0.0461*ACC.3 + 0.0165*IPS.60 −
0.0283*ips45sar2 + 0.3778*ips90tran1 − 0.0055*tran3idle + 0.1345*tran5mi1
+ 0.3966*finj3sar3 − 0.0887*cat3tran1− 0.2636*sar3tran4 − 0.481*flagco
(Fomung, 1999) (4-9)
Where:
AVGSPD is the average speed of the driving cycle in mph;
ACC.3 is the proportion of the driving cycle on acceleration greater than 4.8 kph/s
(3mph/sec);
IPS.X is the proportion of the driving cycle on inertial power surrogate (IPS) (speed x
acceleration) greater than X mph2/sec (Washington et al., 1994). Thus IPS.60 implies
IPS greater than 60 mph2/sec;
ips45sar2 is an interaction between IPS.45 (IPS >= 45 mph2/sec) and a vehicle with
no air injection;
ips90tran1 is an interaction variable for a vehicle with automatic transmission on
IPS.90 IPS >= 90 mph2/sec;
cat3idle is an interaction variable for a 3-speed manual transmission at idle;
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tran5mi1 is an interaction variable for a 5-speed manual transmission vehicle with
mileage <= 25k miles;
finj3sar3 is an interaction variable for a vehicle that has throttle body fuel injection
and pump air injection;
cat3tran1 is an interaction variable for a vehicle with automatic transmission and
TWC;
sar3tran4 is an interaction variable for a vehicle with 4-speed manual transmission
and pump air injection; and
flagco is a flag used to tag a high emitting vehicle under CO emissions.
The prediction format is a more intuitive presentation for prediction purposes
and is given by:
PCO (g/sec) = 1.205 * FTP Bag2 * antilog{0.0809 + 0.002*AVGSPD +
0.0461*ACC.3 + 0.0165*IPS.60 − 0.0283*ips45sar2 + 0.3778*ips90tr1 −
0.0055*tran3idle + 0.1345*tran51 + 0.3966*finj3sar3 − 0.0887*cat3tran1−
0.2636*sar3tran4 − 0.481*flagco} (4-10)
The variables from the emission rate models were used as the response
variables for the data model presented in this work. Only the emission rate models
that related to vehicle activity and apply to the entire fleet were considered. Variables
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that related to subfleet vehicles were not used even if they applied to vehicle activity
such as the variable, ips45sar2 which is the percent of activity with IPS >= 45
mph2/sec for the subfleet of vehicles with no air injection. This type of variable was
not included since data collection could not relate vehicle activity to subfleet
characteristics.
The model variables indicate that the significant modal predictor variables for
carbon monoxide are average speed (AVGSPD), the percent of vehicle activity where
acceleration exceeds 3.0 mph/s (ACC.3 ) and percent of activity where the inertia
power surrogate is greater than or equal to 60 mph2/s (IPS.60). Only AVGSPD and
ACC.3 were included as response variables since the final CO model was developed
after the data analysis was initiated and IPS.60 could not be incorporated in a timely
manner.
Three other variables are related to both the vehicle's modal activity and a
specific characteristic of the fleet. Percent of time spent idling was significant for 3-
way catalyst equipped vehicles (cat3idle). IPS was significant for vehicles with
automatic transmissions when IPS was greater than or equal to 90 mph2/s (ips90tr1).
For vehicles with no excess air injection, IPS >= 45 mph2/s (ips45sar2) was a relevant
variable.
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To determine the emissions at an intersection with the modal emissions model,
the technology group needs to be determined and then the vehicle speed/acceleration
profiles estimated. Once the fleet distribution is known for an intersection, changes in
operational characteristics will only affect the vehicle activity side so that impacts can
be measured by the changes in relevant modal activity. These modal variables were
used to predict emission ratios and combined with the corresponding FTP bag2
emission rate from look-up tables are used to derive emission rates, which are then fed
into MEASURE.
4.7.2 HC Model
The hydrocarbon emission rate model was derived similar to the CO model,
which was described in detail in the above sections. The final emission rate model for
HC is (Fomunug, 1999):
LogRHC = 0.0451 - 0.6707*my79 - 0.1356*my82 + 0.019*AVGSPD +
0.2021*finj2tran4 + 0.1795*cat2sar1 + 0.1651*cat3sar1 + 0.0318*cat3sar2 -
0.1189*sar3tran1 + 0.5646*sar1tran5 + 0.0004*cid - 0.2581*sar3kml -
0.0169*finj2km3 - 0.5144*flaghc - 0.0129*acc1finj2 - 0.1626*acc3cat2 -
0.3891*ips90sar3 + 0.0307*dps8finj2 (4-11)
Where:
my79 = model year < 79;
my83 = 79 < model year < 83;
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AVGSPD = average vehicle speed (mph);
finj2tran4 = interaction variable for a 4-speed manual transmission vehicle
with a carburetor;
cat2sar1 = pre 1981 model year vehicle with "oxidation only" catalyst and
unknown air injection type;
cat3sar1 = pre 1981 model year vehicle with a TWC and unknown air
injection type;
cat3sar2 = vehicle with TWC and no air injection;
sar3tran1 = automatic transmission vehicle with pump air injection;
sar1tran5 = pre-1981 model year, 5-speed manual transmission vehicle of
unknown air injection type;
cid = cubic inches displacement;
sar3km1 = vehicle with pump air injection and mileage <=25k miles;
finj2km3 = vehicle with pump air injection and 50k < mileage <= 100k miles;
flaghc = high emitting vehicle flag under HC emissions;
acc1finj2 = carburetor-equipped vehicle operating with acceleration greater
than 1 mph/s;
acc3cat2 = oxidation only catalyst vehicle with acceleration greater than equal
to 3.0 mph/s;
ips90sar3 = vehicle with air pump and inertial power surrogate greater than or
equal to 90 mph2/s; and
dps8finj2 = proportion of drag power surrogate (DPS) speed x speed x
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acceleration) greater than 8 mph3/s.
Average vehicle speed is the single predictor modal activity variable that
applies to the entire fleet and is the only variable that will be included in the research
model specific to HC.
4.7.3 Oxides of Nitrogen Model
The oxides of nitrogen emission rate model was derived similar to the CO
model, which was described in detail in the above sections. The final emission rate
model for NOx is (Fomunung, 1999):
LogRnox = -0.5864 + 0.0225AVGSPD + 0.3424*IPS.120 + 0.6329*ACC.6 +
0.0247*DEC.2 + 0.0083*finj2km1 + 0.0028finj2km2 - 0.0021*cat2km3 +
0.0026*cat3km2 + 0.0003*cat3km3 - 0.0085*finj1km3flagnox -
0.0068*finj3km3flagnox (4-12)
Where:
IPS.120 = proportion of activity where IPS >= 120 mph2/sec;
ACC.6 = proportion of activity where acceleration >= 6.0 mph/s;
DEC.2 = proportion of deceleration <= -2.0 mph/s;
finj2km1 = carburetor equipped vehicle with mileage < 25k miles;
finj2km2 = carburetor equipped vehicle with 25K , mileage <= 50k miles;
cat2km3 = "oxidation only" catalyst vehicle with 50k < mileage <= 100k
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miles;
cat3km2 = TWC vehicle with 25K mileage <= 50k miles;
cat3km3 = TWC vehicle with 50K < mileage <= 100k miles;
finj1km3flagnox = second order interaction variable for a high emitting vehicle
with port fuel injection and 50k < mileage <= 100k miles; and
finj3km3flagnox = second order interaction variable for a high emitting vehicle
with throttle body fuel injection and 50K < mileage <= 100k miles.
The three modal activity predictor variables for the NOx emission rate model
are proportion of activity where inertial power surrogate is greater than or equal to 120
mph2/sec, proportion of activity where acceleration is greater than or equal to 6.0
mph/s, and proportion of activity where acceleration is less than or equal to 2.0 mph/s.
4.7.4 Final Response Variables
The final model included five response variables which where identified
during the emission rate phase of MEASURE. These five variables are presented in
Table 4-2.
Table 4-2: Modal Predictor Variables for Emission Rate Analysis for Passenger Cars Predictor Variable
Description
AVGSPD Average speed ACC.3 Proportion of activity where acceleration >= 3.0 mph/s IPS.120 Proportion of activity where IPS >= 120 mph2/s ACC.6 Proportion of activity where acceleration >= 6.0 mph/s DEC.2 Proportion of activity where acceleration <= -2.0 mph/s
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4.8 Independent Variables for Vehicle Activity Data Collection
The goal of this research was to investigate the influence of different geometric
and operational characteristics of signalized roadways that will affect modal
frequencies of vehicle activity. It is expected that vehicles behave according to
physical constraints of the vehicle, individual driver behavior, characteristics of the
surrounding traffic stream, and physical characteristics of the roadway. Various
factors may affect both driver behavior and vehicle operation. The Highway Capacity
Manual (TRB, 1994), Traffic Engineering Handbook (ITE, 1994), and other resources
identify several variables commonly shown to affect traffic operation. Factors may be
broken down into categories of driver, vehicle, roadway, traffic, and environmental
(ITE, 1994). The same variables that affect traffic operation are also theorized to
influence modal activity. A list of these variables is shown in Table 4-3. The end
result of the research will be a statistical analysis using the data to derive a relationship
between the dependent variable, modal activity, and independent variables that may be
used as predictors of modal activity. As a result, the factors that may be relevant
independent variables were considered in the data collection process and sites were
selected to represent as diverse a group of variables as was feasible. However, many
variables could not realistically be collected and were not represented. Although the
data collection is presented in Chapter 5, a note is made of whether each variable
presented below was collected in the field or calculated if appropriate.
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Table 4-3: Operational and Geometric Factors Hypothesized to Affect Modal Activity Factor Type Collected or
Calculated Horizontal Curvature Roadway No Vertical Curvature Roadway only as part of grade Grade Roadway Yes
Number of Lanes Roadway Yes Lane Width Roadway Yes Distance Between Intersections Roadway Yes Geographic Location (CBD, Suburban, etc)
Roadway Yes
Speed Limit Roadway Yes Vehicle Mix Traffic Yes Roadway Capacity Traffic Yes Level of Service Traffic Yes Density Traffic No Vehicle's Lane Position Traffic Yes On-Street Parking Traffic No Queue Position Traffic Yes Weather Conditions Environmental Yes Pavement Conditions Environmental No Type of Vehicle Vehicle Yes Trip Distance Driver No Driver Population Characteristics Driver No Trip Purpose Driver No
4.8.1 Driver Variables
The following sections describe variables listed in the Highway Capacity
Manual (TRB, 1994), Traffic Engineering Handbook (ITE, 1994), or other source
which may influence vehicle operation.
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4.8.1.1 Trip Purpose The purpose for which a driver makes a trip may
influence individual vehicle operation. A driver may behave differently for a morning
trip to work than a trip to the store. This information could not be realistically
collected and is not included as a variable. However, the majority of data collection
took place either during the AM or PM peak period. Consequently it is likely that a
high percentage of work trips are represented.
4.8.1.2 Demographics Drivers may behave differently depending on age,
socio-economic status, drug or alcohol use, driving experience, psychological
factors, driver familiarity with the roadway, stress, etc. (ITE, 1994). These factors
may be significant but could not be collected.
4.8.2 Vehicle Variables
A number of individual vehicle variables will affect vehicle activity profiles.
The vehicle's weight, engine size, vehicle make, aerodynamic characteristics, etc. will
determine the amount of fuel used and the physical operating constraints of each
vehicle. The vehicle class was recorded but others specifics could not be collected
given the available labor resources (an additional data collector is necessary for each
sampling location to collect license plate).
4.8.3 Roadway Variables
The physical geometry of the roadway including factors such as horizontal and
vertical curvature may affect driver behavior. Drivers slow around sharp horizontal
curves and adjust speed to compensate for limited line of sight on both horizontal and
vertical curves. Physically, vehicles experience different longitudinal and lateral
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forces on curves than on straight sections and are likely to exhibit different speed
profiles than vehicles on a straight stretch of roadway. Additionally, other geometric
factors such as grade or lane width may affect driver and vehicle behavior.
4.8.3.1 Horizontal and Vertical Curvature Both the horizontal and vertical
alignment of a particular roadway segment will have an impact on vehicle operation.
Horizontal roadway curvature causes lateral acceleration on the vehicle causing
additional load which may translate to either increased engine load and/or changes in
frequencies in speed and acceleration as measured on-road. Klaubert and Jongedyk
(1985) found that at a mean speed of 73 km/h on a 300-foot radius horizontal curve,
road load torque increase by 124 N.m. for the automobiles tested. Given that lateral
acceleration may increase engine loading leading to a possible increase in emission
rates, horizontal curvature may be an important factor. However, the laser
rangefinding equipment used for data collection use geometric equations to calculate
the distance from the rangerfinder to the targeted vehicle and depend on a maintaining
a constant line of sight. Consequently, accurate vehicle activity can only be collected
with the rangefinder and vehicle in the same vertical and horizontal plane. This data
collection method does not accommodate significant changes in horizontal alignment,
so curvature could not be included as a predictive variable.
Vertical curvature also impacts vehicle activity. Vertical curvature per se were
not considered in the study for the same reason as horizontal curvature. However, a
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vertical curve is made up of two different grades along a roadway alignment and grade
was collected.
4.8.3.2 Grade Roadway grade will impact engine load and emissions and
may influence on-road vehicle activity. Emission rates specific to grade will be
necessary to capture the full effect of grade on emissions. Grades affect the way
drivers operate vehicles. Most drivers either increase throttle position to maintain a
constant speed or allow the vehicle to decelerate while maintaining the same throttle
position (Grant, 1998). In either case, the change in engine activity may or may not be
manifested on the road. For example, a driver who increases throttle position will
increase engine load but the vehicle will maintain constant speed. The effect of grade
may be manifested in both vehicle activity profiles as well as emissions rates.
The effect of grade on vehicle operation is described in the Traffic Engineering
Handbook (ITE, 1994). The roadway gradient affects the maximum vehicle
acceleration achievable and is given by the equation
aGV = aLV - Gg/100 (4-13)
where:
aGV = maximum acceleration at speed V on grade (ft/sec2);
aLV = maximum acceleration at speed V in level terrain (ft/sec2);
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G = Gradient (%); and
g = acceleration of gravity (32.2 ft/sec2).
Not all grades may be significant. Grades in the range of a few percent may be
negligible. The Traffic Engineering Handbook (ITE, 1994) states that grades above
3% begin to influence passenger car speeds. The length of the gradient may also
affect modal activity. Grade was included as a variable.
4.8.3.3 Distance Between Adjacent Intersections Drivers are theorized to
behave differently when they expect to stop frequently than when they are driving on
long stretches of roadway. The greatest difference in speed and acceleration
frequencies between segments with varying distances between signals is expected to
occur midblock since higher freeflow speeds can be achieved on longer segments.
Differences may also occur at the stopbar if drivers accelerate differently when
presented with shorter distances between possible stops. Distance between
intersections was collected.
4.8.3.4 Number of Lanes The number of lanes along a street segment will
affect roadway capacity. Number of lanes may also affect vehicle activity. The
presence of multiple lanes may encourage higher speeds. As the number of lanes
increases, additional opportunities for conflict between adjacent vehicles may also
increase, causing drivers to react and behave differently. A related variable is the
vehicle's lane position. Drivers may behave differently depending on whether they are
positioned in a lane opposing on-coming traffic, in a lane adjacent to the curb, or
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sandwiched between other lanes in the lane group. The number of lanes was recorded
for the study locations.
4.8.3.5 Lane Width The width of the traffic lane affects traffic operation.
Narrow widths adversely impact capacity. Additionally, drivers may drive more
conservatively when narrow lane widths exist. Lane widths data were also collected.
4.8.3.6 Speed Limit The posted speed limit may influence the cruise speed a
vehicle attains. Consequently, a vehicle's acceleration and deceleration patterns may
be influenced by the ultimate speed that the driver is trying to attain. The speed limit
may also reflect other characteristics of the roadway such as functional class.
However, evidence exists that drivers travel at the speed they consider safe rather
obeying posted speed limits. Posted speed limits are easy to obtain for a given
segment and were collected for all data collection locations.
4.8.4 Environmental Factors
This section discusses various environmental factors, which are hypothesized
to affect modal activity.
4.8.4.1 Pavement Condition The condition of the roadway affects speed and
acceleration. The coefficient of friction between the tires and roadway affects a
vehicle's ability to accelerate and decelerate. The coefficient of friction for dry
pavement depends on the type of material used for construction, wear on the
pavement, etc. All of the study locations consisted of asphalt roadways. None of the
locations exhibited excessive wear. Further classification of pavement condition was
not practical for this study.
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4.8.4.2 Weather Weather conditions also affect both driver behavior and
vehicle operation. Drivers usually adjust speed, braking, following distance, etc. when
operating on snow, ice, or wet pavement. Drivers may be expected to drive more
cautiously during adverse weather. Weather may also affect drivers psychologically.
In addition to the effect on the driver, weather conditions may affect the operation of
the vehicle. The presence of snow, ice, or water on the roadway reduces the
coefficient of friction.
A variety of weather conditions could not be represented in the data collection
effort. Atlanta, Georgia rarely experiences snow. Additionally, the laser range finders
do not operate well with excessive moisture so data were not collected in the rain.
4.8.5 Other Factors
Other factors exist which may influence vehicle or driver behavior and did not
fit into any of the preceding classifications. These factors are listed below.
4.8.5.1 Pedestrian Activity Pedestrian activity should influence driver
behavior. Whether pedestrians are crossing at the intersection itself, walking
alongside lanes of traffic, or crossing at non-intersection locations, pedestrians may
either physically interfere with traffic operation or influence the way drivers proceed
along the roadway segment. However, this variable was not accounted for as part of
the data collection effort since the overwhelming majority of the data were collected
on arterials in locations where little pedestrian activity was noted.
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4.8.5.2 Location Along Segment Along a street segment with traffic control,
vehicles operations will be influenced by their location along the link in relation to the
traffic signal. For example, vehicles midblock are expected to maintain cruise speed
while at the intersection they are undergoing acceleration and deceleration. All of this
activity is dependent on a vehicle’s location along a segment.
The majority of extreme modal activity is likely to occur at the intersection
stopbar. Once a vehicle reaches cruise speed, they will typically only accelerate or
decelerate only due to interactions with surrounding vehicles, to change position, or
leave the roadway. While not recorded directly, with a known distance to the stopline
and laser output, the location along the link could be calculated.
4.8.5.3 Physical Location of Site The geographic location of an
intersection may influence traffic activity. The landuse characteristics surrounding a
roadway segment may influence both interactions between vehicles and driver
behavior. Segments along retail areas are more likely to have a large percentage of
vehicles exiting or entering via driveways. This can lead to significant variations in
speeds and consequently increased interactions between vehicles. Industrial locations
have less driveway activity but may have more heavy vehicles that interfere with the
traffic stream. The Central Business District (CBD) is a location classification that is
commonly used in traffic engineering applications such as calculation of LOS and
may be characterized by a combination of on-street parking, pedestrian activity, and
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delivery trucks. Suburban areas are located away from the city center and are
characterized by a minimal number of businesses.
Data collection sites were identified given one of the following designations:
• CBD;
• Suburban;
• Commercial; and
• Industrial.
The CBD category is for any sites located in the central business district area of
Atlanta. Suburban describes areas outside the CBD where a minimal number of
driveways or businesses were located. The commercial category indicates areas where
a substantial number of businesses and driveways are located in the study location.
Industrial areas were those located in areas with industrialized land uses.
4.8.5.4 Queue Position The position of the vehicle in the queue is
hypothesized to affect vehicle activity profiles. With free-flow conditions
downstream, the first vehicle in the queue is expected to accelerate unrestrained to the
desired speed. The second and subsequent queue positions will, to various degrees,
have their behavior constrained by the vehicle or vehicles ahead. Vehicle activity may
vary between all queue positions. However, at some position in the queue, it is
expected that vehicle interactions and behavior will become more uniform (i.e. the
tenth vehicle in the queue may behave similar to the ninth vehicle). Queue position
was noted.
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4.8.6 Operational Characteristics
Operational characteristics such as volume or level of service may influence
vehicle activity.
4.8.6.1 Level of Service Level of service is characterized by the average
stopped delay per vehicle over a 15 minute analysis period (TRB, 1994). Delay is a
complex variable based on a number of factors including quality of progression, cycle
length, green ratio, and the v/c ratio. Since delay plays a major role in determing LOS,
significant delay at an intersection with even low volumes may result in degraded
LOS. Hence LOS may only be correlated with vehicle activity if the amount of delay
a vehicle experiences influences the way it accelerates or decelerates.
Level of Service is an indication of the effectiveness used to describe how well
a roadway is functioning. Level of service is easily understood and widely used and
was calculated.
4.8.6.2 Volume to Capacity Ratio The volume to capacity ratio (v/c) is a
measure of capacity sufficiency. It is the ratio of volume or rate of flow to capacity.
A v/c ratio greater than 1 indicates that demand is exceeding the computed capacity of
the roadway segment (McShane & Roess, 1990). Capacity at signalized intersections
is calculated for each lane group and is the maximum rate of flow that can pass
through the intersection under prevailing conditions. Factors that affect capacity
include:
• volumes at other approaches;
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• turning movement distributions;
• bus activity;
• parking;
• pedestrian activity;
• number of lanes;
• grade;
• signal timing;
• percent heavy vehicles; and
• lane width.
For signalized intersections, the capacity of a lane group is calculated by:
ci = si(gi/C) (4-14)
Where:
ci = capacity of lane group i;
si = saturation flow rate for lane group i (vehicles per hour of effective green);
gi/C = effective green ratio for lane group i.
Ideal saturation flow rate (so) is the maximum flow rate capable of passing thru
an intersection for a given lane group given constant green and ideal conditions. The
saturation flow rate used to calculate capacity reflects an adjustment to the ideal
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saturation flow based on prevailing conditions and is impacted by lane width, percent
heavy vehicles, grade, on-street parking, bus activity, area type (CBD versus non-
CBD), and distribution of turning movements (TRB, 1994).
Volume to capacity may impact vehicle activity. At higher v/c, more
interactions between vehicles are expected affecting driving patterns. At lower v/c
the number of interactions between vehicles on the roadway are expected to be
decline. Volume to capacity was calculated.
4.8.6.3 Volume As more vehicles occupy the same amount of roadway, an
increased number of interactions will occur. Additionally, a vehicle's ability to
achieve and maintain it's desired freeflow will be significantly impacted. Volume is
necessary to calculate v/c ratios and is highly correlated. Volume was collected in the
field and is described in Chapter 5.
4.8.6.4 Density Density is the number of vehicles occupying a given section
of roadway at a particular instant. It is a function of rate of flow and average speed
given by:
D = v/S (4-15)
where:
D = density;
v = rate of flow; and
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S = average travel speed (mph) (McShane & Roess, 1990).
Density may provide a more realistic measure of vehicle interactions than
volume to capacity. Volume to capacity at the intersection only indicates the
relationship between volume of the roadway and the number of vehicles that can be
discharged from the intersection. Because average speed was not collected for the
entire intersection, density could not be calculated.
4.8.6.5 Fleet Mix Fleet mix is the proportion and types of vehicles
occupying a given roadway segment. The vehicle type describes the physical limits of
activity that an individual vehicle is capable of achieving. The types of vehicles in the
traffic stream will influence the ability of other vehicles to operate. For example,
heavy vehicles are physically incapable of achieving the same acceleration rates at a
given velocity than passenger vehicles. The percent of heavy vehicles in a traffic
stream will therefore affect the speed and acceleration of passenger cars around them.
Fleet mix was collected via vehicle counts.
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CHAPTER V
5. DATA PROTOCOLS
The primary research goal was to develop representative distributions of
vehicle activity at signalized intersections as a function of vehicle attributes, physical
roadway characteristics, or roadway operating characteristics. Modal data were
collected through empirical measurement of speeds and accelerations of vehicles with
laser rangefinders (LRF). Data collection, data preparation, data handling, and
attribute integration protocols used in this research are detailed in the following
sections. The data collection procedure is described followed by an overview of how
attribute data were calculated and matched to field datapoints.
A total of 26 locations representing a range of geometric and operation
characteristics were studied. Several locations were studied on more than one date.
5.1 Data Collection
The data collection methodology is presented in this section, including a
technical description of the hardware used. The selection of sampling locations is
given in Section 5.1.1, the equipment used for data collection is described in Sections
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5.1.2 and 5.1.3, and data collection protocol and a description of site attributes that
were collected are presented in Sections 5.1.4 and 5.1.6.
5.1.1 Selection of Sampling Locations
Sampling procedure is a critical component of experimental design. An effort
was made to collect as much data as could logistically be collected, reflecting as many
of the independent variables as possible. However, time and resource constraints
limited the actual amount of data that could be collected in the field.
Study sites were chosen based on three criteria. First, candidate locations were
selected to represent as many of the independent variables covered in Chapter 4 as
possible. The following is a list of the minimum variables that were considered in the
site selection process:
§ grade;
§ level of service;
§ volume to capacity;
§ location;
§ distance between signalized intersections;
§ vehicle type; and
§ percent heavy-duty vehicles.
Physical constraints of the data collection process served as the second criteria for
selecting study locations. Because data collection occurred alongside roadways, sites
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had to be chosen to minimize interference with surrounding objects, such as trees, or
adverse geometry, abrupt changes in grade or horizontal alignment. Most data
collection locations were selected so that a consistent grade existed throughout the
intersection approach.
The third consideration in site selection was to minimize influence on interaction
with the traffic stream. Areas with sidewalks or wide shoulders were selected so that
data collection personnel could be safely located away from the traffic stream.
Additionally, locations were chosen and equipment set up so that data collection was
as unobtrusive as possible to minimize distraction to drivers or influence driver
behavior.
Ideally, specific information about each vehicle "tracked", such as model,
make, year, engine size, etc., would be recorded and speed-acceleration activity
related to individual vehicle characteristics. Initially an attempt was made to record
each vehicle's license plate so that information for each vehicle could be extracted
from the Georgia vehicle registration database. This approach was abandoned early in
the data collection process for several reasons. First, the number of data collection
personnel available was limited. It was difficult for the person track the vehicle to
also record the license plate. Second, a number of vehicles had no plate, unreadable
plates, or were from outside the state. Discarding otherwise "good" datapoints
because the license plate wasn’t available would have seriously compromised the final
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sample size. Third, even if data could be disaggregated by individual vehicle type,
given all the variables that would be part of the statistical analysis, it would become
almost impossible to derive relationships on as detailed a level as individual vehicle
parameters. Additionally, even if the data could be disaggregated to the level of the
individual vehicle, it would be difficult for an agency to provide fleet mix at this level
of detail. In many cases, fleet mix is only defined by percent passenger cars and
percent heavy trucks rather than by separate technology groups.
However, different vehicles do exhibit different operational parameters.
Vehicles were divided into several categories including passenger cars, passenger
trucks, vans, buses, and heavy trucks. During data collection, each vehicle was
assigned a corresponding vehicle category. Passenger trucks include light duty trucks,
Jeeps, sport utility vehicles, etc. Vans include minivans and other vehicles reasonably
classified as passenger vehicles. Vans larger than normal passenger vehicles, such as
transit vehicles, were classified as buses. Passenger cars were designated as passenger
vehicle not falling into one of the two preceding categories. Buses included any type
of bus or large commercial van. Heavy trucks were designated when possible, with
their official classification (2A6, 3AD, etc.) and included all trucks with six or more
wheels.
5.1.2 Advantage Laser Rangefinder
Individual vehicle activity profiles were collected in the field using hand-held
laser rangefinding devices, also called “laser guns”. The equipment used were
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Advantage Laser Rangefinders manufactured by Laser Atlanta Optics. The LRF are
portable, handheld devices capable of measuring the distance to an object at a high
sampling frequency (238.4 distance measurements per second) with a manufacturer’s
accuracy specification of 0.1 feet (rms) over 2,500 feet (Laser Atlanta, 1997). No
minimum effective range for the LRF exists. The maximum effective range is 2,500
feet. Actual range is governed by practical considerations such as the type of vehicle,
sight constraints, and interference between the vehicle "tracked" and surrounding
vehicles and in all cases the actual range was less than the maximum range of 2,500
feet. Readings from the laser gun can be stored by either outputting the datafile to a
computer via serial port interface or by storing data on a SRAM PCMCIA card, which
inserts into the rear of the gun. For data collection, SRAM cards were used. Data
streamed to the output port are stored in null data files that were created on the card.
Each time the LRF trigger is pulled, all subsequent readings are stored to the first
available null data file on the SRAM card. Consequently, a unique file is stored on the
SRAM card for each vehicle observed (Grant, 1997). For a more in-depth discussion
on laser-range finding technology, the reader is referred to Grant, 1998.
5.1.3 JAMAR Boards
JAMAR boards are industry standard data collection devices commonly used
in traffic engineering studies. They are used for traffic engineering data collection
including volume counts, vehicle classification studies, and intersection turning
movement counts. JAMAR boards have the capability of recording up to three
directional movements for a total of four intersection approaches. They also have the
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ability to simultaneously bin volume counts into one of three individual bins so that a
vehicle mix can be monitored concurrently with volume counts.
JAMAR boards were used for turning movement counts for the study sites in
question. Turning movement counts were collected as well as classification of heavy
vehicles. Using the classification buttons, vehicles were assigned to one of three
classes:
§ passenger vehicle : includes passenger cars, light duty trucks, and vans;
§ heavy trucks: defined as any vehicle with more than 4 wheels; or
§ bus: includes buses of all sizes.
Turning movement counts were downloaded from the JAMAR boards to a PC
using the JAMAR technologies proprietary software, PETRA. From PETRA, counts
were output to a text file. Each file contained the time interval and volume counts by
movement for each of the three bins. Final output from the JAMAR boards is a tally
of vehicle volumes by lane group for each approach in 1-minute intervals. The 1-
minute intervals were later aggregated to 15-minute periods.
5.1.4 Vehicle Attribute Data
Concurrent with laser gun data collection, attribute information was recorded
for each vehicle "tracked." Since the laser gun did not have a time stamp, the only
method to attach one, when using the SRAM cards, was to manually record the time
and later attach this to the file. A time stamp was only necessary to match volume,
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LOS, and V/C to the data. The time was recorded manually on the data collection
sheet every few minutes and corresponded to individual vehicles. Other attributes
recorded for each vehicle, including the type of vehicle, lane the vehicle was
occupying, queue position, and the unique number from the LRF, described above
were recorded for each vehicle. An example of an attribute sheet is shown in Table 5-
1.
5.1.5 Site Attributes
General information such as the weather conditions, location, date, etc. were
recorded for the study session. Information about each location, including grade,
distance to the nearest upstream and downstream intersection, lane width, number of
lanes, posted speed limit were recorded for each session.
Table 5-1: Example Data Collection Attribute Sheet
Jimmy Carter at Live Oak 11-May-97 Weather: hot, sunny Distance to stopline: 104 feet
Time Vehicle Type Queue Position Lane P=xxxxx 7:22 Car 1 2 7865 7:24 2A6 3 1 13277 7:25 Car Thru 1 3455 7:25 Car Thru 2 5690 7:28 Van 1 1 898 7:30 Car 1 2 7724
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5.1.6 Data Collection Protocol
The signal timing for each intersection studied was also collected in the field.
Signal timing is necessary for calculation of volume to capacity ratios as well as level
of service calculations.
For optimal data collection, sites were selected and set up to be unobtrusive as
possible. Personnel and equipment were located either on the sidewalk or in the right
of way, as far away from the traffic stream as feasible without compromising line of
sight. LRFs were mounted on tripods to allow for continuous and uninterrupted
vehicle tracking.
Data collection consisted of the data collector "locking" the laser gun onto a
selected vehicle and then following that vehicle until loss of lock occurred. Data
collectors attempt to "lock" onto a location on the vehicle, such as the license plate,
and then maintain lock on that position. Data for each vehicle are downloaded from
the LRF and stored as a unique file on a data card.
5.2 Data Handling
Once data were collected in the field, they were later downloaded from the
data storage cards (SRAM cards) and reduced to usable datasets. A flowchart
detailing the data collection and reduction procedure is provided in Figure 5-2. A
description of the data reduction process follows.
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Figure 5-1: Data Collection and Reduction Methodology
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5.2.1 Laser Rangefinder
During each data collection session, data were stored on 2 MB SRAM cards.
The LRF output for each observation was streamed at the rate of 238.4 readings per
second to the next available null file on the card. Each card has the ability to hold the
lesser of either 100 files or 2 megabytes of data. At the end of the session, data were
downloaded to a PC via a MS-DOS batch file (CAPTURE.C), which copies each file
off the PCMCIA card and then systematically creates null files on the PCMCIA card.
Downloaded data files were named following the naming convention DATA.000,
DATA.001, ……, DATA.099. As a result, data files from each data collection session
had the same file names, so once data were downloaded they were zipped and stored
under a specific zip filename and directory.
Once a vehicle has been "tracked" and the trigger released, the LRF displays a
unique number in the visual display (P=xxxxx). Each file will also occupy the number
of bytes corresponding to the recorded P=xxxx value. For example, if the value
P=8891 was observed, once the file was downloaded it would occupy 8,891 bytes.
Because it is statistically unlikely that any two records contain the same number of
bytes, given the LRF sampling frequency, this number was unique. The number was
recorded and later correlated with other manually recorded data collected for the
vehicle such as type of vehicle or queue position.
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5.2.2 RANGE.C Program
After data were downloaded and stored in unique directories to prevent
overwriting data from one session with another, a program written in C language was
used to calculate speed and acceleration from the distance information. RANGE.C
was written by Chris Grant of Georgia Tech as part of his dissertation work (Grant,
1998). The program expects datafiles as input with the naming convention DATA.xxx
in order, starting with DATA.000, which are located in the same directory. Each
datafile is read consecutively until the last data file in the directory is reached. For
each directory, RANGE70.C reads each datafile and then records results to a single
output file for the directory. For each second of data, time, distance from the laser
gun, speed, and acceleration followed by the vehicle number are reported.
RANGE70.C calculates speed and acceleration using a smoothing algorithm. It
also attempts to throw out erroneous readings. Table 5-2 provides an example of
RANGE70.C output. Additionally, RANGE70.C requires the offset distance between
the LRF and the data collection as input and with this value, calculates actual
Euclidean distances between successive movements of the vehicle. Because data
collection takes place at the side of the road, the laser gun is not able to take a straight-
line reading to the vehicle. The readings actually report the hypotenuse of the distance
between the vehicle and the LRF. RANGE70.C accounts for this and computes the
straight-line distance to the vehicle for speed and acceleration calculations and
distance output. This is illustrated in Figure 5-2. Because different offsets will affect
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final output, each data file was run using the distance from the laser gun to the center
of each lane where data collection took place. For example, if data collection occurred
six feet from the edge of pavement and two twelve foot lanes were sampled,
RANGE70.C would have been run twice. First an offset distance to the center of the
first lane of 12 feet (6 + 12/2) would be used. Next, RANGE would be rerun using an
offset of 24 feet for the distance to the center of the second lane (6+12+12/2).
Often during the data collection process, other vehicles interfered with
"tracking" a targeted vehicle. This usually resulted in no data output for the vehicle in
question or a series of speeds and accelerations near 0 as output. An example of this is
found in the data output for vehicle 3 in Table 5-2. These data were manually
removed so that "bad" data did not skew analytical results. Additionally, each vehicle
in queue was tracked from rest if possible so that several to many seconds of idling
were recorded. Idling time was removed from the record sets because total delay
could not be captured for each vehicle and was not the subject of this research. Delay
can be calculated using a number of programs including the Highway Capacity
Software (HCS) and can be represented as seconds of activity in zero acceleration and
zero speed.
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Figure 5-2: LRF Geometry Accounted for in RANGE70.C
115
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Table 5-2: Example Output from RANGE Laser Offset : 12.0 Time=17.65, Dist= 33.9, Speed= 0.0, Accel=-0.1 Time=18.66, Dist= 37.0, Speed= 2.1, Accel= 2.0 Time=19.66, Dist= 43.2, Speed= 4.2, Accel= 2.1 Time=20.67, Dist= 54.1, Speed= 7.4, Accel= 3.1 Time=21.68, Dist= 69.5, Speed= 10.5, Accel= 3.1 Time=22.68, Dist= 89.4, Speed= 13.5, Accel= 3.0 Time=23.69, Dist= 110.4, Speed= 14.2, Accel= 0.7 Time=24.70, Dist= 131.3, Speed= 14.1, Accel=-0.1 Time=25.70, Dist= 152.9, Speed= 14.6, Accel= 0.5 Time=26.71, Dist= 177.5, Speed= 16.7, Accel= 2.0 Time=27.72, Dist= 205.1, Speed= 18.7, Accel= 2.0 Time=28.72, Dist= 234.9, Speed= 20.2, Accel= 1.5 Time=29.73, Dist= 267.2, Speed= 21.8, Accel= 1.6 Time=30.74, Dist= 301.0, Speed= 22.9, Accel= 1.1 Time=31.74, Dist= 335.0, Speed= 23.0, Accel= 0.1 # 1 Vehicle Time= 4.56, Dist= 292.7, Speed= 28.1, Accel=-2.5 Time= 5.57, Dist= 330.3, Speed= 25.5, Accel=-2.6 Time= 6.58, Dist= 366.0, Speed= 24.2, Accel=-1.3 Time= 7.58, Dist= 400.8, Speed= 23.6, Accel=-0.6 Time= 8.59, Dist= 436.2, Speed= 24.0, Accel= 0.4 Time= 9.60, Dist= 473.1, Speed= 25.0, Accel= 1.0 Time=10.60, Dist= 510.4, Speed= 25.2, Accel= 0.2 # 2 Vehicle Time= 2.55, Dist= 268.1, Speed= 0, Accel=0 Time= 3.56, Dist= 311.2, Speed= 0, Accel=0 Time= 4.56, Dist= 311.2, Speed= 0, Accel=0 Time= 5.56, Dist= 311.2, Speed= 0, Accel=0 Time= 6.56, Dist= 311.2, Speed= 0, Accel=0 # 3 Vehicle Time=13.62, Dist= 26.1, Speed= -0.0, Accel=-0.0 Time=14.63, Dist= 28.1, Speed= 1.4, Accel= 1.4 Time=15.64, Dist= 33.0, Speed= 3.4, Accel= 2.0 Time=16.64, Dist= 43.3, Speed= 6.9, Accel= 3.6 Time=17.65, Dist= 59.1, Speed= 10.7, Accel= 3.7 # 4 Vehicle
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5.2.3 ATTACH.C
Attribute data for each vehicle were manually collected during the data
collection process as described earlier and later matched with output from the laser
rangefinders so that observations of modal activity for individual vehicles could be
sorted by lane, queue position, vehicle type, etc. Attributes including a vehicle
identification number, data collection time, queue position, lane, grade, distance to
upstream and downstream intersections, and speed limit were recorded for each
vehicle and manually entered in a spreadsheet after data collection. Data were later
exported to a column delimited text file.
A program written in C, ATTACH.C, was used to match attribute output with
actual vehicle data output from RANGE70. ATTACH.C outputs comma delimited data
that can be easily be imported to a spreadsheet or database file. A final dataset for
each card used during each data collection session was created. An example of a final
dataset is shown in Table 5-3. The following sections describe the attribute data.
5.2.4 Stopline Distance
Using the known distance from the where the LRF was positioned to the
intersection stopline and the location output as part of RANGE.c, the vehicle's
instantaneous location from the intersection stopline was calculated and attached as an
attribute to each record which represented on second of vehicle activity.
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Table 5-3: Final Dataset Format Northside @ Deering
ID Time Type Queue Lane Stop Dist
VC LOS Speed (mph)
Accel (mph/s)
UP Vol
Down Vol
% HV
FILE Up Dist
Down Dist.
Gr ade Speed Limit
Lane s Lane Width
Locat-ion
Cond-ition
28 10:10 2A6 1 1 -31 0.3 A 0 0 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 -31 0.3 A 0.1 0.1 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 -24 0.3 A 4.6 4.5 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 -8 0.3 A 10.7 6.1 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 15 0.3 A 15.9 5.1 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 45 0.3 A 20.1 4.2 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 79 0.3 A 23.2 3.1 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 116 0.3 A 25.1 1.9 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 156 0.3 A 27.1 2 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 198 0.3 A 28.6 1.5 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 243 0.3 A 30.3 1.6 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 290 0.3 A 31.6 1.4 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 339 0.3 A 33.3 1.6 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 390 0.3 A 34.4 1.2 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 443 0.3 A 35.9 1.5 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY 28 10:10 2A6 1 1 497 0.3 A 36.8 0.9 776 620 4 DEER1 1523 1833 9 35 2 11 IND DRY
114 118
119
5.2.5 Volume Calculations
Volume counts for each study location were taken in one-minute intervals
using JAMAR boards. Counts were output from the JAMAR boards using JAMAR
Technologies software, PETRA and turning movement volumes calculated by 15-
minute intervals for the duration of the study period by vehicle type. Final volumes
reflect merging of passenger car, heavy truck, and bus bins for each interval. Upstream
volumes were determined by adding all turning movement volumes for the upstream
approach for the 15-minute interval. Downstream volumes were calculated by
summing the through movements for the study approach plus the volume of vehicles
from other approaches turning either left or right into the downstream link of the
approach.
5.2.6 Percent Heavy Vehicles Calculations
Heavy vehicle percents were calculated using the following equation:
Phv = (H + B)/(H+B+C) (5-1)
Where:
Phv = percent heavy vehicles for the 15 minute period;
H = total number of heavy trucks for the 15 minute period;
B = total number of buses for the 15 minute period;
C = total number of passenger cars for the 15 minute period.
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5.2.7 LOS and V/C Ratio
Later V/C and level of service were calculated and manually added to the
spreadsheet files. V/C and LOS were calculated for 15-minute intervals using the
Highway Capacity Software and were manually related to the data by the
corresponding time period.
Once data have been reduced and attributes attached, data can be binned by
desired groupings such as activity on specific grade or under a particular LOS. Data
can be sorted by location along a link so that critical locations for modal activity and
possible enrichment are identified.
5.3 DATA COLLECTION SITES
A total of 26 locations were studied in the Atlanta, Georgia metropolitan area
resulting in a total of 95 datafiles. Each datafile represents data collected on a single
card during the data collection process. Each datafile represents between 200 and 500
seconds of vehicle activity. A summary of data collection activity is shown in Table
5-4.
Final datasets represent LOS ranging from A to F with levels A, B, and C
being the most represented. V/c ranges from 0.2 to 1.2. Per lane volumes vary from a
minimum of 143 to a maximum of 1159. The following grades are represented: -9%,
-8%, -5%, -4%, -3%, -2%, -1%, 0, +1%, +2%, +3%, +4%, +%5, 8% and +9%. From
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2 to 5 lanes were represented. A two or three lane roadway was the most common
configuration with lane widths varying from 9 feet to 12 feet. Posted speed limits
were 30, 35, 40, and 45 mph. Downstream distances varied from 756 to 4,118 feet
and upstream distances varied from 300 to 5,544 feet. The most sampled queue
positions were the first or second in the queue or a "thru" vehicle since they were the
easiest to sample and were also the most common. However, this did not skew test
results since vehicles with different queue positions were analyzed separately.
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Table 5-4: Data Collection Sites Date Day Filename Intersection Location Starting
Time Approach Lanes Lane
Width Grade Speed
Limit Upstream Distance
DownstreamDistance
25-Oct-96 Friday Chrisatt 10th & West Peachtree
Midblock 3:45 PM WB 2 10 1% 35 578 578
25-Oct-96 Friday Dharmnet 10th & Peachtree
Acceleration 3:45 PM NB 2 9.5 -1% 35 1139 514
7-Nov-96 Thurs Nov7cd1 Peachtree & 10th
Acceleration 4:30 PM NB 2 9.5 -1% 35 1139 514
7-Nov-96 Thurs Nov7cd2 Peachtree & 10th
Acceleration 4:30 PM NB 2 9.5 -1% 35 1139 514
21-Feb-97 Friday Will1 Jimmy Carter & Williams
Deceleration 8:33 AM WB 2 12 3% 45 2640 1320
21-Feb-97 Friday Will2 Jimmy Carter & Williams
Deceleration 9:18 AM WB 2 12 3% 45 2640 1320
21-Feb-97 Friday Will3 Jimmy Carter & Williams
Acceleration 8:37 AM WB 2 12 3% 45 2640 1320
21-Feb-97 Friday Will4 Jimmy Carter & Williams
Acceleration 9:23 AM WB 2 12 3% 45 2640 1320
7-Mar-97 Friday Rockbd1 Rockbridge midblock 9:05 AM WB 2 12 3% 40 2376 2376 7-Mar-97 Friday Rockbd2 Rockbridge midblock 9:18 AM WB 2 12 3% 40 2376 2376 7-Mar-97 Friday Rockbd3 Rockbridge acceleration 8:25 AM WB 3 12 2% 40 528 1320
20-Mar-97 Thurs Deer1cd1 Northside & Deering
acceleration 5:03 PM NB 2 10.5 -8% 35 1833 1523
20-Mar-97 Thurs Deer1cd2 Northside & Deering
acceleration 5:51 PM NB 2 10.5 -8% 35 1833 1523
20-Mar-97 Thurs Deer1cd3 Northside & Deering
deceleration 5:03 PM NB 2 10.5 -9% 35 1833 1523
20-Mar-97 Thurs Deer1wht Northside & Deering
deceleration 5:41 PM NB 2 10.5 -9% 35 1833 1523
21-Mar-97 Friday Deer1cd1 Northside & Deering
acceleration 8:15 AM SB 2 10.5 9% 35 1523 1833
21-Mar-97 Friday Deercd2 Northside & Deering
acceleration 9:01 AM SB 2 10.5 9% 35 1523 1833
4-Apr-97 Friday Deer3cd1 Northside & Deering
acceleration 8:13 AM SB 2 10.5 9% 35 1523 1833
122
124
Table 5-4: Data Collection Sites (Cont.) Date Day Filename Intersection Location Start Time Approach Lanes Lane
Width Grade Speed
Limit Upstream Distance
Downstream Distance
4-Apr-97 Friday Deer3cd3 Northside & Deering
deceleration 8:09 AM SB 2 10.5 9% 35 1523 1833
4-Apr-97 Friday Deer3wht Northside & Deering
deceleration 8:40 AM SB 2 10.5 9% 35 1523 1833
9-Apr-97 Wed Deer4cd1 Northside & Deering
acceleration 5:17 PM NB 2 10.5 -8% 35 1833 1523
16-Apr-97 Wed Deer5cd1 Northside & Deering
acceleration 5:04 PM NB 2 10.5 -8% 35 1833 1523
16-Apr-97 Wed Deer5cd2 Northside & Deering
acceleration 5:57 PM NB 2 10.5 -8% 35 1833 1523
16-Apr-97 Wed Deer5cd3 Northside & Deering
deceleration 5:05 PM NB 2 10.5 -9% 35 1833 1523
21-Apr-97 Monday Wp&15wht West Peachtree & 15th
acceleration 8:25 AM NB 5 9 -3% 35 756 500
21-Apr-97 Monday Wp&15cd1 West Peachtree & 15th
acceleration 9:15 AM NB 5 9 -3% 35 756 500
22-Apr-97 Tuesday Ev&jccd1 Everest & Jimmy Carter
deceleration 8:43 AM WB 2 12 -5% 45 3696 2640
22-Apr-97 Tuesday Ev&jccd3 Everest & Jimmy Carter
acceleration 8:49 AM WB 2 12 -5% 45 3696 2640
22-Apr-97 Tuesday Ev&jcwht Everest & Jimmy Carter
Acceleration 9:30 AM WB 2 12 -5% 45 3696 2640
1-May-97 Thurs Ndruid2a North Druid Hills & LaVista
Deceleration 8:23 AM WB 2 11 1 40 2500 4200
1-May-97 Thurs Ndruid2b North Druid Hills & LaVista
Deceleration 8:56 AM WB 2 11 1 40 2500 4200
1-May-97 Thurs Ndruidwht North Druid Hills & LaVista
acceleration 8:16 AM WB 2 11 1 40 2500 4200
9-May-97 Friday Piedcd2 Piedmont acceleration 8:00 AM EB 2 11 1 40 700 300 9-May-97 Friday Card3out Piedmont deceleration 7:58 AM EB 2 11 1 40 700 300 9-May-97 Friday Whiteout Piedmont deceleration 8:43 AM EB 2 11 1 40 700 300
16-May-97 Friday Nt&10wh1 Northside & 10th
midblock 8:13 AM SB 3 11 4% 35 1584 2112
16-May-97 Friday Nt&10wh2 Northside & 10th
midblock 8:53 AM SB 3 11 4% 35 1584 2112
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125
Table 5-4: Data Collection Sites (Cont.)
Date Day Filename Intersection Location Time Approach Lanes Lane Width
Grade Speed Limit
Upstream Distance
Downstream Distance
16-May-97 Friday nt&10cd3 Northside & 10th
acceleration 9:00 AM SB 3 11 1% 35 1584 2112
16-May-97 Friday nt&10cd2 Northside & 10th
acceleration 8:07 AM SB 3 11 1% 35 1584 2112
21-May-97 Wed Mari1cd2 Marietta & Chatahochee
acceleration 4:53 PM WB 2 12 2% 45 2839 3696
21-May-97 Wed Mari1cd3 Marietta & Chatahochee
acceleration 5:24 PM WB 2 12 2% 45 2839 3696
23-May-97 Friday Mari2cd2 Marietta & Chatahochee
acceleration 7:47 AM EB 2 12 -2% 45 3696 2839
23-May-97 Friday Mari2wht Marietta & Chatahochee
acceleration 8:21 AM EB 2 12 -2% 45 3696 2839
28-May-97 Wed Mari3cd1 Marietta & Chatahochee
deceleration 5:35 PM WB 2 12 1% 45 2839 3696
28-May-97 Wed Mari3wht Marietta & Chatahochee
deceleration 6:17 PM WB 2 12 1% 45 2839 3696
6-Jun-97 Friday Pc&lkcda Peachtree & Lakeview
deceleration 8:03 AM SB 3 9 -3% 35 892 806
6-Jun-97 Friday Pc&lkcdb Peachtree & Lakeview
deceleration 8:45 AM SB 3 9 -3% 35 892 806
9-Jul-97 Wed Pc&jowht Peachtree Industrial & Johnson Ferry
acceleration 5:35 PM NB 2 10 2% 45 1320 1056
9-Jul-97 Wed Pc&jocd2 Peachtree Industrial & Johnson Ferry
both 5:40 PM NB 2 10 2% 45 1320 1056
15-Aug-97 Wed 1hwy29bk Hwy 29 & North Druid Hills
deceleration 8:52 AM SB 2 12 -4% 45 3168 2904
15-Aug-97 Wed 1hwy29wh Hwy 29 & North Druid Hills
deceleration 8:08 AM SB 2 12 -4% 45 3168 2904
29-Aug-97 Friday Sp&16cd1 Spring &16th deceleration 8:38 AM SB 4 9.5 -1% 35 1056 1181
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126
Table 5-4: Data Collection Sites (Cont.)
Date Day Filename Intersection Location Time Approach Lanes Lane Width
Grade Speed Limit
Downstream Distance
Upstream Distance
29-Aug-97 Friday Sp&16cd2 Spring &16th acceleration 9:16 AM SB 4 9.5 -1% 35 1056 1181 29-Aug-97 Friday Sp&16wht Spring &16th deceleration 8:00 AM SB 4 9.5 -1% 35 1056 1181 5-Sep-97 Friday Carrolc2 Marietta &
Carrol deceleration 9:18 AM EB 3 12 2% 45 2839 5544
5-Sep-97 Friday Carrolc1 Marietta & Carrol
deceleration 8:43 AM EB 3 12 2% 45 2839 5544
5-Sep-97 Friday Carrolwh Marietta & Carrol
deceleration 8:05 AM EB 3 12 2% 45 2839 5544
12-Sep-97 Friday Pch&key1 Peachtree Industrial & Cross Key
acceleration 8:55 AM SB 3 11 1% 45 1584 1584
12-Sep-97 Friday Pch&key2 Peachtree Industrial & Cross Key
acceleration 9:36 AM SB 3 11 1% 45 1584 1584
12-Sep-97 Friday Pch&keyw Peachtree Industrial & Cross Key
acceleration 8:20 AM SB 3 11 1% 45 1584 1584
1-Oct-97 Wed Pc&ky2c1 Peachtree & Cross Key
acceleration 9:12 AM SB 3 11 1% 45 1584 1584
1-Oct-97 Wed Pc&ky2c2 Peachtree & Cross Key
acceleration 8:09 AM SB 3 11 1% 45 1584 1584
1-Oct-97 Wed Pc&key2wh
Peachtree & Cross Key
acceleration 8:45 AM SB 3 11 1% 45 1584 1584
6-Oct-97 Monday Phill1cd1 Pleasant Hill & Satellite
deceleration 7:34 AM EB 3 11 1% 40 818 800
6-Oct-97 Monday Phill1cd2 Pleasant Hill & Satellite
deceleration 8:15 AM EB 3 11 1% 40 818 800
6-Oct-97 Monday Phill1wht Pleasant Hill & Satellite
acceleration 9:00 AM EB 3 11 1% 40 818 800
13-Oct-97 Monday Phill2cd2 Pleasant Hill & Satellite
both 8:09 AM EB 3 11 1% 40 818 800
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127
Table 5-4: Data Collection Sites (Cont.) Date Day Filename Intersection Location Time Approach Lanes Lane
Width Grade Speed
Limit Upstream Distance
Downstream Distance
13-Oct-97 Monday Phill2cd1 Pleasant Hill & Satellite
both 7:31 AM EB 3 11 1% 40 818 800
13-Oct-97 Monday Phill2wht Pleasant Hill & Satellite
both 8:44 AM EB 3 11 1% 40 818 800
27-Oct-97 Monday 2hwy29c1 Highway 29 & North Druid Hills
deceleration 7:40 AM SB 2 12 -4% 45 3168 2904
27-Oct-97 Monday 2hwy29c2 Highway 29 & North Druid Hills
deceleration 8:13 AM SB 2 12 -4% 45 3168 2904
3-Nov-97 Monday 2sp&16c2 Spring &16th both 8:50 AM SB 4 9.5 -1% 35 1056 1181 3-Nov-97 Monday 2sp&16c3 Spring &16th both 8:12 AM SB 4 9.5 -1% 35 1056 1181 3-Nov-97 Monday 2sp&16wh Spring &16th both 7:29 AM SB 4 9.5 -1% 35 1056 1181 3-Dec-97 Wed Mr-mdwb Marietta &
Chatahochee midblock 11:43 AM WB 3 12 -2% 45 1156 1683
3-Dec-97 Wed Mari-mid Marietta & Chatahochee
midblock 12:26 PM EB 3 12 2% 45 1683 1156
19-Dec-97 Friday Law-mid Lawrenceville Hwy
midblock 11:25 AM EB 2 12 -3% 40 4118 4118
19-Dec-97 Friday Ind-mdc1 Indian Trails by I_85
midblock 1:38 PM WB 3 12 -3% 45 982 982
19-Dec-97 Friday Ind-mdc2 Indian Trails by I_85
midblock 1:14 PM WB 3 12 -3% 45 982 982
19-Dec-97 Friday Ind-mdc3 Indian Trails by I_85
midblock 12:46 PM WB 3 12 -3% 45 982 982
20-Apr-98 Monday Ch420c1 Marietta & Chatahochee
both 7:58 AM EB 2 12 -2% 45 3696 2839
20-Apr-98 Monday Ch420c2 Marietta & Chatahochee
deceleration 7:14 AM EB 2 12 -2% 45 3696 2839
11-May-98 Monday j&ok1cd1 Jimmy Carter & Live Oak
acceleration 7:15 AM WB 3 12 1% 45 2640 3693
11-May-98 Monday j&ok1cd2 Jimmy Carter & Live Oak
acceleration 7:50 AM WB 3 12 1% 45 2640 3696
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128
Table 5-4: Data Collection Sites (Cont.) Date Day Filename Intersection Location Time Approach Lanes Lane
Width Grade Speed
Limit Upstream Distance
Downstream Distance
11-May-98 Monday j&ok1wht Jimmy Carter & Live Oak
acceleration 8:27 AM W 3 12 1% 45 3640 3696
4-Jun-98 Thursday
d0604cd1 Northside & Deering
acceleration 11:04 AM SB 2 10.5 9% 35 1523 1833
4-Jun-98 Thursday
d0604cd2 Northside & Deering
acceleration 12:10 PM SB 2 10.5 9% 35 1523 1833
8-Jun-98 Monday Deer0608 Northside & Deering
acceleration 10:09 AM SB 2 10.5 9% 35 1523 1833
8-Jun-98 Monday j&ok2cd1 Jimmy Carter & Live Oak
both 7:36 AM WB 3 12 1% 45 3696 2839
8-Jun-98 Monday j&ok2cd2 Jimmy Carter & Live Oak
both 8:09 AM WB 3 12 1% 45 3696 2839
8-Jun-98 Monday j&ok2wht Jimmy Carter & Live Oak
both 8:45 AM WB 3 12 1% 45 3696 2839
22-Jun-98 Monday j&ok3cd2 Jimmy Carter & Live Oak
both 7:34 AM WB 3 12 1% 45 3696 2839
22-Jun-98 Monday j&ok3wht Jimmy Carter & Live Oak
both 8:09 AM WB 3 12 1% 45 3696 2839
7-May-97 Wed e&jc2c2 Everest & Jimmy Carter
acceleration 4:59 PM EB 2 12 5% 45 2640 3696
7-May-97 Wed e&jc2c3 Everest & Jimmy Carter
acceleration 5:44 PM EB 2 12 5% 45 2640 3696
127
128
CHAPTER VI
6. PRESENTATION OF DATA
This chapter presents the data analysis segment for this research work. A total of 26
locations in the Atlanta, Georgia metropolitan area were sampled in the data collection
process. For the 26 sites, at total of 95 data files were downloaded from the PCMCIA
cards. Over all sites surveyed, a total of 4,097 passenger vehicles and 326 heavy vehicles
were sampled. A total of 26,941 seconds of passenger vehicle activity and 3,830 seconds
of heavy vehicle activity were recorded and were available for data analysis.
6.1 Data Preparation
After data processing as described in Chapter 5, a unique spreadsheet was created
for each datafile (one per SRAM for each site). The spreadsheet contained a second by
second profile for each vehicle with the related attributes such as queue position or grade.
Prior to statistical analysis, each spreadsheet was converted to a common file format
readable by S-PLUS statistical software.
Data were separated into two vehicle type categories. The "passenger vehicle"
designation included vehicles such as cars, light duty trucks with 4 wheels, passenger
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vans, and sport utility vehicles. "Heavy vehicles" included trucks with 6 or more wheels.
Various vehicle activity profiles were observed for buses. However, the MEASURE model
does not currently include parameters for buses so this data were not used in the analysis.
Once data were separated by vehicle type, they were disaggregated into two
hundred-foot incremental distances according to a vehicle’s position from the point of
queuing. Data were disaggregated in this manner for two reasons. First, when collecting data
it was almost impossible to sample a complete vehicle trace as was shown in Figure 4-1. A
complete vehicle trace would follow a vehicle from rest to a distance downstream, such as
1000 feet, without interruption. In reality complete vehicle traces could not be collected
because of interference in tracking the vehicle. Interference came from a number of sources
such as surrounding vehicles, vegetation, the “tracked” vehicle changing lanes, etc.
Consequently, by analyzing data in specific segments, incomplete vehicle traces can be used
without compromising the integrity of the data. Second, it was expected that activity would
differ by location from the intersection stopline. For example, vehicles behave differently
when starting from rest at the intersection than when they are cruising midblock. However,
at some point along a link it is expected that activity will become homogenous and can be
grouped. Additionally, although activity for the first and tenth vehicle in a queue is
130
expected to be dissimilar as the vehicles accelerate off the stopline, at some point
downstream, both vehicles should have reached their cruising speed and may have similar
vehicle profiles. Partitioning the data allows locations where the data act more similarly to be
identified. Data were partitioned according to the grouping conventions listed in Table 6-1
and an example of this disaggregation is shown in Figure 6-1.
To determine the fraction of activity in each response variable category, each of the
95 datafiles were prepared according to the following criteria:
1) Data were separated by queue position, level of service, volume to capacity, percent
heavy vehicles, upstream per lane volume, and downstream per lane volume. In most cases
upstream and downstream distances, grade, number of lanes, width, etc. were consistent for
the entire data collection site.
2) Data were then divided by 200-foot increments from the queuing point according to the
convention described above.
3) Seconds of activity for each response variable were calculated (i.e. seconds of activity
for the group where acceleration >= 6 mph/s).
4) Disaggregated data were summed by total seconds of activity and total seconds of
activity in each response category were calculated.
5) Percent of activity in each response category, such as % activity with acceleration >= 3.0
mph/s, was calculated by:
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% Activity = Seconds of response activity ÷ total seconds of activity. Table 6-1: Data Partitioning Name Description ACCEL Vehicle activity from the stopping point downstream 200 feet
for vehicles stopped by the traffic signal. ACCELPLUS200 Activity from 200 to 400 feet downstream of vehicle's initial
stopping point ACCELPLUS400 Activity from 400 to 600 feet downstream downstream of
vehicle's initial stopping point ACCELPLUS600 Activity from 600 to 800 feet downstream downstream of
vehicle's initial stopping point ACCELPLUS800 Activity from 800 to 1000 feet downstream downstream of
vehicle's initial stopping point ACCELPLUS1000 Activity from 1000 to 1200 feet downstream downstream of
vehicle's initial stopping point THRU Activity for vehicles not stopped by the traffic signal and
vehicles captured during "midblock" data collection. Data were divided by 200 foot increments before and after the intersection stopbar
DECEL Vehicle activity from 200 feet upstream of the vehicle's stopping point to the stopping point for vehicles stopped by the traffic signal.
DECELNEG200 Vehicle activity from 400 to 200 feet upstream of the vehicle's stopping point.
DECELNEG400 Vehicle activity from 600 to 400 feet upstream of the vehicle's stopping point.
DECELNEG600 Vehicle activity from 800 to 600 feet upstream of the vehicle's stopping point.
DECELNEG800 Vehicle activity from 1000 to 800 feet upstream of the vehicle's stopping point.
DECELNEG1000 Vehicle activity from 1200 to 1000 feet upstream of the vehicle's stopping point.
132
133
Figure 6-1: Schematic of Distance Partions
132
134
6.2 Data Analysis
Data were analyzed using hierachachial tree based regression analysis and then
validated using the Kolmorgorov-Smirnov two sample test in S-PLUS statistical software
version 4.5 from Mathsoft (Mathsoft, 1997). This analysis technique generates a "tree"
structure by dividing the sample data recursively into a number of groups. The groups are
selected to maximize some measure of difference in the response variable in the resulting
groups. One of the advantages of regression tree analysis over traditional regression analysis
is that it is a non-parametric method, which by definition does not require any distribution
assumptions and is more resistant to the effects of outliers (Roberts, 1999).
In growing a regression tree, the binary partitioning algorithm recursively splits the
data in each node until the node is homogenous or the node contains too few observations. If
left unconstrained, a regression tree model can "grow" until it results in a complex model with
a single observation at each terminal node that explains all the deviance.
However, for application purposes, it is desirable to create an end product that
balances the model's ability to explain the maximum amount of deviation with a simpler
model that is easy to interpret and apply. The software allows the user to interact with the
data in the following manner to select variables and help simplify the final model:
135
• Response variable: the response variable is selected by the user from a list of fields from
the data set;
• Predictor variables: one or more independent variables can be selected by the user from
a list of fields associated with the dataset;
• Minimum number of observations allowed in a single split: sets the minimum number of
observations that must be present before a split is allowed (default is 5);
• Minimum node size: sets the allowed sample size at each node (default is 10);
• Minimum node deviance: the deviance allowed at each node (default is 0.01).
Tree size is not limited and the resulting model may be more complex than necessary. To
simplify the model, several methods can be used. First, the minimum number of
observations, minimum node size, and minimum node deviance can be increased or
decreased either singly or in combination. Three other functions can be used to simplify the
tree without sacrificing goodness-of-fit. Pruning reduces the nodes on a tree by
successively snipping off the least important splits. The importance of a subtree is measured
by a cost-complexity measure defined by:
Dk(T') = D(T') + k . size(T') (6-1)
where:
Dk(T') = deviance of the subtree T';
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k = cost-complexity parameter; and
size(T') = number of terminal nodes of T'.
Cost complexity pruning determines the subtree T' that minimizes Dk(T') over all subtrees.
The larger the value for k, the fewer subnodes that will result (Mathsoft, 1997).
The second function that can be used to simplify the model is shrinking. Shrinking
reduces that number of effective nodes by shrinking the fitted value of each node towards its
parent node. The shrunken fitted values are computed according the following algorithm:
y(node) = k .? (node) + (1 - k) . y(parent) (6-2)
where:
k = shrinking parameter, may be either a scalar of vector (0<k<1);
? (node) = the usual fitted value for a node; and
y(parent) = the shrunken fitted value for the node's parent.
Snipping (snip.tree) allows the user to interactively remove nodes and try various
modifications to the original model. Implications of using any of the procedures (prune,
shrink, snip, modifying minimum number of observations, modifying minimum node size, or
modifying minimum node deviance) can be evaluated by observing normal probability plots
of the residuals for the “tree” object, comparing residual mean deviance for different models,
137
or inspecting a plot of the reduction in deviance with the addition of nodes. Breiman et al.
(1984) indicate that too large a tree will have a higher true misclassification rate than the right
sized tree, while too small a tree will not use some of the classification information available.
Breiman et al. (1984) suggest starting with an initial large tree model and then pruning back
to the right root node.
The residual mean deviance (RMD) is an indicator of regression tree "fit". It is the
mean deviance of the data samples in the terminal nodes of an estimated tree model. RMD
is calculated by summing of the deviance of all the data samples for all the terminal nodes.
The summed deviance is then divided by the number of terminal nodes. A lower value for
RMD indicates a "better" fit (Roberts, 1999). Under a normal (Gaussian) assumption, terms
in the residual mean deviance are the squared differences between the observations and the
predicted values (Mathsoft, 1997).
A plot of the model in S-PLUS may also be used to estimate the relative importance
of splits on a particular variable. When using the parameter of non-uniform spacing to plot
the regression tree model, the software plots the tree legs in approximation to the importance
of the split. Consequently, longer tree legs indicate that the variable explained more variation
than a shorter tree leg (Mathsoft, 1997).
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6.2.1 Identification of Microscopic Activity Distribution Dependent Variables
As discussed in Section 4.7, various microscopic activity variables have been
identified which may be highly relevant to emission producing activity. An in-depth overview
of the dependent variables was provided in that section. In short the following dependent or
response variables used in the statistical modeling are:
1) Acceleration >= 3.0 mph/s (ACC.3): The proportion of activity for the segment
where instantaneous acceleration rates are greater than or equal to 3.0 mph/s.
2) Acceleration >= 6.0 mph/s (ACC.6): The proportion of activity for the segment
where instantaneous acceleration rates are greater than or equal to 6.0 mph/s.
3) Deceleration <= -2.0 mph/s (DEC.2): The proportion of activity for the
segment where instantaneous acceleration rates are less than or equal to -2.0
mph/s.
4) Average Speed (AVGSPD): The average speed for the segment (mph).
5) Inertial Power Surrogate >= 120.0 mph2/s (IPS120): The proportion of activity
for the segment where inertial power surrogate (approximated by the product of
velocity and acceleration) is greater than or equal to 120.0 mph2/s.
6.2.2 Identification of Microscopic Activity Distribution Independent Variables
139
Section 4.8 detailed 21 variables that were hypothesized to influence
microscopic activity. There may be additional variables, which were not considered and
may have contributed to model error. It is theorized that the single most relevant variable in
predicting microscopic vehicle activity is driver behavior. Variables that can serve as
surrogate variables for individual driver characteristics include trip purpose (work commute,
shopping, recreation, education) and driver characteristics (age, income, occupation, etc.).
Unfortunately, with the type of study performed, it was impossible to collect any of the
variables related to individual drivers.
Of the 21 original variables considered, the final data model was only able to
realistically include 13 variables. A more in-depth discussion of how each variable was
calculated is provided in Chapter 5. Following is the final list of the predictor variables used
in the statistical analysis with their designation name in the database in parentheses:
• Vehicle queue position (QUEUE): represents the position of the vehicle in queue at the
stopbar of the intersection (1, 2, 3, 4 ….). Vehicles not stopped at the intersection were
designated as “THRU” vehicles.
• Volume to capacity (VC): the volume to capacity ratio for the segment calculated using
HCS in 15-minute intervals.
• Level of Service (LOS): level of service for the segment, calculated using HCS in 15-
minute intervals.
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• Number of lanes (NO_LANES): the number of lanes in the direction of travel for the
segment studied.
• Lane width (WIDTH): the average lane width for the segment.
• Upstream volume (UPSTREAM): volume by 15-minute intervals for the upstream
segment of the intersection studied adjusted to hourly volume
• Volume was divided by the number of lanes yielding per lane volume.
• Downstream volume (DOWNSTREAM): volume by 15-minute intervals for the
downstream segment of the intersection studied adjusted to hourly volume. Volume was
divided by the number of lanes yielding per lane volume.
• Upstream distance (UPDIST): distance from the intersection studied to the nearest
upstream signalized intersection.
• Downstream distance (DOWNDIST): distance from the intersection studied to the
nearest downstream-signalized intersection.
• Grade (GRADE): grade for the segment.
• Percent heavy vehicles (PER_HV): percent heavy vehicles for the link.
• Speed limit (SPEEDLIMIT): the posted speed limit for the link studied.
• Location (LOCATION): a categorical variable that indicates the most typical land use
surrounding the link being studied. The designations include a) Industrial, b)
Commercial, c) Suburban, and d) Central Business District (CBD).
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• Link length (LINKDIST): this variable was used for "thru" vehicles and was the length
of the street segment from signalized intersection to signalized intersection where data
collection took place. This was used in place of upstream link distance and downstream
link distance since it was difficult to interpret what upstream and downstream distances
were for thru vehicles since they occupied positions both before and after the intersection
stopbar.
• Link volume (VOLUME): this variable was the per lane volume of the street segment
where data collection took place and was used for "thru" vehicles only instead of
upstream and downstream volumes.
Several of the variables, which were considered and collected, were not included in the
final statistical analysis. Density was identified as a variable that may be influential in affecting
vehicle activity. Although, it is relatively easy to calculate, it requires the average speed for
the segment. Speeds were available by queue categories, such as average speed for
"THRU" vehicles for the segment or average speed for the first vehicle in the queue.
However, an average speed representative of all activity on the segment could not be
calculated. Consequently, density was not included. Pavement condition (wet, dry, icy) was
also dropped as an independent variable. As discussed previously, most data collection
took place under dry pavement conditions.
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Before proceeding with the statistical analysis, the various predictor variables were
investigated to determine whether they were correlated. Correlation between variables may
result in false partitioning of data. Correlation was found to exist between the following
variables:
• LOS and upstream per lane volume;
• LOS and downstream per lane volume;
• Volume to capacity and upstream per lane volume;
• Volume to capacity and downstream per lane volume; and
• Volume to capacity and LOS.
Figure 6-2 demonstrates the degree of correlation between volume to capacity and
upstream per lane volume. Correlation indicates that two or more of the independent
variables had a high level of linear relationship between them. Because of the strong
correlation, only one of the correlated variables was tested at a time and the variable yielding
the “best” model was selected for the final analysis. For example, volume to capacity would
first be included as a predictor variable along with the other non-correlated variables such as
grade. Variables correlated with V/C would be excluded from the analysis (LOS, up and
downstream volume). Second, LOS would be tested without volume to capacity or
upstream or downstream volume. Third, upstream and downstream volumes were be used
as separate independent variables along with the non-correlated variables. The best of the
three models would then be selected.
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Figure 6-2: Correlation Between V/C and Upstream Per Lane Volume (R2 = 0.64) Variables such as lane width, grade, percent heavy vehicles, and CBD vs. non-CBD were
used in the calculation of volume to capacity and level of service. However, a strong
correlation was not detected between any of these variables and no further action was taken.
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6.3 Results of Statistical Analysis for Passenger Cars
Final results of regression tree results and model validation for each data partion unit
as listed in Table 6-1 are presented below for both passenger cars and heavy vehicles. An
in-depth discussion of the statistical analysis, assumptions, final
model selection, and model validation for each response variable for the data partion
ACCEL is presented below. The data partion, ACCEL, represents queued passenger cars
from the initial queuing position downstream 200 feet. Since the analysis procedure is
similar, the final model for each subsequent data partion is provided in the following sections
without a detailed description of interim analysis steps and final model selection protocol.
6.3.1 Activity for Queue Vehicles From Stopping Point to 200 Feet Downstream
ACCEL Model
Described below are the five models (one for each of the response variables) for
passenger cars stopped at the traffic signal. Data were analyzed for a distance of 200 feet
downstream of the vehicle's initial queuing position. Next, model validation is discussed and
the final model is presented.
6.3.1.1 Percent Activity >= 6.0 mph/s (ACC.6) To arrive at the "best" initial
model, various regression tree models were created. Since several of the variables were
highly correlated, a test run was made with different combinations of correlated variables as
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described above. The initial model with the lowest deviation or best fit was used. Next, to
simplify the model, various combinations of:
1) increasing allowed deviance at the nodes,
2) increasing or decreasing the minimum number of observations required before a split
occurs, and
3) increasing or decreasing the minimum number of nodes
were tested to simplify and improve model simplicity and "fit". The initial model was created
by allowing the tree to grow unconstrained for the first cut. Once an initial model was
created, the "snip.tree" function in S-PLUS was used to simplify the model by removing the
lower branches of the "tree" that explained the least deviance. Each resulting "tree" was
examined to ensure that the model's predictive ability wasn't compromised by allowing the
overall amount of deviance to increase significantly.
Figure 6-3 illustrates the initial tree model used for ACC6 (percent of activity >= 6.0
mph/s) for data from queue vehicles from the stopping point to a distance 200 feet
downstream. Results for the initial model are given in Table 6-2. As noted, the tree grew
into a complex model with a considerable number of branches and 13 terminal nodes. To
simplify the model, various combinations of the prune, snip, and shrink functions were
experimented with. The "snip.tree" function ended up being the most useful tool in simplifying
trees. As explained previously, the first split in the regression tree explains the most deviation
with following split subsequently explaining less of the deviation. Figure 6-4 illustrates the
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amount of deviance explained corresponding to the number of terminal nodes. As shown,
the first 13 nodes (not terminal nodes) explain 92% of the deviance. The additional 26
nodes combined only, explain 8% of the deviance. Figure 6-5 illustrates a normal probability
plot of the residuals for the original untrimmed tree.
Table 6-2: Full Untrimmed Regression Tree Results for ACC6 for Passenger Cars From Stopping Point to 200 Feet Downstream Summary(acc6accel.tree) Regression tree: Tree(formula = ACC6 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + LOCATION + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "QUEUE" "GRADE" "DOWNSTREAM" "DOWNDIST" "UPSTREAM" "LOCATION" Number of terminal nodes: 13 Residual mean deviance: 49.89 = 19260 / 386 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -18.21 -3.074 -1.507 1.389e-015 1.52 36.48
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Figure 6-3: Original Untrimmed Regression Tree Model for ACC6 for Passenger Cars From Stopping Point to 200 Feet Downstream
Figure 6-4: Reduction in Deviance with the Addition of Nodes
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Figure 6-5: Normal Probability Plot of the Residuals for the Original Untrimmed Tree
A simplified model was derived which ends in six terminal nodes as compared to the
13 terminal nodes in the initial model. The residual mean deviance only increased from
49.89 to 57.27 and yielded a much cleaner model that the initial one. Results are shown in
Table 6-3 and Figure 6-6. As noted the independent model variables are queue position,
roadway grade, and downstream per lane volume.
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Table: 6-3: Trimmed ACC6 Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = ACC6 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + LOCATION + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = a6accel.snip3, nodes = 5) Variables actually used in tree construction: [1] "QUEUE" "GRADE" "DOWNSTREAM" Number of terminal nodes: 5 Residual mean deviance: 57.27 = 22560 / 394 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -17.5 -5.328 -1.507 2.353e-015 0.983 44.66
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Figure 6-6: Trimmed ACC6 Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream
6.3.1.2 Percent Activity >= 3.0 mph/s (ACC.3) This section describes the final
regression tree models for the response variable ACC.3 (percent of activity >= 3.0 mph/s).
Table 6-4 provides model results and Figure 6-7 shows the final regression tree model. In
the final model, queue position and grade were the most significant variables. The final
model had a rather poor fit with a RMD of 364.1.
6.3.1.3 Percent Activity Where Acceleration <= -2.0 mph/s (DEC.2)
Regression tree results for the response variable DEC.2 (percent of vehicle activity for the
indicated position where deceleration was less than or equal to -2.0 mph/s) are given in
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Table 6-5 and Figure 6-8. Note that downstream per lane volume with a single split on per
lane volume of 862 was the only variable for the final regression tree model.
Table: 6-4: Trimmed ACC.3 Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: Tree(formula = ACC3 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + WIDTH + LOCATION + NO.LANES + SPEEDLIMIT, Data = CarsAccelClean, na.action = na.omit, mincut = 5, Minsize = 10, mindev = 0.1) Snip.tree(tree = a3accel.snip3, nodes = 3) Variables actually used in tree construction: [1] "QUEUE" "GRADE" Number of terminal nodes: 3 Residual mean deviance: 364.1 = 144200 / 396 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -55.08 -11.49 2.172 –3.651e-016 13.12 46.45
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Figure 6-7: Trimmed ACC.3 Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream
Table: 6-5: Trimmed DEC.2 Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = Decel2 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + WIDTH + LOCATION + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 2) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 89.71 = 35620 / 397 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -3.861 -3.861 -3.861 4.761e-015 –0.4611 81.84
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Figure 6-8: Trimmed DEC.2 Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream
6.3.1.4 Average Vehicle Speed (AVG-SPD) The next response variable was
average speed for the indicated position in mph. For the data partion from 0 to 200 feet
from the point of queue, the single predictor variable for average speed was queue position
with a residual mean deviance of 15.95. Table 6-6 provides model
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results and Figure 6-9 shows the final regression tree model. The analysis showed that
queue positions 1, 2, and 3 were similar and queue positions 4 and higher were similar.
6.3.1.5 Inertial Power Surrogate >= 120 mph2/s (IPS120) The response
variable is inertial power surrogate (IPS120--the product of speed and acceleration) that
equaled or exceeded 120 mph/s2 for the indicated position. Table 6-7 provides model
results and Figure 6-10 shows the final regression tree model. The final variables included
queue position and roadway grade, with the 1st queue position in one split and all other
queue positions in the other. For the first queue position, grade was divided into values < -
0.5 and values >= -0.5. Grade did not apply to higher queue positions.
Table: 6-6: Trimmed AVG_SPD Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = SPEED ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + WIDTH + LOCATION + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = spdaccel.snip3, nodes = c(3, 2)) Variables actually used in tree construction: [1] "QUEUE" Number of terminal nodes: 2 Residual mean deviance: 15.95 = 6331 / 397 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -14.02 -2.197 -0.6202 -4.661e-015 2.053 13.63
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Figure 6-9: Trimmed AVG_SPD Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Table: 6-7: Trimmed IPS120 Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: Tree(formula = PKE120 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + WIDTH + NO.LANES + SPEEDLIMIT, Data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Snip.tree(tree = last.tree, nodes = c(3, 4)) Variables actually used in tree construction: [1] "QUEUE" "GRADE" Number of terminal nodes: 3 Residual mean deviance: 62.33 = 24680 / 396 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -12.1 -1.774 -1.774 2.435e-015 -1.774 71.22
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Figure 6-10: Trimmed IPS120 Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream
6.3.1.6 Summarization of Results for ACCEL As described in section 4.6, the
statistical approach used for data analysis involved a two-step process. Hierarchical based
regression tree analysis was first used, as described in the preceding sections, to identify the
predictor variables with the greatest power to explain the most variation in each of the five
response variables. Next, the predictor variables were used to stratify the original datasets,
into three-dimensional matrices in the form of a Joint Acceleration-Speed Probability Density
Function that can be used as input to MEASURE. Because data were originally collected in
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one-second intervals, JASPROD are in one-second "bins". JASPRODs are created by
dividing vehicle traces into a matrix of speed and associated accelerations bins according to
the operational or geometric characteristics, which were shown to be statistically significant.
6.3.1.7 Final Predictor Model for ACCEL The variables that were shown to
be the most relevant from regression tree analysis in influencing activity traces for passenger
cars from the initial point of queuing at the signalized intersection to a point 200 feet
downstream, for all the response variables, include roadway grade, queue position, and
downstream per lane volume. Relevant queue positions include the first vehicle in queue,
second and third vehicles in queue combined, and the fourth vehicle in queue and higher
combined. Grade is significant for the first, second, and third queue positions. According to
the data analysis, vehicle activity for this segment should be stratified by queue position, and
then other variables as shown in Table 6-8.
Table 6-8: Breakpoints for Data Stratification From the Initial Queue Position Downstream 200 Feet 1st in Queue 2nd and 3rd in Queue 4th in Queue and Grade < -4.5 Grade < -4.5 Down per lane < 862
Down per lane < 862 Down per lane < 862 Down per lane >= 862 ⇒ Down per lane >= 862
⇒ Down per lane >= 862
-1.5 > Grade > = -4.5 -1.5 > Grade >= -4.5 -0.5 > Grade >= -1.5 Grade >= -1.5 Grade >= -0.5 Down per lane < 862
Down per lane < 862 ⇒
Down per lane >= 862 ⇒ Down per lane >= 862
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6.3.1.8 Model Validation for ACCEL Model validation was difficult since the
dataset was not large enough to reserve a subset of sufficient size for validation.
Additionally, resources did not allow additional data collection to provide a "control" data
sample. However, the methodology can be validated internally. Following is description of
data validation to demonstrate the process of internal validation. Results are presented for
passenger cars for the data segment from the initial stopping point downstream 200 feet.
To validate model results, initial raw field data for the indicated segment were
divided by the factors listed in Table 6-9. Distributions of speed and acceleration for data
subsets were each compared using the non-parametric Kolmogorov-Smirnov goodness of fit
test for two independent samples using S-PLUS 4.5. The Kolmorgorov-Smirnov test was
described in more detail in section 4.5.2. A description follows for a comparison of two
datasets. Results of the K-S test for the first dataset (queue position = 1, grade < -4.5%,
downstream per lane volume < 862 {out1}) versus the second dataset, where queue
position and downstream per lane volume were held constant and the grade changed (queue
position = 1, grade >= -0.5, and downstream per lane volume < 862 {out10}) are provided
in Tables 6-9 and 6-10. The K-S was used to compare both speed and acceleration. As
shown, the null hypothesis that the distributions are the same was rejected for both speed
and acceleration. This indicated that the data should indeed be divided by these parameters
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from the regression tree analysis. Figure 6-11 compares the cumulative distributions for the
two datasets.
Table 6-9: K-S Test Statistic for Comparison of Datasets 1 and 10 for Acceleration Distributions Ks.gof(out1accel,out10accel) Two-Sample Kolmogorov-Smirnov Test Data: out1 and out10accel Ks = 0.1763, p-value = 0 Alternative hypothesis: Cdf of out1 does not equal the cdf of out10accel for at least one sample point. Table 6-10: K-S Test Statistic for Comparison of Datasets 1 and 10 for Speed Distributions Two-Sample Kolmogorov-Smirnov Test Data: out1speed and out10speed Ks = 0.0915, p-value = 0.0251 Alternative hypothesis: cdf of out1speed does not equal the cdf of out10speed for at least one sample point.
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Figure 6-11: Comparison of CDFs for Dataset Out1 and Out10
If the K-S test indicates that there is no statistical difference between the acceleration
and speed distributions of two data subsets, a strong case can be made for aggregating the
data up a level.
6.3.1.9 Final Model for Queued Vehicles for ACCEL After the K-S tests were
performed to validate the results of the regression tree analysis, a final model was selected
which reflected any changes to the data divisions indicated by the K-S tests. If the K-S test
indicated that the distributions were similar, the data from the two distributions were
combined. The final model, which governed how the final datasets were disaggregated for
MEASURE is presented in Table 6-11. As noted the only difference between the original
divisions of data suggested by the regression tree analysis, Table 6-8, and the final model
was in how the downstream per lane volume variable was ultimately divided. The original
three divisions for downstream per lane volume were:
1) downstream < 862;
2) 862 <= downstream < 902; and
3) downstream > =902.
The three were collapsed into two divisions after using the K-S test:
A) downstream < 862 and
B) downstream >= 862
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Table 6-11: Breakpoints for Data Stratification From the Initial Queue Position Downstream 200 Feet 1st in Queue 2nd and 3rd in Queue 4th in Queue and
Higher Grade < -4.5 Grade < -4.5 Down per lane < 862
Down per lane < 862 Down per lane < 862 Down per lane >= 862 ⇒ Down per lane >= 862
⇒ Down per lane >= 862
-1.5 > Grade > = -4.5 -1.5 > Grade >= -4.5 -0.5 > Grade >= -1.5 Grade >= -1.5 Grade >= -0.5 Down per lane < 862
Down per lane < 862 ⇒
Down per lane >= 862 ⇒ Down per lane >= 862
since division 2 (862<= downstream < 902) was shown to have the same distribution as
division 3 ( downstream >= 902).
6.3.2 Activity for Queued Vehicles From 200 to 400 Feet Downstream of Initial
Stopping Point (ACCELPLUS200)
The next data partion modeled was passenger vehicle activity that encompassed a
distance from 200 feet downstream of the queued vehicle's initial position to a point 400 feet
downstream. The final regression tree model results are presented in Appendix B.
Regression tree analysis and the K-S test were used and indicated that queue position and
grade were the most relevant variables in explaining variation. Table 6-12 illustrates the final
data breakdown by queue position.
Table 6-12 Breakpoints for Data Stratification From the 200 to 400 Feet Downstream of the Initial Queue Position
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1st in Queue 2nd and 3rd in Queue 4th and Higher in Queue Grade < -6.5 Grade < -4.5 Grade < -4.5 -4.5 > Grade >= -6.5 -1.5 > Grade >= -4.5 -1.5 > Grade >= -4.5 -1.5 > Grade >= -4.5 Grade >= -1.5 Grade >= -1.5 Grade >= -1.5 6.3.3 Activity for Queue Vehicles From 400 to 600 Feet Downstream of Initial
Stopping Point (ACCELPLUS400)
The next data partion was activity from 400 feet downstream of the queued vehicle's
initial queuing point to a point 600 feet from the initial queuing point. The final regression tree
model results are presented in Appendix B. For this data segment, queue position,
downstream per lane volume, distance to the nearest downstream intersection and percent
heavy vehicles were indicated as being relevant. According to model results, the first and
second vehicles in queue should be combined and 3rd and higher queue positions combined.
For the 1st and 2nd queue positions, distance to the nearest downstream intersection was
relevant. For 3rd and higher queue positions, percent heavy vehicles in the traffic stream was
significant. Final operational and geometric predictor variables after model validation are
demonstrated in Table 6-13.
Table 6-13: Breakpoints for Data Stratification From the 200 to 400 Feet Downstream of the Initial Queue Position 1st or 2nd in Queue 3rd or Higher in Queue Down per lane < 451 Down per lane < 878
Downdist < 803 Percent trucks < 5.5 ⇒ Downdist >= 803
⇒ Percent trucks >= 5.5
878 > Down per lane >= 451 Down per lane >= 878 Down per lane >= 878
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6.3.4 Activity for Queue Vehicles From 600 to 1,000 Feet Downstream of Initial
Stopping Point (ACCELPLUS600 and ACCELPLUS800)
The next data partion was activity that covered distances from a point 600 feet
downstream of the queued vehicle's initial queuing point to a point 1000 feet from the initial
queuing point. Data were initially divided by 200 feet increments. However, data were
combined from two segments, ACCELPLUS600 and ACCELPLUS800, since fewer data
were collected at increasing distances from the data collection location. Additionally, at
some point along a signalized link, it is expected that vehicle activity will become more
homogenous. The distance segment was included as a variable to test whether it was in
important factor in influencing vehicle activity (i.e were data from ACCELPLUS600
measurably different from ACCELPLUS800). The final regression tree model results are
given in Appendix B.
Statistical analysis indicated that posted speed limit, grade, and downstream per lane
volume are the most relevant variables that influence vehicle activity for this data segment.
Data should be divided first by the posted link speed limit with speeds less than 45 mph in
one set and posted speeds of 45 mph and higher in another and then further divided by
grade and downstream per lane volume. The final model is shown in Table 6-14.
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Table 6-14: Breakpoints for Data Stratification From the 200 to 400 Feet Downstream of the Initial Queue Position Speedlimit < 45 mph Speedlimit >= 45 mph Down per lane < 491 Down per lane < 491 Down per lane >= 491 Grade < -1.5 ⇒
Grade >= -1.5 Down per lane >= 491
Grade < -1.5
⇒ Grade >= -1.5
6.3.5 Activity for Queue Vehicles From Initial Stopping Point Upstream 200 Feet
(DECEL)
After data collected from the stopping point forward for queue vehicles were
analyzed for various distances, deceleration activity that occurred prior to the vehicle's
queuing position was analyzed. The first deceleration data partion was activity from the
vehicle's queuing position upstream 200 feet. The final regression tree model results are
found in Appendix B. The final combination of geometric and operational variables that
influence vehicle activity for this data segment include distance to the nearest upstream
signalized intersection, upstream per lane volume, and queue position. The data should first
be stratified by data collected at locations where the upstream distance is less than 1,168
and then data collected in locations with a distance to the nearest upstream intersection is
greater than 1,168 and less than 3,432 feet. The next set of data should be divided by
segments where the nearest upstream intersection is greater than 3,432 feet. The final rules
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for division of data according to regression tree and K-S test results for this data segment
are provided in Table 6-15.
Table 6-15: Breakpoints for Data Stratification From the Initial Queue Position Upstream 200 Feet Updist < 1168 3432 > Updist >= 1168 Updist > 3432 1st & 2nd in Queue 1st & 2nd in Queue 1st & 2nd in Queue
Up per lane < 613 Up per lane < 613 Up per lane < 613 ⇒ Up per lane >= 613
⇒ Up per lane >= 613
⇒ Up per lane >= 613
3rd and higher queue positions
3rd thru 8th position in queue 3rd and higher queue positions
Up per lane < 613 Up per lane < 613 Up per lane < 613 ⇒ Up per lane >= 613
⇒ Up per lane >= 613
⇒ Up per lane >= 613
9th in queue and higher Up per lane < 613
⇒ Up per lane >= 613
6.3.6 Activity for Queue Vehicles From 200 Feet Upstream of the Initial Stopping
Point to a 400 Feet Upstream (DECELNEG200)
The second deceleration data partion was activity from 200 feet to 400 feet
upstream of the vehicle's queuing position. The final regression tree model results are
presented in Appendix B. The final combination of variables that were shown to be the most
relevant in influencing activity traces according were grade, upstream per lane volume, and
queue position. According to the data analysis, vehicle activity for this segment should be
stratified by queue position and then other variables as shown in Table 6-16.
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Table 6-16: Breakpoints for Data Stratification From 200 to 400 Feet Upstream of the Initial Queue Position 1st and 2nd in Queue 3rd in Queue 4th in Queue and Higher Grade < -6.5 Grade < -6.5 Grade < -6.5 0 > Grade >= -6.5 Grade >= -6.5 0 > Grade >= -6.5
Up per lane < 447 Grade >= 0 ⇒ Up per lane >= 447
Grade >= 0
6.3.7 Activity for Queued Vehicles From 400 Feet Upstream of the Initial Stopping
Point to a 600 Feet Upstream (DECELNEG400)
For the data segment from 400 to 600 feet upstream of the initial queuing position,
only a single variable influenced vehicle activity. No activity was observed for the response
variables of acceleration >= 6.0 mph/s, acceleration >= 3.0 mph/s, or IPS >= 120. The
single predictor variable which explained the most deviation in both average speed and
percent of activity where acceleration <= -2.0 mph/s is upstream per lane volume with splits
on upstream < 601 vehicles per lane per hour and upstream >= 601 vehicles per lane per
hour.
6.3.8 "THRU" Vehicles at All locations
Vehicles not stopped at the intersection were analyzed separately from stopped
vehicles stopped since their vehicle activity traces are expected to be much different in the
vicinity of the intersection. Data were partitioned into 200-foot segments as for queued
vehicles. However all data partions were included in a single analysis for "THRU" vehicles
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and distance was included as a variables to test whether the location from the stopline affects
vehicle activity. The variables downstream and upstream volume were replaced by the
variable VOLUME as described in Section 6.2.2. The variable LINKDIST was also
included which reflected the length of the link where data collection was taking place and is
explained in section 6.2.2.
Including midblock data, the distances for data collection ranged from 2,000 feet
upstream of the intersection stopbar to 1,200 feet downstream of the intersection stopbar.
Regression tree analysis indicated that midblock data were statistically different from
upstream and downstream data positions. The designation for “THRU” data are those from
a distance 1000 feet upstream of the intersection stopline to 1200 feet downstream. All
other locations may be considered “MIDBLOCK”. Additionally, the posted link speed
limit, link volume, and link distance were shown to influence “THRU” vehicle activity. The
final data divisions are shown in Table 6-17.
Table 6-17: Breakpoints for Data Stratification For “Thru” Vehicles for All Distances Upstream and Downstream of the Data Collection Intersection Midblock Link distance < 3004 Link distance >= 3004
At intersection stopline
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Speed limit = 30
Speed limit = 35 or 40 Speed limit > 40
Link vol. < 543 Link vol. < 543 777 > Link vol. >= 543 Link length < 3004 856 > Link vol. >= 777
⇒ Link length >= 3004
Link Vol. >= 856 856 > Link Vol. >= 543 Link length < 3004 ⇒ Link length >= 3004
Link vol >= 856
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6.4 Heavy Trucks
The various regression tree models for heavy vehicles were much easier to run. In
many cases most of the initial regression tree models were simple enough that further
trimming was not warranted. This is likely due to the fact that heavy vehicle activity has
much less variation to begin with than passenger car activity since vehicle operation may be
constrained by vehicle rather than driver constraints. Presented below are the final models
from regression tree analysis and K-S validation for each data segment position for heavy
trucks.
6.4.1 Heavy Vehicle Activity for Queue Vehicles From Stopping Point to 200 Feet
Downstream (ACCEL) Model
This model provides results for heavy vehicles that were stopped at the traffic signal
and includes data for a distance from the vehicle’s initial queuing position downstream 200
feet. The variables that were shown to be the most relevant are roadway grade and queue
position as shown in Table 6-18.
Table 6-18: Breakpoints for Data Stratification From the Initial Queue Position Downstream 200 Feet 1st and 2nd Queue Positions
3rd thru 6th Queue Positions
7th and Higher Queue Positions
Grade < -4.5 8.5 > Grade >= -4.5 Grade > 8.5
No further division necessary No further division necessary
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6.4.2 Heavy Vehicle Activity From 200 feet From Stopping Point to 800 Feet
Downstream (ACCELPLUS200 to ACCELPLUS600)
This model provides results for heavy vehicles that were stopped at the traffic signal
and include data from a point 200 feet downstream of the vehicle's initial queuing position to
a position 800 feet from the initial stopping point. Two data partions were combined, so
distance from the initial stopping point was also included as an independent variable. The
variables shown to be the most relevant in influencing activity traces for this data segment for
heavy trucks include speed limit, grade, and percent trucks. According to the final data
analysis, vehicle activity for this segment should be stratified by the variables as shown in
Table 6-19.
6.4.3 Heavy Vehicle Activity From 200 feet Upstream to Stopping Point (DECEL)
The final combination of geometric and operational variables that influence vehicle
activity from the initial point of queue to a position 200 feet upstream include queue position
and grade. According to the regression tree analysis and K-S, vehicle
Table 6-19: Breakpoints for Data Stratification From 200 to 600 Feet Downstream of the Initial Queue Position Speed limit < 36 Speed limit >= 36 Grade < -4.5 Grade < -4.5 Grade >= -4.5 Grade >= -4.5
Percent trucks < 2.5 Percent trucks < 3.5
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⇒ Percent trucks < 2.5 ⇒ Percent trucks < 3.5
Percent trucks >= 2.5 Percent trucks >= 3.5 activity for the first, second, and third queue positions behaved similarly and should be
combined. Then data for the 4th and higher queue positions should be combined. The final
rules for division of data for this data segment is provided in Table 6-20.
6.4.4 Heavy Vehicle Activity for Queue Vehicles From 200 feet up to All Prior
Upstream Positions (DECELNEG200 to DECELNEG400)
This data segment was analyzed by including datasets for activity from a point 200
feet above the initial queuing location to any point upstream of that position. Data include
activity from 200 feet to 600 feet upstream. Distance from the initial queuing position was
also included as an independent variable to test if the distance from the signal was relevant.
The only variables shown to be relevant in influencing activity traces for heavy trucks
was upstream per lane volume as shown in Table 6-21.
Table 6-20: Breakpoints for Data Stratification From the Initial Queue Position Upstream 200 Feet 1st , 2nd and 3rd in Queue 4th and Higher in Queue Grade < 3.5 Grade < 3.5 Grade >= 3.5 Grade >= 3.5
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Table 6-21: Breakpoints for Data Stratification From 200 to 600 Feet Upstream of the Initial Queue Position All queue positions Upstream < 605 Upstream >= 605
6.4.5 Heavy Vehicle Activity for "THRU" Vehicles for All Positions
This model provides results for heavy vehicles that were not stopped at the traffic
signal and includes data for all distances before and after the stopbar including midblock.
Data for all “THRU” vehicles were combined and was composed of midblock data, data
collected immediately upstream of the intersection, and data collected immediately
downstream of the intersection. Link per lane volume (VOLUME) and link distance
(LINKDIST) were also included as variables as explained for the passenger vehicle “THRU”
data segment. Regression tree analysis indicated that midblock data were not statistically
different from upstream and downstream data positions. After regression tree and K-S
analysis the only relevant variable was percent grade of the segment being studied as shown
in Table 6-22.
6.5 Comparison of Data to Existing Relationships
In this section, field data are compared against other relationships that describe
speed and acceleration activity. A presentation of the ranges of acceleration found by speed
range is presented. Data are also compared against the values from the Traffic Engineering
Handbook (ITE, 1992), simulation models, and NCHRP 185. Activity
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Table 6-22: Breakpoints for Data Stratification For “Thru” Vehicles for All Distances Upstream and Downstream of the Data Collection Intersection All midblock and intersection activity Grade < -4.5 Grade >= -4.5
collected in the field that fell outside the range of activity in the FTP was also included.
6.5.1 Ranges of Field Data
An overview of the data collected is given in Table 6-23, which provides a bin count
by speed and acceleration range for all recorded values for all speed ranges for passenger
cars. Accelerations greater than and equal to 11.5 mph/s were combined into the 12 mph/s
bin. Accelerations less than and equal to -11.5 mph/s were combined into the -12 mph/s
bin. Figure 6-12 illustrates a graph of acceleration ranges by speed category (each speed
category sums to 1). This shows the variation in acceleration activity by speed range. As
shown, a significant variety exists in the data for accelerations across all speed ranges. This
data was intended to show that relationships that model acceleration as an inversely
proportional linear relationship to speed, do not provide a statistical distribution of actual on-
road vehicle activity. As noted, the most variation in acceleration ranges occurs at the lower
speed ranges from 0 to 35 mph speed bins.
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Table 6-23: Field Data Acceleration Observations by Speed Range Velocity (mph) Acceleration
(mph/s) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 -12 Plus 3 0 2 0 1 1 0 0 0 0 0 0 0 0 0 -11 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 -10 3 0 1 2 1 2 1 0 0 0 0 0 0 0 0 -9 0 2 4 5 3 5 3 3 0 1 0 0 0 0 0 -8 1 5 9 5 13 11 6 1 2 0 0 0 0 0 0 -7 4 16 27 27 22 25 13 10 5 2 0 0 0 0 0 -6 12 27 54 67 78 57 41 20 8 5 1 0 0 0 0 -5 25 90 124 138 126 114 86 20 23 10 2 1 1 0 0 -4 39 137 203 238 221 203 145 94 32 17 9 2 1 0 0 -3 110 251 220 229 251 249 210 144 96 39 22 6 4 2 1 -2 184 224 186 184 228 245 266 231 161 102 56 22 7 1 0 -1 274 147 102 141 192 287 354 404 374 326 249 122 32 5 1 0 1029 83 64 116 227 393 526 750 896 1026 925 460 205 28 7 1 410 77 69 174 298 520 641 660 557 562 420 230 111 27 1 2 133 158 106 259 424 581 591 405 280 151 106 58 33 9 1 3 3 240 165 302 443 471 340 192 111 50 43 17 9 0 0 4 0 197 221 280 300 223 155 63 37 24 13 7 3 2 0 5 2 96 219 187 124 86 53 31 17 4 5 2 0 2 0 6 0 16 119 67 40 23 26 8 9 5 2 2 0 0 0 7 0 2 33 36 19 7 4 1 2 1 0 1 0 0 0 8 0 0 8 11 4 4 6 1 0 0 0 0 0 0 0 9 0 0 5 1 5 1 0 4 0 0 0 1 0 0 0 10 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 2 0 1 0 1 0 0 0 0 0 0 12 Plus 0 0 0 0 0 0 1 0 0 1 0 2 0 0 0 Column Total 2232 1768 1942 2469 3023 3508 3471 3042 2611 2326 1853 933 406 76 11
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177
Figure 6-12: Acceleration Distribution (mph/s) by Speed Ranges (mph)
173
178
6.5.2 Comparison of Research to Existing Simulation Modeling
The use of simulation models by various research groups to output individual activity
profiles was discussed in Chapter 3. Simulation models offer attractive advantages for
modal activity modeling. They are readily available and often allow differing levels of analysis
with both simple and detailed data input. A major advantage to simulation modeling is the
ability to make multiple runs and compare different scenarios, such as comparing the effect of
different traffic timing plans on individual vehicle delay. The use of simulation models for
signalized intersections is especially promising because intersections are locations of
significant modal activity. Along signalized links, vehicle activity is particularly impacted by
intersection characteristics such as cycle length, which can easily be modeled by simulation.
However, simulation models often employ theoretical profiles of vehicle acceleration
and speed relationships. The algorithms were intended to model gross measures of traffic
activity, such as changes in cycle length or the effect of an incident. The models have been
validated under these conditions and perform well for the applications for which they were
developed. Internal algorithms, however, remain unvalidated for predicting individual vehicle
activity. Additionally, most models are incapable of integrating temporal and spatial
characteristics of traffic and roadways.
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To explore whether simulation models can be used to output realistic estimates of
individual vehicle activity and to identify drawbacks in their use, a companion study to this
research work (Hallmark and Guensler, 1999) compared individual activity output from a
simulation model with the field-collected vehicle profiles at signalized intersections that was
part of this work. For the comparison, a single study intersection was modeled using
simulation runs from NETSIM, the non-freeway, urban traffic simulation module of the
TRAF (CORSIM) traffic simulation model family. Instantaneous speed/acceleration output
from NETSIM for the study intersection was compared with the field data. A brief overview
of the results are discussed below, for a more detailed explanation, the reader is referred to
Hallmark and Guensler (1999).
Comparison of NETSIM and field data for the same sample intersection
demonstrated significant differences. Figure 6-13 and Figure 6-14 shows frequency of
activity by acceleration range for each model and frequency of activity by speed range for a
500-foot segment. Note that NETSIM underpredicts higher acceleration ranges (3 to 8
mph/s) for the study intersection. As shown, NETSIM also underpredicts vehicle activity in
the higher speed ranges (45 to 65 mph).
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Figure 6-13: Comparison of Percent Time Spent in Each Acceleration Range for Field Data and NETSIM (-250 to 250 feet from the stopbar)
Figure 6-14: Comparison of Percent Time Spent in Each Speed Range for
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Field Data and NETSIM (-250 to 250 feet from the stopbar)
The subset of midblock activity data was also analyzed. Figures 6-15 and 6-16
show frequency plots by speed and acceleration for a 500-foot segment of vehicle activity
2000 feet downstream of the study intersection. Unlike on-road vehicle activity, NETSIM
predicts few midblock acceleration events. Once a vehicle achieves it’s desired speed,
modeled acceleration activity remains fairly static. NETSIM also has a narrow range of
midblock speeds, ranging from 25 to 55 mph. Field data speeds range from 0 to 65 mph.
Field data show much greater acceleration variations and wider speed ranges. As
demonstrated in Figure 6-15, the field data midblock shows accelerations ranging from - 6
mph/s to 7 mph/s. The simulation model data only show activity for the acceleration ranges
from -4 to 3 mph/s. As shown in Figure 6-16, NETSIM has much narrower speed ranges
than demonstrated by the field data. No downstream queuing or significant driveway
interactions were noted, which would influence variations in speed and acceleration in the
field data.
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Figure 6-15: Comparison of Percent Time Spent in Each Acceleration Range for Field Data and NETSIM (midblock)
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
Freq
uenc
y
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Speed (mph)
Field Data
NETSIM
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Fre
qu
ency
-10 -8 -6 -4 -2 0 2 4 6 8 10
Acceleration (mph/s)
Field
NETSIM
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Figure 6-16: Comparison of Percent Time Spent in Each Speed Range for Field Data and NETSIM (midblock)
Results of the study indicate that even though the NETSIM model may be calibrated
correctly to predict aggregate flows or speeds, it is not necessarily calibrated to provide
accurate speed/acceleration profiles.
If NETSIM or similar simulation models do not predict speed/acceleration profiles
correctly, the ultimate impact is largely dependent on the emission factors that are applied to
the data. Emissions predicted from modal emission rate models, which predict significantly
higher emissions at higher engine loads, will be adversely affected by errors in predicted
speed/acceleration profiles, especially in the extreme speed/acceleration bins. When modal
emission factors indicate that average speeds are a highly significant variable (as they are for
oxides of nitrogen), NETSIM outputs are likely to underestimate modal emissions. When
high accelerations at low to medium speed ranges are more significant, NETSIM has the
potential to over-represent emissions (Hallmark and Guensler 1999).
One of the main reasons simulation models are unable to realistically model vehicle
activity are the underlying assumptions about vehicle behavior used in the model. In models,
such as NETSIM, a desired speed is assigned to each vehicle, which then attempts to reach
that target speed. The actual speeds attained are a function of interference with traffic
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control devices and interference with surrounding vehicles. The accelerations corresponding
to each instantaneously generated speed are constrained by car-following logic and an upper
bound maximum acceleration, which is a function of speed. The maximum acceleration at
any given speed is determined by a linear speed-acceleration relationship with maximum
acceleration occurring at zero velocity and zero acceleration at the maximum velocity. The
relationship is similar to that reported in NCHRP 185 (11 from TRB1999). TRAF version
5.0, used in the analyses reported here, allows users to define the maximum acceleration for
zero speed on dry level roads for a specified vehicle type (USDOT, 1995). A later version
of the program allows user defined maximum acceleration rates for specified speed ranges
(FHWA, 1995).
The problem with activity modeling that uses this linear speed-acceleration where
maximum acceleration is constrained by upper bound depending on the particular speed, is
that a vehicle can select any acceleration range up to that upper bound. No statistical
distribution of actual speeds and corresponding acceleration is actually incorporated into the
model. A plot of speed versus acceleration for data 0 to 250 feet from the stopbar for the
first vehicle is shown in Figure 6-17. for the first vehicle in the queue from the NETSIM
dataset described above, with the field data set. Data were extracted from NETSIM for 212
"first in the queue" vehicles and field data provided 37 "first in the queue" vehicles. Even
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though data were available for roughly three times as many vehicles, the NETSIM simulation
data show much less variation
Figure 6-17: Comparison of Field and NETSIM Data for the First Vehicle in the Queue (stopbar to 250 feet downstream)
than the field data. Additionally, acceleration peaks are noted in the 7 to 22 mph speed
range for the field data and from 0 to 10 mph for the simulation data.
Although the NETSIM microsimulation model has been presented, other simulation
models also have potential pitfalls that affect their ability to accurately model microscopic
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vehicle activity. The TRANSIMS simulation model based vehicle activity and position on
car-following theory rather than field studies of vehicle activity. One main drawback to the
model is that the cellular automata model describes vehicle position in units of cells, velocity
in units of cells per second and acceleration in units of cells per second per second. Since
the typical cell size is 7.5 meters, speed is modeled in 16 mph increments, which is too
aggregated for direct use in modal emissions modeling. Another drawback is that it does not
accurately represent acceleration events, which are a major variable in emissions (Williams et
al., 1999).
Other traffic simulation and optimization models such as TRANSYT-7F,
INTEGRATION, FREQ, NETSIM, and INTRAS calculate emissions but base output on
existing logic which is not expected to realistically model microscopic vehicle activity since
none of the models were developed based on on-road emission or vehicle activity data (Yu,
1999).
The simulation model proposed by Rakha et al. (1999) bases vehicle activity on car
following logic constrained by a linear acceleration decay function and may be characterized
by unrealistically high accelerations. To compensate, the model uses a linear acceleration
decay function that decreases. However, the application of the linear decay function has not
been validated with field studies.
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6.5.3 Comparison of Research to Traffic Engineering Rates
Evaluation of field data indicated that measured on-road maximum acceleration
exceed the published values from the Traffic Engineering Handbook (ITE, 1994) as listed in
Tables 3-1 and 3-2 in Chapter 3. A comparison of field data with the Traffic Engineering
Handbook values is provided in Table 6-24. Values in the Traffic Engineering Handbook
were listed by weight to power ratio. Since this value was not available for the field data, the
maximum value for any weight to power ratio from the Traffic Engineering Handbook were
compared to the field collected values. All data are for level roadways (-1% to 1% grades).
As noted, all field values exceeded the maximum published values for both passenger cars
and heavy trucks, indicating that commonly used acceleration rates may not adequately
represent on-road acceleration.
6.5.4 Comparison of Data to NCHRP 185
Some of the earlier speed acceleration relationships in traffic engineering were based on
NCHRP 185, which derived a linear speed-acceleration relationship as described in Section
3.3.1. A comparison of this relationship with field data for the
Table 6-24: Comparison of Field Data and Traffic Engineering Handbook Maximum Acceleration by Speed Range (mph/s) Vehicle Type 0 to 10
mph 10 to 20 mph
20 to 30 mph
30 to 40 mph
40 to 50 mph
50 to 60 mph
Passenger Cars from Traffic Eng. Handbook
6.3 6.1 5.3 4.8 4.3 3.8
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Passenger Cars from Field Data
9.9 9.4 8.8 8.8 6.7 5.5
Heavy Trucks from Traffic Eng. Handbook
2.0 1.6 1.4 1.0 0.7 0.4
Heavy Trucks from Field Data
4.9 5.0 4.2 5.1 4.7 4.5
first vehicle in queue for acceleration off the stopbar is shown in Figure 6-18. Only data for
the first vehicle in queue are presented since they are the only vehicles in the traffic stream
that enjoy unconstrained movement. Only data collection sites with no downstream backup
were included so that vehicle activity represents unconstrained acceleration. As shown,
vehicle activity does not follow a linear relationship. At low speeds, the vehicle is unable to
achieve high on-road acceleration. Acceleration ability increases with increasing speed until
approximately the 10 to 25 mph speed
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Figure 6-18: Comparison of Field Data for First Vehicle in Queue with Linear Speed-Acceleration Relationship
range when on-road acceleration decreases. Also demonstrated by this figure, is that on-
road vehicles undergo a wide distribution of vehicle activity at any given speed range beyond
0-5 mph. This indicates that the linear speed-acceleration relationship is too simplistic to
adequately model on-road vehicle activity for specialized applications such as air quality
modeling.
6.5.5 Comparison of Data to FTP Range of Activity
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As discussed previously, one of the most significant drawbacks for both activity and
emission factor modeling is the inability to model actual vehicle behavior, especially activity
outside the range of the FTP. Several studies referred to earlier in this work indicated that a
significant amount of on-road driving activity occurs outside the range of activity represented
in the Federal Test Procedure (LeBlanc et al., 1995; St. Denis et al., 1994; Effa and
Larsen, 1994).
A comparison of the total activity collected for passenger cars by percent of total
activity in each speed/ acceleration range is presented in Table 6-25. The data represent the
total activity collected over all intersections for passenger cars (sum of all columns and rows
= 1). While, data are not normalized to represent complete vehicle traces, a sense of the
magnitude of activity that falls outside the FTP can be gained. For a total of 29,673 seconds
of data collected, 6922 seconds of data fall outside the FTP (shaded area of the table). This
represents 23% of total recorded activity.
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Table 6-25: Percent Activity by Speed-Acceleration Ranges Outside the FTP (Shaded Area Represents FTP)
Velocity (mph) Acceleration (mph/s) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
-12 + 0.01 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -11 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -10 0.01 0.00 0.00 0.01 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -9 0.00 0.01 0.01 0.02 0.01 0.02 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -8 0.00 0.02 0.03 0.02 0.04 0.04 0.02 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 -7 0.01 0.05 0.09 0.09 0.07 0.08 0.04 0.03 0.02 0.01 0.00 0.00 0.00 0.00 0.00 -6 0.04 0.09 0.18 0.23 0.26 0.19 0.14 0.07 0.03 0.02 0.00 0.00 0.00 0.00 0.00 -5 0.08 0.30 0.42 0.47 0.42 0.38 0.29 0.07 0.08 0.03 0.01 0.00 0.00 0.00 0.00 -4 0.13 0.46 0.68 0.80 0.74 0.68 0.49 0.32 0.11 0.06 0.03 0.01 0.00 0.00 0.00 -3 0.37 0.85 0.74 0.77 0.85 0.84 0.71 0.49 0.32 0.13 0.07 0.02 0.01 0.01 0.00 -2 0.62 0.75 0.63 0.62 0.77 0.83 0.90 0.78 0.54 0.34 0.19 0.07 0.02 0.00 0.00 -1 0.92 0.50 0.34 0.48 0.65 0.97 1.19 1.36 1.26 1.10 0.84 0.41 0.11 0.02 0.00 0 3.47 0.28 0.22 0.39 0.77 1.32 1.77 2.53 3.02 3.46 3.12 1.55 0.69 0.09 0.02 1 1.38 0.26 0.23 0.59 1.00 1.75 2.16 2.22 1.88 1.89 1.42 0.78 0.37 0.09 0.00 2 0.45 0.53 0.36 0.87 1.43 1.96 1.99 1.36 0.94 0.51 0.36 0.20 0.11 0.03 0.00 3 0.01 0.81 0.56 1.02 1.49 1.59 1.15 0.65 0.37 0.17 0.14 0.06 0.03 0.00 0.00 4 0.00 0.66 0.74 0.94 1.01 0.75 0.52 0.21 0.12 0.08 0.04 0.02 0.01 0.01 0.00 5 0.01 0.32 0.74 0.63 0.42 0.29 0.18 0.10 0.06 0.01 0.02 0.01 0.00 0.01 0.00 6 0.00 0.05 0.40 0.23 0.13 0.08 0.09 0.03 0.03 0.02 0.01 0.01 0.00 0.00 0.00 7 0.00 0.01 0.11 0.12 0.06 0.02 0.01 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 8 0.00 0.00 0.03 0.04 0.01 0.01 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9 0.00 0.00 0.02 0.00 0.02 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00
10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 11 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
12 + 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00
187
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CHAPTER VII
7. DISCUSSION AND CONCLUSIONS ON MODAL MODELS
To address the lack of validated vehicle activity and to provide temporal and spatial
resolution of vehicle activity to provide more realistic input to air quality models, field studies
using laser rangefinding devices were undertaken to quantify actual vehicle behavior along
signalized links and at signal-controlled intersections. Data were analyzed to determine the
fractions of vehicle activity spent in different operating modes, especially those that may lead
to high engine load and elevated emissions. Statistical analysis using hierchachal tree based
regression was used to identify operational and geometric characteristics of studied
intersections which influence fractions of activity spent in individual operating mode.
Results indicate that for passenger cars, the most influential independent variables
include:
• grade of the study link
• queue position of the vehicle tracked
• downstream per lane volume for the data collection location
• percent trucks for the study link
• posted speed limit of the study link
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• upstream per lane volume for the data collection location
• distance to the nearest upstream signalized intersection from the data collection location
• distance to the nearest downstream signalized intersection from the data collection
location.
For heavy trucks, the most influential independent variables include:
• queue position of the vehicle tracked
• distance to the nearest down stream signalized intersection from the data collection
location
• grade of the study link
• posted speed limit of the study link
• percent trucks for the study link
• upstream per lane volume for the data collection location
• whether data collection occurred in the CBD, industrial area, suburban area, or
commercial area.
7.1 Model Limitations
Although, this research offers a step toward predicting microscopic vehicle activity at
signalized intersections, several limitations to the study exist which should be acknowledged.
One of the main drawbacks to this research model is that the ability did not exist with the
data collection approach used to provide a complete cycle of activity from intersection to
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intersection. Use of the LRF necessitated data collection in "snippets" rather than complete
traces. This method of data collection also influenced how data were analyzed. Ideally, data
traces following a vehicle through a complete cycle of activity would be highly useful in
predicting vehicle activity. The tradeoff between a car-following technique, such as that
described by Roberts (1999) and stationary data collection, employed in this research, is the
ability to collect complete vehicle traces versus the ability to collect a much larger sample
size.
Another limitation is that data collection only occurred in the Atlanta metropolitan
area. Data were collected at a wide variety of locations around the Atlanta area and
surrounding areas. However, it is unknown if the results of this study can unilaterally be
applied to other metropolitan areas.
Another limitation to this work is that vehicle activity may be more complex than can
be modeled with the amount of data that could be collected. Relationships between data
variables were shown to be complex.
Model validation was difficult since the dataset was not large enough to reserve a
subset of sufficient size for validation. Additionally, resources did not allow additional data
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collection to provide a "control" data sample, although, the methodology can be validated
internally.
Ideally data would have been collected for all influential geometric characteristics
across all operational ranges. However, for example, data would be collected for all grades
under all levels of service, V/C, etc. However to represent only two variables, grade from -
9% to +9% in 1% increments and LOS (A, B, C, D, E, and F), a total of 95 data collection
sessions would be required assuming all other variables remained constant (19 grade
intervals {-9, -8, ..... 0, .... +8, +9} x 5 LOS = 95). Consequently the major limitation of
this study was the ability to represent a wide range of geometric characteristics with all
operational conditions fully accounted for. This was due in part to resource limitations as
well as actually encountering data collection sites to meet all criteria. For example, it may be
possible to encounter several viable locations with a +9% grade. However, it is possible that
none of those locations exceeded LOS C so that LOS E and F on a 9% grade could not be
represented.
The independent variables used in the data collection process also limit the use of the
models. Since data collection could not represent all possible combinations of on-road
conditions, practical limitations exist on the extent to which the model can be applied. The
model cannot automatically be extended to make predictions outside the range of values
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collected for the independent variables. The limits of prediction by independent variable is
provided in Table 7-1.
Table 7-1: Limits of Prediction for Independent Variables Variable Minimum Value Maximum Value Level of Service A F Volume to Capacity 0.2 1.2 Upstream Distance 756 4,118 Downstream Distance 300 5,544 Upstream Per Lane Volume 143 924 Downstream Per Lane Volume
143 1,159
Grade -9 9 Percent Trucks 1% 35% Number of Lanes 2 5 Speed Limit 30 45 Lane Width 9 feet 12 feet Location Suburban, Commercial, Industrial, CBD Queue Position 1 15
7.2 Future Research Needs
One of the major limitations to this study is that data collection only took place in the
Atlanta Metropolitan area. Additional data should be collected and analyzed to “flesh” out
the models that were derived as part of this work. Since a number of variables were shown
to be significant, future work could focus on collecting data according to those variables.
The next logical step in this research would be to use the same data collection approach and
sample vehicle traces at signalized intersections in other areas of the country. It would be
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useful to compare results from cities similar in size to Atlanta as well as compare results to
medium and small cities.
Comparison of field results with simulation model output was also touched on in an
earlier section. Now that various deficiencies are apparent in using simulation model output
for microscopic vehicle activity for use in air quality models, a more in-depth study could be
undertaken which attempts to calibrate different simulation models. Calibration can be
attempted to determine if simulation models can be adjusted to give more accurate output.
7.3 Conclusions
To provide better estimates of microscopic vehicle activity, field studies using laser
rangefinding devices were conducted to quantify actual vehicle behavior along signalized
arterials and at signal-controlled intersections in Atlanta, Georgia. Data were analyzed to
determine the fractions of vehicle activity spent in different operating modes, especially those
that may lead to high engine load and elevated emissions. Statistical analysis, using
Hierchachal Regression Tree Analysis, of the data yielded various models for prediction of
microscopic vehicle activity based on geometric and operational characteristics of the
roadway. Data were divided into specific segments based on distance from the signalized
intersection where data collection occurred and analyzed. Overall results indicate that queue
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position, grade, downstream and upstream per lane volume, distance to the nearest
downstream intersection, percent heavy vehicles, and posted link speed limit are the
operational and geometric characteristics that most influence microscopic vehicle activity for
passenger vehicles. Results also indicate that queue position, distance to the nearest
downstream signalized intersection, grade, percent heavy vehicles, posted link speed limit
and upstream and downstream per lane volume are the critical variables that influence heavy-
duty vehicle microscopic activity.
Research results provide the ability to estimate microscopic vehicle activity as input
to both local and regional transportation-related air quality models, moving the
implementation of modal emission models closer to reality. Results have also indicated that
simulation modeling has several drawbacks as applied to microscopic transportation-related
air quality modeling and that existing traffic engineering relationships, which describe vehicle
activity, are not adequate to accurately describe vehicle activity relationships.
Because the results have described microscopic vehicle activity, research findings
may also enhance current methods for estimating capacity and modeling traffic flow and may
have applications for intelligent transportation systems (ITS).
196
196
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APPENDIX A
A.1 MECHANICS OF VEHICLE OPERATION
An overview of the actual mechanics of vehicle operation is presented in this
section. This information is presented so that an understanding can be gained of they
dynamics and constraints as that influence a vehicle's ability to accelerate from rest
since this activity makes up a significant portion of intersection activity.
The maximum longitudinal acceleration of a motor vehicle is constrained by
two primary factors. On the vehicle side, the maximum acceleration achievable is
limited by the tractive effort available at the wheels, which is simply the force
available at the roadway surface to perform work. In English units, work is expressed
in pounds. On the ground side, the resistance against forward movement limits the
maximum achievable acceleration by opposing forces, such as aerodynamic drag, and
is manifested at the wheel. Maximum performance in longitudinal acceleration is
determined by either engine power or traction limits on the drive wheels. The limit
that prevails may depend on the vehicle's speed. At lower speeds, tire traction may be
the limiting factor, while at higher speeds the engine power may account for the limits.
A.1.1 Tractive Effort
The tractive effort available at the wheels is a function of the force determined
by the engine. The amount of tractive force generated is a function of various engine
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factors such as the shape of the combustion chamber, the quantity of air drawn into the
combustion chamber during the induction phase, type of fuel used, and fuel intake
design. The power of an engine is the rate at which work is done. Power is a function
of the mean effective pressure, diameter of cylinders, length of stroke, revolutions per
minute, number of effective strokes per minute, type of fuel, fuel intake design,
number of cylinders, etc. Useful power developed at the engine shaft is reduced by
the amount of power expended in overcoming the frictional resistance of the engine.
There are various variables that influence the engine's performance. These influential
factors are listed in the sections below. The most common measures of engine output
are horsepower and torque. Torque is the work generated by the engine. Torque is
defined as twisting moment and the units are foot-pounds (ft-lb). Horsepower is the
rate of engine work.
Propulsive power is provided by the engine, and is characterized by engine
torque and power curves as a function of speed. Gasoline engines usually have a
torque curve that peaks in the mid-range of operating speeds depending on operating
system characteristics. Actual torque delivered to the drivetrain is reduced by the
amount required to accelerate the inertia of the rotating components and accessory
loads (Gillespie, 1992). Diesel engines are characterized by flatter torque curves.
Power is a function of speed and torque, which are represented by:
P(ft-lb/sec) = T x S; (A-1)
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P (kw) = 0.746 x HP; (A-2) HP = T x RPM/5252; (A-3)
where:
P = power ;
T = torque (ft-lb); and
S = Speed (radian/sec);
HP = horsepower (1 hp = 550 ft-lb/sec); and
RPM = revolutions per minute.
A.1.1.1 Spark Timing Spark timing is important in determing pressure
development in the engine cylinder. If combustion occurs too early in the cycle, work
transfer from the piston to the gases in the cylinder at the end of the compression
stroke is too large. On, the other hand if combustion starts too late, the cylinder
pressure is reduced, decreasing the expansion stroke and work transfer from the gas to
the piston. A maximum engine torque is possible for a specific spark timing at a fixed
speed, fuel mixture composition and flow rate. Firing order is also important for
optimum distribution of fuel to all cylinders.
A.1.1.2 Fuel Mixture Composition The fuel mixture in the engine cylinder
prior to firing is a mixture of fuel, air, and burned gases. For optimum engine
performance, a stoichiometric mixture with the exact proportion of air and fuel is
necessary for complete combustion. The throttle position controls the flow of air and
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fuel, when sensors indicate that the engine needs an extra supply of fuel for
acceleration, the throttle suddenly opens allowing the flow of fuel to increase more
rapidly than the flow of air. In order to get maximum power out of an engine, a
maximum quantity of chemical energy is required, resulting in an enriched fuel:air
mixture. For maximum power, all the air has to be burned, while for economical
cruising all the fuel must be burned.
Throttle position affects the fuel:air ratio as do ambient temperature, ambient
pressure and humidity, and engine temperature. The fuel:air control is also the
dominant factor in emissions production. The fuel is delivered to the engine by one of
three technologies; carburation, throttle body injection, or point fuel injection. The
majority of new vehicles have one of the two injection systems.
A carburetor delivers fuel as air rushes into the intake manifold via a narrow
chamber. When the accelerator pedal is pressed, the butterfly valve is actuated leading
to more air being allowed in the manifold. The speed of the engine and the throttle
position determine the amount of air allowed in the intake manifold.
Throttle body injection uses a fuel pump, pressure regulator, and injector to
control the fuel:air mixture. Sensors monitor the airflow and the computer system
decides on the amount of fuel that will be mixed with the air stream. The fuel pump
circulates fuel to the injector at a constant pressure with a needle valve in the injector
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opening for a set period of time to allow a pulse of fuel to mix with the air. Port fuel
injection delivers a spray of fuel above the intake valve leading to more uniform fuel
delivery in each cylinder. Commonly, the injector system maintains a constant
pressure in the fuel line and delivery of fuel is time controlled.
A.1.1.3 On-board Sensors and Computer Systems Currently, the electronic
engine control system has evolved into an integrated system. The main sensors in the
control system that relate to engine performance are:
• Airflow quantity sensor: senses and regulates the airflow injected into the
cylinder;
• Drive shaft speed angular position sensor: constitute timing base and is essential
for engine control;
• Oxygen concentration sensor: detects fuel:air ratios in exhaust and regulates
fuel:air ratios for fuel economy;
• Throttle valve position: monitors throttle position and helps control fuel amounts;
and
• Ignition timing: controls and optimizes combustion with the cylinder powerstroke
for optimum engine performance.
Because available power depends on the correct fuel:air mix, especially for
acceleration, vehicle performance is tied to the computer’s control system. For
starting the system has to go from closed-loop to open-loop system for proper fuel:air
mix. For heavy loading, such as uphill acceleration, the system goes into enrichment.
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A.1.2 Power Delivered to the Wheels
The first order determinant of vehicle acceleration performance is the ratio of
engine power to vehicle weight. Simplistically, acceleration is described according to
Newton's second law of motion (Gillespie, 1992):
Max = Fx (A-4)
where:
M = vehicle's mass = weight/gravitational constant;
Ax = forward acceleration; and
Fx = tractive force at the drive wheels.
Substituting the relationship of the drive power being the tractive force time the
forward speed, the following equation is given (Gillespie, 1992):
ax = (1/M)Fx = 550(g/V)(HP/W) (A-5)
where:
g = gravitational constant (32.2 ft/sec2);
V = speed (ft/sec);
HP = engine horsepower; and
W = vehicle weight.
The velocity term in the denominator indicates that acceleration capability decreases
with speed. To better describe acceleration performance, modeling the mechanical
systems whereby engine power is transmitted to the ground is necessary. Torque
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delivered from the engine through the clutch as input to the transmission can be
expressed as:
Tc = Te - Ieαe (A-6)
where:
Tc = torque at the clutch (input to the transmission);
Te = engine torque from dynamometer data at a specific speed;
Ie = engine rotational inertia;
αe = engine rotational acceleration.
Torque at the output of the transmission is increased by the gear ratio of the
transmission and decreased by inertial losses in the gears and shafts and is
approximated by (Gillespie, 1992):
Td = (Tc - Itαe)Nt (A-7)
where:
Td = torque output at the driveshaft;
Tc = torque at the clutch;
It = rotation inertia of the transmission;
αe = engine rotational inertia; and
Nt = numerical ratio of the transmission.
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Finally, torque delivered to the axles to provide tractive force at the ground is
amplified by the final drive ratio which is reduced somewhat by inertia of the driveline
components between the transmission and final drive and is given by (Gillespie,
1992):
Ta = Fxr + Iwαw = (Td - Idαd)Nf (A-8)
where:
Ta = torque on the drive axles;
Fx = tractive force on the ground;
r = wheel radius;
Iw = rotational inertia of the wheel and axle shafts;
αw = rotational inertia of the wheels;
Td = torque output to the driveshaft;
Id = rotational inertia of the driveshaft;
αd = rotational acceleration of the driveshaft; and
Nf = numerical ratio of the final drive.
Further solving for acceleration as a function of the wheel rotational acceleration and
the tire radius and incorporating inefficiencies due to mechanical and viscous losses in
the driveline components reducing the engine torque in proportion to the product of
the efficiencies of the individual components gives (Gillespie, 1992):
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ax = (TeNt fηt f - Rx - DA - Rhx - Wsinθ)/(M + Mr) (A-9)
where:
M = mass of the vehicle (W/g);
Mr = equivalent mass of the rotating components;
ax = acceleration (f/sec2);
W = vehicle weight;
Te = engine torque at a given speed;
Nt f = combined ratio of transmission and final drive;
ηt f = combined efficiency of transmission and final drive;
Rx = rolling resistance forces;
DA = aerodynamic drag force;
Rhx = hitch or towing forces; and
sinθ = grade.
Except for grade, all other forces vary with the speed of the vehicle.
Constant power is equal to the maximum power of the engine, which is the
upper limit of tractive effort available minus driveline losses and is only approached
when the engine reaches the speed where it develops maximum power. The tractive
force for each gear is the engine torque curve adjusted by the ratios for that gear. For
maximum acceleration performance, optimum shift point occurs between gears
(Gillespie, 1992).
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A.2 Resistive Forces
Besides actual vehicle constraints, various forces must be overcome by motor
vehicles if they are to move forward. Resistive forces acting against vehicle
movement involve a complex relationship between the vehicle's weight and the
distribution of that weight including the effect of grade, aerodynamic wind resistance,
roadway friction, and rolling resistance. Simply explained, the expression of these
forces is manifested where the tire touches the roadway
A.2.1 Vehicle Load
All of the factors contributing to a vehicle's load and can be represented as
front and rear axle loads, which is then distributed to the four tires. The following
factors contribute to vehicle load.
A.2.2 Weight
Vehicle weight acts at the center of gravity of the vehicle with the relationship
of vehicle mass times the acceleration of gravity. At low speeds, the relationship
between vehicle weight and axle loads are given by (Gillespie, 1992):
Wf = W(c/L - (ax /L)(h/L) ) (A-10)
where:
Wf = front axle load
W = vehicle weight
ax = forward acceleration
h = distance to vertical center of gravity position
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L = distance from front to back axle
c = distance from horizontal center of gravity to rear axle
g = acceleration of gravity.
A.2.3 Grade
As a vehicle operates on a grade it must overcome the gravitational forces
pulling the car backwards down the slope plus the force required to propel it forwards.
Vehicle operation against a grade is roughly the normal weight of the vehicle (W) is
increased by a tangent of the horizontal weight component, WsinΥ and vertical weight
component, WcosΥ . Υ is the arc tangent of the slopes rise over run. More simply,
grade resistance force is given by (Gillespie, 1992):
Rg = WG/100 (A-11)
where:
Rg = grade resistance force (lb);
W = gross vehicle weight (lb); and
G = roadway gradient (%) (Pline, 1992).
A.2.4 Aerodynamic Drag
Aerodynamic drag is the longitudinal resistance as a result of the air stream
interacting with the vehicle. It is related to the density of the air, velocity of the air
relative to the car, frontal area of the car, and an aerodynamic drag coefficient. Air
resistance is the frictional force of air passing over the vehicle's surface and the partial
vacuum created behind the vehicle and can be estimated by:
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Ra = 0.5 (2.15ρCDAV2)/g (A-12)
where:
Ra = air resistance force (lb);
ρ = air density (0.002385 lb/ft3 at sea level);
CD = aerodynamic drag coefficient;
A = frontal cross-sectional area (ft2);
V = vehicle speed (mph); and
g = acceleration of gravity (32.2 ft/sec2) (Pline, 1992).
The aerodynamic drag coefficient is usually 0.5 for passenger cars on the road. Newer
vehicles may have a lower drag coefficient as low as 0.3 (ITE, 1994). At low speeds
and for a vehicle starting out from rest, influences of aerodynamic drag may be
negligible.
A.2.5 Curve Resistance
Curve resistance is the force that acts through the front-wheel contact with the
pavement required to deflect a vehicle along a curvilinear path and is represented by:
Rc = 0.5 (2.15V2W)/Gr (A-13)
where:
Rc = curve resistance force (lb);
V = vehicle speed (mph);
W = gross vehicle weight (lb);
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g = acceleration of gravity (32.2 ft/sec2); and
R = radius of curvature (ft) (Pline, 1992).
A.2.6 Rolling Resistance
Rolling resistance is one of the major resistive forces acting against a vehicle. It
is manifested from the time the vehicles begin to turn. Following are the main factors
contributing to rolling resistance:
• tire temperature affecting deflection and energy loss, this diminishes as the vehicle
moves and the temperature in the tire rises;
• tire inflation pressure/load which determines tire elasticity leading to deflection in
the sidewall and contact region;
• the coefficient of surface friction;
• velocity;
• tire wear; and
• tire slip (Gillespie, 1992).
At low speeds, the primary resistive force is rolling resistance rather than
aerodynamic drag. The mathematical representation of rolling resistance is given by:
Rr = (Crs + 2.15CrvV2)W (A-14)
where:
Rr = rolling resistance (lb);
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Crs = a constant (typically 0.012 for passenger cars);
Crv = also a constant (typically 0.65 x 10-6 sec2/ft2 for passenger cars);
V = vehicle speed (mph); and
W = gross vehicle weight (lb) (ITE, 1994).
A.2.7 Road-Load Power
Road-load power is the power required to drive the vehicle on a level road at
constant speed. It is the power required to overcome all the resistive forces to the
vehicle’s movement including rolling resistance and aerodynamic drag. Rolling
resistance is caused by the friction between the tires and the roadway and aerodynamic
drag is wind resistance. An approximate relationship is given by (Heywood, 1988):
Pr = (CRMvg + ½ñaCDAvSv
2)Sv (A-15)
where:
Pr = road-load power;
CR = coefficient of rolling resistance (0.012<Cr<0.015)3;
Mv = mass of vehicle;
g = acceleration due to gravity;
ña = ambient air density;
CD = drag coefficient (for passenger cars 0.3<CD<0.5)3;
Av = vehicle’s frontal area;
Sv = speed of vehicle. (Heywood, 1988)
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Both aerodynamic drag and rolling resistance add to the power required to
keep the vehicle moving. Rolling resistance remains fairly constant while,
aerodynamic drag increases exponentially with speed (Gillespie, 1992).
A.2.8 Inertial Resistance
Inertial resistance is the force that a vehicle must overcome to change speed
and is given by:
Ri = Wa/g (A-16)
where:
Ri = inertial resistance force (lb);
W = gross vehicle weight (lb);
a = acceleration rate (ft/sec2); and
g = acceleration of gravity (32.2 ft/sec2) (ITE, 1994).
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APPENDIX B
RESEARCH RESULTS This section details the results of the regression tree analysis from Chapter 6.
B.1 Passenger Cars
The following sections describe the regression tree models developed using data for
passenger vehicles. Passenger vehicles are defined as non-commercial vans, buses, and
trucks. They include passenger vans, cars, light duty trucks (< 6 wheels), and sport utility
vehicles.
B.1.1 Passenger Cars Percent Activity >= 6.0 mph/s (ACC.6)
The following sections present the regression tree models for the response variable
of percent activity where acceleration is greater than or equal to 6.0 mph/s. Data are
presented for each data partion.
B.1.1.1 Activity for Queue Vehicles From Stopping Point to 200 Feet
Downstream ACCEL Model The final model for the stopping point to 200 feet
downstream yielded a “tree” with a residual mean deviance (RMD) of 57.27. Results are
shown in Table B-1 and Figure B-1. As noted, the independent model variables are queue
position, roadway grade, and downstream per lane volume.
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Table: B-1: Trimmed ACC6 Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = ACC6 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + LOCATION + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = a6accel.snip3, nodes = 5) Variables actually used in tree construction: [1] "QUEUE" "GRADE" "DOWNSTREAM" Number of terminal nodes: 5 Residual mean deviance: 57.27 = 22560 / 394 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -17.5 -5.328 -1.507 2.353e-015 0.983 44.66
Figure B-1: Trimmed ACC6 Model for Queued Passenger Cars From
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Stopping Point to 200 Feet Downstream
B.1.1.2 Activity for Queue Vehicles From 200 to 400 Feet Downstream of
Initial Stopping Point (ACCELPLUS200) The next data partion is activity that
encompassed a distance from 200 feet downstream of the queued vehicle's initial queuing
point to a point 400 feet from the initial queuing point. The final regression tree model results
are presented in Table B-2 and Figure B-2. As shown for the response variable of percent
activity >= 6.0 mph/s, the significant variable is downstream per lane volume. The residual
mean deviance for the final model was 12.72, indicating a fairly "good" model fit.
Table: B-2: Trimmed ACC6 Model Results for Queued Passenger Cars From 200 Feet from Stopping Point to 400 Feet Downstream Regression tree: Tree(formula = ACC6 ~ QUEUE + DOWNSTREAM + PerTrucks + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsAccelP200Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 2) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 13.08 = 2968 / 227 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -1.398 -1.398 -0.11 -6.991e-016 -0.11 31.92
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Figure B-2: Trimmed ACC6 Model for Queued Passenger Cars 200 Feet From Stopping Point to 400 Feet Downstream
B.1.1.3 Activity for Queue Vehicles From 400 to 600 Feet Downstream of
Initial Stopping Point (ACCELPLUS400) The next data partion was activity from 400
feet downstream of the queued vehicle's initial queuing point to a point 600 feet from the
initial queuing point. The final regression tree model results are presented in Table B-3 and
Figure B-3. As shown the only model variables is downstream per lane volume and distance
to the nearest downstream signalized intersection.
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224
Table: B-3: Trimmed ACC6 Model Results for Queued Passenger Cars From 400 Feet from Stopping Point to 600 Feet Downstream Regression tree: tree(formula = ACC6 ~ QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsAccelP400Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 2) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 10.42 = 885.3 / 85 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -3.124 -0.3162 -0.3162 4.824e-016 -0.3162 21.87
Figure B-3: Trimmed ACC6 Model for Queued Passenger Cars 400 Feet
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From Stopping Point to 600 Feet Downstream B.1.1.4 Activity for Queue Vehicles From 600 to 1,000 Feet Downstream of
Initial Stopping Point (ACCELPLUS600 and ACCELPLUS800) The next data partion
was activity that encompassed a distances from a point 600 feet downstream of the queued
vehicle's initial queuing point to a point 1000 feet from the initial queuing point. No activity
was observed for these datapoints where acceleration >= 6.0 mph/s
B.1.1.5 Activity for Queue Vehicles From Initial Stopping Point Upstream
200 Feet (DECEL) After data collected from the stopping point forward for queue
vehicles were analyzed for various distances, deceleration activity that occurred prior to the
vehicle's queuing position was analyzed. The first deceleration data partion was activity that
encompassed a distance of 200 feet upstream of the vehicle's queuing position up to the
queued vehicle's initial queuing point. The final regression tree model results are presented in
Table B-4 and Figure B-4. As shown, the only significant variable was the downstream per
lane volume.
Table B-4: Trimmed ACC6 Model for Queued Passenger Cars 200 Feet Before up to the Stopping Point Regression tree: Tree(formula = ACC6 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsDecelClean, na.action = na.omit, mincut = 5, Minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 2) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 0.03694 = 11.64 / 315
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Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -0.057 4.337e-17 4.33e-17 2.07e-017 4.337e-17 3.383
Figure B-4: Trimmed ACC6 Model for Queued Passenger Cars 200 Feet Before up to Stopping Point
B.1.1.6 Activity for Queue Vehicles From 200 Feet Upstream of the Initial
Stopping Point to a 400 Feet Upstream (DECELNEG200) No model is presented for
percent of activity greater or equal to 6.0 mph/s since no activity in this acceleration range
was noted in any of the datasets.
227
B.1.1.7 Activity for Queue Vehicles From 400 Feet Upstream of the Initial
Stopping Point to a 600 Feet Upstream (DECELNEG400) No model is presented for
percent of activity greater or equal to 6.0 mph/s since no activity in this acceleration range
was noted in any of the datasets.
B.1.1.8 "THRU" Vehicles at All locations Vehicles not stopped at the
intersection were analyzed separately from vehicles which stopped at the intersection, since
their vehicle activity traces are expected to be somewhat different in the vicinity of a
signalized intersection than midblock. Data were partitioned into 200-foot segments as for
queued vehicles. However all data partions were included in a single analysis for "THRU"
vehicles and distance was included as a variables to test whether the location from the
stopline affects vehicle activity. The variables downstream and upstream volume were
converted to a field for per lane volume on the link in question since data before and after the
stopbar were included. Including midblock data the distances ranged from 2,000 feet before
the intersection stopbar to 1,200 past the intersection stopbar. The single relevant predictor
variable is posted speed limit. added upper accel and decel. As noted the model has a fairly
good fit with an RMD of only 1.0. Results are provided in Table B-5 and Figure B-5.
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Table B-5: Trimmed ACC6 Model for "THRU" Vehicles For All Distances Regression tree: snip.tree(tree = a6thru.snip5, nodes = 3) tree(formula = ACC6 ~ Distance + VOLUME + LINKDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1 ) Variables actually used in tree construction: [1] "SPEEDLIMIT" Number of terminal nodes: 2 Residual mean deviance: 1.009 = 602.1 / 597 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -1.041 -0.1209 -0.1209 -3.149e-016 -0.1209 11.45
Figure B-5: Trimmed ACC6 Model for "THRU" Vehicles For All Distances
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B.1.2 Percent Activity >= 3.0 mph/s (ACC3)
The following sections describe the final regression tree models for each distance
partion using the percent of activity >= 3.0 mph/s as the response variable.
B.1.2.1 Activity for Queue Vehicles From Stopping Point to 200 Feet
Downstream (ACCEL) This model provides results for passenger cars that were stopped
at the traffic signal and includes data for a distance of 200 feet downstream of the vehicle's
initial queuing position. The response variable is percent of vehicle activity for the indicated
position where acceleration equal or exceed 3.0 mph/s. Table B-6 provides model results
and Figure B-6 shows the final regression tree model. In the final model, queue position, and
grade were the most significant variables. The final model had a rather poor fit with a RMD
of 364.1.
Table: B-6: Trimmed ACC3 Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = ACC3 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + WIDTH + LOCATION + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = a3accel.snip3, nodes = 3) Variables actually used in tree construction: [1] "QUEUE" "GRADE" Number of terminal nodes: 3 Residual mean deviance: 364.1 = 144200 / 396 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -55.08 -11.49 2.172 -3.651e-016 13.12 46.45
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Figure B-6: Trimmed ACC3 Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream B.1.2.2 Activity for Queue Vehicles From 200 to 400 Feet Downstream of Initial
Stopping Point (ACCELPLUS200) The next data partion was activity that encompassed
from 200 feet downstream of the queued vehicle's initial queuing point to a point 400 feet
from the initial queuing point. The final regression tree model results are presented in Table
B-7 and Figure B-7. As shown the significant variables include roadway grade, and queue
position. Again, the model fit was rather poor with a residual mean deviance over 500.
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Table: B-7: Trimmed ACC3 Model Results for Queued Passenger Cars From 200 Feet from Stopping Point to 400 Feet Downstream Regression tree: tree(formula = ACC3 ~ QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsAccelP200Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = c(7, 6, 5)) Variables actually used in tree construction: [1] "QUEUE" "GRADE" Number of terminal nodes: 4 Residual mean deviance: 561.7 = 126400 / 225 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -57.97 -14.59 –6.717 7.354e-015 14.81 85.4
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Figure B-7: Trimmed ACC3 Model for Queued Passenger Cars 200 Feet From Stopping Point to 400 Feet Downstream
B.1.2.3 Activity for Queue Vehicles From 400 Feet Downstream of the
Initial Stopping Point to a 600 Feet Downstream (ACCELPLUS400) The next
acceleration data partion was activity from a distance of 400 feet downstream of the
vehicle's queuing position to a point 600 feet downstream from the queued vehicle's initial
queuing point. The final regression tree model results are presented in Table B-8 and Figure
B-8. As shown, the predictor variables from the model are queue position and downstream
per lane volume. As for the other data partions, model fit only gave an RMD of 245.4.
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Table B-8: Trimmed ACC3 Model for Queued Passenger Cars 400 Feet to 600 Feet Downstream of the Initial Stopping Point for Queued Vehicles Regression tree: tree(formula = ACC3 ~ QUEUE + UPSTREAM + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsAccelP400Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = c(4, 5)) Variables actually used in tree construction: [1] "QUEUE" "DOWNSTREAM" Number of terminal nodes: 3 Residual mean deviance: 245.4 = 20610 / 84 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -28.59 -10.05 -2.838 7.708e-016 4.731 48.07
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Figure B-8: Trimmed ACC3 Model for Queued Passenger Cars 400 Feet to 600 Feet Downstream of the Initial Stopping Point
B.1.2.4 Activity for Queue Vehicles From 600 to 1000 Feet Downstream of
Initial Stopping Point (ACCELPLUS600 and ACCELPLUS800) The next data partion
was activity that encompassed a distances from a point 600 feet downstream of the queued
vehicle's initial queuing point to a point 1000 feet from the initial queuing point. Data were
initially divided by 200 feet increments so this analysis combined all data partions greater
than and including 600 feet from the initial queuing point. This was done since less data were
235
collected at increasing distances from the data collection location. Additionally, at some
point along a signalized link, it is expected that vehicle activity will become more
homogenous. The distance variable was included to test whether distance was in important
factor in influencing vehicle activity. The final regression tree model results are presented in
Table B-9 and Figure B-9. As shown the only significant variable is downstream per lane
volume. The model had an acceptable fit with RMD of 44.27.
Table: B-9: Trimmed ACC3 Model Results for Queued Passenger Cars From 600 Feet from Stopping Point to 1,000 Feet Downstream Regression tree: Tree(formula = ACC3 ~ Distance + QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsAccelP600Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 44.27 = 973.9 / 22 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -7.008 -2.136 -0.512 2.961e-016 -0.512 17.98
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Figure B-9: Trimmed ACC3 Model for Queued Passenger Cars 600 Feet From Stopping Point to 1,000 Feet Downstream
B.1.2.5 Activity for Queue Vehicles From Initial Stopping Point Upstream
200 Feet (DECEL) Deceleration activity for a distance from a point 200 feet upstream of
the vehicle's queuing position up to from queued vehicle's initial queuing point was analyzed
for percent activity with acceleration greater than 3.0 mph/s. The final regression tree model
results are presented in Table B-10 and Figure B-10. As shown, the only significant variable
was the upstream per lane volume.
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Table B-10: Trimmed ACC3 Model for Queued Passenger Cars 200 Feet Before up to Stopping Point Regression tree: tree(formula = ACC3 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsDecelClean, na.action=na.omit, mincut=5, minsize=10, mindev = 0.1) snip.tree(tree = a3decel.snip2, nodes = 3) Variables actually used in tree construction: [1] "UPSTREAM" Number of terminal nodes: 2 Residual mean deviance: 15.5 = 4883 / 315 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -4.473 -0.6188 -0.6188 4.304e-015 -0.6188 49.37
Figure B-10: Trimmed ACC3 Model for Queued Passenger Cars 200 Feet Before up to Stopping Point
238
B.1.2.6 Activity for Queue Vehicles From 200 Feet Upstream of the Initial
Stopping Point to a 400 Feet Upstream (DECELNEG200) The second deceleration
data partion was activity that included from 200 feet to 400 feet upstream of the vehicle's
queuing position. The final regression tree model results are presented in Table B-11 and
Figure B-11. As shown, the only significant variables are roadway grade and queue
position.
Table B-11: Trimmed ACC3 Model for Queued Passenger Cars 400 Feet Before up to 200 Feet Behind Stopping Point Regression tree:tree(formula = ACC3 ~ QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsDecelPlus200Clean, na.action = na.omit, mincut = 3, minsize = 6, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNSTREAM" "QUEUE" Number of terminal nodes: 3 Residual mean deviance: 1.88 = 139.2 / 74 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -8.58 -5.24e-018 -5.24e-018 -4.6e-017 -5.2e-018 8.08
239
Figure B-11: Trimmed ACC3 Model for Queued Passenger Cars 400 Feet Before up to 200 Feet Behind Stopping Point
B.1.2.7 Activity for Queue Vehicles From 400 Feet Upstream of the Initial
Stopping Point to a 600 Feet Upstream (DECELNEG400) No model is presented for
percent of activity greater or equal to 3.0 mph/s since no activity in this acceleration range
was noted in any of the datasets for this distance range.
B.1.2.8 "THRU" Vehicles at All locations Vehicles not stopped at the
intersection were analyzed separately since their vehicle activity traces are expected to
240
somewhat different in the vicinity to the signalized intersection. Data were partitioned into
200-foot segments as for queued vehicles. However all data partions were included in a
single analysis for "THRU" vehicles and distance was included as a variables to test whether
the location from the stopline affects vehicle activity. Including midblock data the distances
ranged from 2,000 feet before the intersection stopbar to 1,200 past the intersection
stopbar. The most relevant predictor variables are link distance, posted link speed limit, and
link per lane volume . Results are provided in Table B-12 and Figure B-12, which show link
distance where data collection occurred, link posted speed limit, and the per lane volume of
the link where data collection took place to be final model variables.
Table B-12: Trimmed ACC3 Model for "THRU" Vehicles for All Locations Regression tree: tree(formula = ACC3 ~ Distance + VOLUME + PER.TRUCKS + LINKDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = a3thru.snip3, nodes = 4) Variables actually used in tree construction: [1] "LINKDIST" "SPEEDLIMIT" "VOLUME" Number of terminal nodes: 4 Residual mean deviance: 82.12 = 47220 / 575 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -20.04 -3.785 -1.355 6.895e-016 0.002061 94.95
241
Figure B-12: Trimmed ACC3 Model for "THRU" Vehicles for All Locations B.1.3 Percent Activity Where Acceleration <= -2.0 mph/s (DECEL2)
The following sections describe the final regression tree models for each distance
partion using the percent of activity where deceleration <= -2.0 mph/s.
B.1.3.1 Activity for Queue Vehicles From Stopping Point to 200 Feet
Downstream (ACCEL) This model provides results for passenger cars that were stopped
at the traffic signal and includes data for a distance of 200 feet downstream of the vehicle's
initial queuing position. The response variable is percent of vehicle activity for the indicated
242
position where deceleration was less than or equal to -2.0 mph/s. In Table B-13 and Figure
B-13, the final regression tree model variable, downstream per lane volume, is presented.
Table: B-13: Trimmed DECEL2 Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = Decel2 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + WIDTH + LOCATION + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 2) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 89.71 = 35620 / 397 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -3.861 -3.861 -3.861 4.761e-015 -0.4611 81.84
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Figure B-13: Trimmed DECEL2 Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream
B.1.3.2 Activity for Queue Vehicles From 200 to 400 Feet Downstream of
Initial Stopping Point (ACCELPLUS200) The next data partion was activity from 200
feet downstream of the queued vehicle's initial queuing point to 400 feet from the initial
queuing point. The final regression tree model results are presented in Table B-14 and
Figure B-14. As shown the final model variable is roadway grade.
Table: B-14: Trimmed DECEL2 Model Results for Queued Passenger Cars From 200 Feet from Stopping Point to 400 Feet Downstream Regression tree: tree(formula = Decel2 ~ QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsAccelP200Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = c(2, 3)) Variables actually used in tree construction: [1] "GRADE" Number of terminal nodes: 2 Residual mean deviance: 45.17 = 10250 / 227 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -5.731 -1.834 -1.834 5.162e-015 -1.834 31.49
244
Figure B-14: Trimmed DECEL2 Model for Queued Passenger Cars 200 Feet From Stopping Point to 400 Feet Downstream
B.1.3.3 Activity for Queue Vehicles From 400 Feet Downstream of the
Initial Stopping Point to a 600 Feet Downstream (ACCELPLUS400) Vehicle activity
for the section 400 feet upstream of the vehicle's queuing position to point 600 feet
downstream from the queued vehicle's initial queuing point is presented here. The final
regression tree model results are in Table B-15 and Figure B-15. Downstream per lane
volume, distance to the nearest downstream signalized intersection and downstream per lane
volume are the final independent model variables.
245
Table B-15: Trimmed DECEL2 Model for Queued Passenger Cars 400 Feet to 600 Feet Downstream of the Initial Stopping Point for Queued Vehicles Regression tree: tree(formula = Decel2 ~ QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsAccelP400Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = d2accel400.snip2, nodes = 4) Variables actually used in tree construction: [1] "DOWNSTREAM" "DOWNDIST" Number of terminal nodes: 3 Residual mean deviance: 193.3 = 16240 / 84 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -16.07 -3.067 -3.067 1.582e-016 -3.067 59.3
Figure B-15: Trimmed DECEL2 Model for Queued Passenger Cars 400
246
Feet to 600 Feet Downstream of the Initial Stopping Point
B.1.3.4 Activity for Queue Vehicles From 600 to 1000 Feet Downstream of
Initial Stopping Point (ACCELPLUS600) The next data partion was activity including
distances from a point 600 feet downstream of the queued vehicle's initial queuing point to a
point 1000 feet from the initial queuing point. Data were initially divided by 200 feet
increments so this analysis combined all data partions greater than and including 600 feet
from the initial queuing point. This was done since fewer data were collected at increasing
distances from the data collection location. Additionally, at some point along a signalized
link, it is expected that vehicle activity will become more homogenous. The distance variable
was included to test whether distance was in important factor in influencing vehicle activity.
The final regression tree model results are presented in Table B-16 and Figure B-16.
Downstream per lane volume is the only predictor variable for the response variable
DECEL2.
Table: B-16: Trimmed DECEL2 Model Results for Queued Passenger Cars From 600 Feet from Stopping Point to 1000 Feet Downstream Regression tree: tree(formula = Decel2 ~ Distance + QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsAccelP600Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2
247
Residual mean deviance: 53.49 = 1177 / 22 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -8.885 -1.249 -1.249 -4.256e-016 -1.249 24.44
Figure B-16: Trimmed DECEL2 Model for Queued Passenger Cars 600 Feet From Stopping Point to 1000 Feet Downstream
B.1.3.5 Activity for Queue Vehicles From Initial Stopping Point Upstream
200 Feet (DECEL) After data collected from the stopping point forward for queue
vehicles were analyzed for various distances, deceleration activity that occurred previous to
248
the vehicle's queuing position was analyzed. The first deceleration data partion was activity
that covered a distance from the initial queuing point upstream 200 feet. The final regression
tree model results are presented in Table B-17 and Figure B-17. As shown, significant
independent variables were the distance to the nearest upstream signalized intersection and
queue position with a RMD of 443.6 which is rather poor but represented the best model
that could be derived.
Table B-17: Trimmed DECEL2 Model for Queued Passenger Cars 200 Feet Before up to Stopping Point Regression tree: tree(formula = Decel2 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + WIDTH, data = CarsDecelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = d2decel.snip2, nodes = 4) Variables actually used in tree construction: [1] "UPDIST" "QUEUE" Number of terminal nodes: 4 Residual mean deviance: 443.6 = 138800 / 313 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -70.1 -7.727 4.173 8.069e-016 17.4 41.44
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Figure B-17: Trimmed DECEL2 Model for Queued Passenger Cars 200 Feet Before up to Stopping Point
B.1.3.6 Activity for Queue Vehicles From 200 Feet Upstream of the Initial
Stopping Point to 400 Feet Upstream (DECELNEG200) Data for activity that fell in
the distance range from 200 feet to 400 feet upstream of the point where the vehicle stopped
in queue are presented below. The final regression tree model results are presented in Table
B-18 and Figure B-18. As shown, the only significant variables are roadway grade and
upstream per lane volume. The RMD is over 1000, indicating a rather "poor" model fit.
Table B-18: Trimmed DECEL2 Model for Queued Passenger Cars 400 Feet
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Before up to 200 Feet Behind Stopping Point Regression tree: tree(formula = Decel2 ~ QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsDecelPlus200Clean, na.action = na.omit, mincut = 3, minsize = 6, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNSTREAM" "GRADE" Number of terminal nodes: 4 Residual mean deviance: 975 = 71170 / 73 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -66.73 -23.2 -0.06605 4.614e-015 33.26 47.11
Figure B-18: Trimmed DECEL2 Model for Queued Passenger Cars 400 Feet Before up to 200 Feet Behind Stopping Point
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B.1.3.7 Activity for Queue Vehicles From 400 Feet Upstream of the Initial
Stopping Point to a 600 Feet Upstream (DECELNEG400) The next deceleration data
partition was activity that fell within 400 to 600 feet upstream of the vehicle's queuing
position. The final regression tree model results are presented in Table B-19 and Figure B-
19. As shown, the only significant variable is upstream per lane volume.
Table B-19: Trimmed DECEL2 Model for Queued Passenger Cars 400 Feet to 600 Feet Upstream of the Initial Stopping Point for Queued Vehicles Regression tree: tree(formula = Decel2 ~ QUEUE + DOWNSTREAM + PER.TRUCKS, data = CarsDecelPlus400UpClean, na.action = na.omit, mincut = 3, minsize = 6, mindev= 0.1) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 406.4 = 4064 / 10 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -25.69 -5.553 -5.553 -1.036e-015 2.427 40.97
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Figure B-19: Trimmed DECEL2 Model for Queued Passenger Cars 400 Feet to 600 Feet Upstream of the Initial Stopping Point
B.1.3.8 "THRU" Vehicles at All locations Vehicles not stopped at the
intersection were analyzed separately from queued vehicles, since their vehicle activity traces
are expected to somewhat different in the vicinity to the signalized intersection. Data were
partitioned into 200-foot segments as for queued vehicles. However all data partions were
included in a single analysis for "THRU" vehicles and distance was included as a variables to
test whether the location from the stopline affects vehicle activity. Including midblock data,
the distances ranged from 2,000 feet before the intersection stopbar to 1,200 past the
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intersection stopbar. The most relevant predictor variable is link volume, which is shown in
Table B-20 and Figure B-20.
Table B-20: Trimmed DECEL2 Model for "THRU" Vehicles for All Locations Regression tree: tree(formula = Decel2 ~ VOLUME + PER.TRUCKS + UPDIST + LINKDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = c(2, 3)) Variables actually used in tree construction: [1] "VOLUME" Number of terminal nodes: 2 Residual mean deviance: 266.4 = 153700 / 577 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -24.66 -8.412 -8.412 -7.219e-014 4.078 91.58
Figure B-20: Trimmed DECEL2 Model for "THRU" Vehicles for All Locations
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B.1.4 Average Vehicle Speed
The following sections describe the final regression tree models for each distance
partion for the response variable average vehicle speed by dataset.
B.1.4.1 Activity for Queue Vehicles From Stopping Point to 200 Feet
Downstream (ACCEL) This model provides results for passenger cars that were
stopped at the traffic signal and includes data for a distance of 200 feet downstream of the
vehicle's initial queuing position. The response variable is average speed for the indicated
position in mph. Table A2-21 provides model results and Figure A2-21 shows the final
regression tree model. The predictor variable in the final model is queue position with a
residual mean deviance of 15.95.
Table: B-21: Trimmed AVG_SPD Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = SPEED ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + WIDTH + LOCATION + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = spdaccel.snip3, nodes = c(3, 2)) Variables actually used in tree construction: [1] "QUEUE" Number of terminal nodes: 2 Residual mean deviance: 15.95 = 6331 / 397 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -14.02 -2.197 -0.6202 -4.661e-015 2.053 13.63
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Figure B-21: Trimmed AVG_SPD Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream
B.1.4.2 Activity for Queue Vehicles From 200 to 400 Feet Downstream of
Initial Stopping Point (ACCELPLUS200) The next data partion was activity from 200
feet downstream of the queued vehicle's initial queuing point to a point 400 feet downstream
from the initial queuing point. The final regression tree model results are presented in Table
B-22 and Figure B-22. As shown the significant variables include roadway grade and queue
position.
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Table: B-22: Trimmed AVG_SPD Model Results for Queued Passenger Cars From 200 Feet from Stopping Point to 400 Feet Downstream Regression tree: tree(formula = SPEED ~ QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsAccelP200Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1)snip.tree(tree = last.tree, nodes snip.tree(tree = spdaccel200.snip3, nodes = 4) Variables actually used in tree construction: [1] "QUEUE" "GRADE" Number of terminal nodes: 3 Residual mean deviance: 18.34 = 4146 / 226 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -18.74 -2.441 0.3595 2.746e-015 2.421 13.93
Figure B-22: Trimmed AVG_SPD Model for Queued Passenger Cars 200 Feet From Stopping Point to 400 Feet Downstream
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B.1.4.3 Activity for Queue Vehicles From 400 Feet Downstream of the
Initial Stopping Point to a 600 Feet Downstream (ACCELPLUS400) The next
deceleration data partion was activity from 400 feet downstream of the vehicle's queuing
position to a point 600 feet downstream from the queued vehicle's initial queuing point. The
final regression tree model results are presented in Table B-23 and Figure B-23. As shown,
the only significant variables are distance to nearest downstream signalized intersection and
queue position.
Table B-23: Trimmed Average Speed Model for Queued Passenger Cars 400 Feet to 600 Feet Downstream of the Initial Stopping Point Regression tree: tree(formula = SPEED ~ QUEUE + UPSTREAM + DOWNSTREAM + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsAccelP400Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = spda400.snip4, nodes = 7) Variables actually used in tree construction: [1] "DOWNDIST" "QUEUE" Number of terminal nodes: 3 Residual mean deviance: 36.01 = 3313 / 92 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -23.88 -3.485 0.5151 1.518e-014 4.053 13.22
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Figure B-23: Trimmed Average Speed Model for Queued Passenger Cars 400 Feet to 600 Feet Downstream of the Initial Stopping Point
B.1.4.4 Activity for Queue Vehicles From 600 to 1000 Feet Downstream of
Initial Stopping Point (ACCELPLUS600) The next data partion was activity for a
distance 600 feet downstream of the queued vehicle's initial queuing point to 1000 feet from
the initial queuing point. Data were initially divided by 200 feet increments so this analysis
combined all data partions greater than and including 600 feet from the initial queuing point.
This was done since fewer data were collected at increasing distances from the data
collection location. Additionally, at some point along a signalized link, it is expected that
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vehicle activity will become more homogenous. The distance variable was included to test
whether distance was in important factor in influencing vehicle activity. The final regression
tree model results are presented in Table B-24 and Figure B-24. As shown the significant
variable is posted link speed limit.
Table: B-24: Trimmed AVG_SPD Model Results for Queued Passenger Cars From 600 Feet from Stopping Point to 1000 Feet Downstream Regression tree: tree(formula = SPEED ~ Distance + QUEUE + DOWNSTREAM + PerTrucks + GRADE + SPEEDLIMIT + NO.LANES + DOWNDIST + LOCATION + WIDTH, data = CarsAccelP600Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 3) Variables actually used in tree construction: [1] "SPEEDLIMIT" Number of terminal nodes: 2 Residual mean deviance: 17.49 = 384.9 / 22 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -10.71 -2.487 -0.6702 1.48e-016 1.871 8.388
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Figure B-24: Trimmed AVG_SPD Model for Queued Passenger Cars 600 Feet From Stopping Point to 1000 Feet Downstream
B.1.4.5 Activity for Queue Vehicles From Initial Stopping Point Upstream
200 Feet (DECEL) After data collected from the stopping point forward for queue
vehicles were analyzed for various distances, deceleration activity that occurred previous to
the vehicle's queuing position was analyzed. The first deceleration data partion was activity
from the initial queue position upstream 200 feet upstream. The final regression tree model
results are presented in Table B-25 and Figure B-25. As shown, the only significant
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variables were the upstream per lane volume and distance to the nearest upstream-signalized
intersection.
Table B-25: Trimmed AVG_SPD Model for Queued Passenger Cars 200 Feet Before up to Stopping Point Regression tree: tree(formula = SPEED ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + GRADE, data = CarsDecelClean, na.action = na.omit, mincut = 5,minsize = 10, mindev = 0.1) snip.tree(tree = spddecel.snip2, nodes = c(13, 12)) Variables actually used in tree construction: [1] "UPDIST" "UPSTREAM" Number of terminal nodes: 4 Residual mean deviance: 30.72 = 9614 / 313 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -16.68 -3.481 -0.09889 -3.53e-016 3.207 21.97
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Figure B-25: Trimmed AVG_SPD Model for Queued Passenger Cars 200 Feet Before up to Stopping Point
B.1.4.6 Activity for Queue Vehicles From 200 Feet Upstream of the Initial
Stopping Point to a 400 Feet Upstream (DECELNEG200) Presented in this section
are regression tree model results for average speed as the dependent variable for data
included in a 200-foot segment from 200 to 400 feet upstream of the "tracked" vehicle's
initial queuing point. The final regression tree model results are presented in Table B-26 and
Figure B-26. As shown, the resulting predictor variables are roadway grade and queue
position.
Table B-26: Trimmed AVG_SPD Model for Queued Passenger Cars 400 Feet Before up to 200 Feet Behind Stopping Point Regression tree: tree(formula = SPEED ~ QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + NO.LANES + SPEEDLIMIT + WIDTH + LOCATION, data = CarsDecelPlus200Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "QUEUE" "GRADE" Number of terminal nodes: 4 Residual mean deviance: 17.09 = 1248 / 73 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -10.15 -2.347 -0.05 2.122e-015 2.253 14.16
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Figure B-26: Trimmed AVG_SPD Model for Queued Passenger Cars 400 Feet Before up to 200 Feet Behind Stopping Point
B.1.4.7 Activity for Queue Vehicles From 400 Feet Upstream of the Initial
Stopping Point to a 600 Feet Upstream (DECELNEG400) The next deceleration data
partion was activity that encompassed a distance of 400 feet upstream of the vehicle's
queuing position to a point 600 feet upstream from the queued vehicle's initial queuing point.
The final regression tree model results are presented in Table B-27 and Figure B-27. As
shown, the only significant variables upstream per lane volume with a RMD of only 26.02.
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Table B-27: Trimmed AVG_SPD Model for Queued Passenger Cars 400 Feet to 600 Feet Upstream of the Initial Stopping Point for Queued Vehicles Regression tree: tree(formula = SPEED ~ QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE, data = CarsDecelPlus400UpClean, na.action = na.omit, mincut = 3, minsize = 6, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 19.51 = 195.1 / 10 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -9.633 -1.767 0.95 -2.961e-015 2.533 5.133
Figure B-27: Trimmed AVG_SPD Model for Queued Passenger Cars 400 Feet to 600 Feet Upstream of the Initial Stopping Point for Queued Vehicles
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B.1.4.8 "THRU" Vehicles at All locations Vehicles not stopped at the
intersection were analyzed separately since their vehicle activity traces are expected to
somewhat different in the vicinity to the signalized intersection. Data were partitioned into
200-foot segments as for queued vehicles. However all data partions were included in a
single analysis for "THRU" vehicles and distance was included as a variables to test whether
the location from the stopline affects vehicle activity. Including midblock data the distances
ranged from 2,000 feet before the intersection stopbar to 1,200 past the intersection
stopbar. The most relevant predictor variables, shown in Table B-28 and Figure B-28 are
posted speed limit for the link, per lane volume, and link length.
Table B-28: Trimmed AVG_SPD Model for "THRU" Vehicles for All Locations Regression tree: tree(formula = SPEED ~ Distance + VOLUME + PER.TRUCKS + LINKDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1 ) snip.tree(tree = spdthru.snip2, nodes = 6) Variables actually used in tree construction: [1] "SPEEDLIMIT" "VOLUME" "Distance" Number of terminal nodes: 4 Residual mean deviance: 64.91 = 37330 / 575 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -26.36 -3.714 0.2513 -1.27e-014 4.295 86.84
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Figure B-28: Trimmed AVG_SPD Model for "THRU" Vehicles for All Locations
B.1.5 Inertial Power Surrogate >= 120 mph2/s (IPS120) The following
sections describe the final regression tree models for each distance partion for the inertial
power surrogate greater than or equal to 120 mph2/s. Inertial power surrogate is
approximated by the product of velocity and acceleration.
B.1.5.1 Activity for Queue Vehicles From Stopping Point to 200 Feet
Downstream (ACCEL)
This model provides results for passenger cars that were stopped at the traffic signal
and includes data for a distance of 200 feet downstream of the vehicle's initial queuing
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position. The response variable is inertial power surrogate (the product of speed and
acceleration) that equals or exceeds 120 mph/s2 for the indicated position. Table B-29
provides model results and Figure B-29 shows the final regression tree model. Final
variables include queue position and roadway grade.
Table: B-29: Trimmed IPS120 Model Results for Queued Passenger Cars From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = PKE120 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + WIDTH + NO.LANES + SPEEDLIMIT, data = CarsAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = c(3, 4)) Variables actually used in tree construction: [1] "QUEUE" "GRADE" Number of terminal nodes: 3 Residual mean deviance: 62.33 = 24680 / 396 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -12.1 -1.774 -1.774 2.435e-015 -1.774 71.22
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Figure B-29: Trimmed IPS120 Model for Queued Passenger Cars From Stopping Point to 200 Feet Downstream
B.1.5.2 Activity for Queue Vehicles From 200 to 400 Feet Downstream of
Initial Stopping Point (ACCELPLUS200) The next data partion was activity from 200
feet to 400 feet downstream of the "tracked" vehicle's initial queuing point at the intersection.
The final regression tree model results are presented in Table B-30 and Figure B-30. As
shown the significant variables include roadway grade and queue position.
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Table: B-30: Trimmed IPS120 Model Results for Queued Passenger Cars From 200 Feet from Stopping Point to 400 Feet Downstream Regression tree: tree(formula = PKE120 ~ QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = CarsAccelP200Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = c(3, 4)) Variables actually used in tree construction: [1] "GRADE" "QUEUE" Number of terminal nodes: 3 Residual mean deviance: 276 = 62390 / 226 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -21.47 -5.123 -5.123 4.206e-015 -3.287 78.52
Figure B-30: Trimmed IPS120 Model for Queued Passenger Cars 200 Feet From Stopping Point to 400 Feet Downstream
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B.1.5.3 Activity for Queue Vehicles From 400 Feet Downstream of the Initial
Stopping Point to a 600 Feet Downstream (ACCELPLUS400) The next data partition
was activity that encompassed a distance of 400 feet downstream of the vehicle's queuing
position to a point 600 feet downstream. The final regression tree model results are
presented in Table B-31 and Figure B-31. As shown, the only significant variables are
queue position and percent trucks.
Table B-31: Trimmed IPS120 Model for Queued Passenger Cars 400 Feet to 600 Feet Downstream of the Initial Stopping Point for Queued Vehicles Regression tree: tree(formula = PKE120 ~ QUEUE + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsAccelP400Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = pkeaccel400.snip2, nodes = 4) Variables actually used in tree construction: [1] "QUEUE" "PerTrucks" Number of terminal nodes: 3 Residual mean deviance: 213.8 = 17960 / 84 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -32.49 -9.971 -0.2389 4.769e-016 -0.2389 67.5
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Figure B-31: Trimmed IPS120 Model for Queued Passenger Cars 400 Feet to 600 Feet Downstream of the Initial Stopping Point
B.1.5.4 Activity for Queue Vehicles From 600 to 1000 Feet Downstream of
Initial Stopping Point (ACCELPLUS600 The next data partion was activity that
encompassed a distances from a point 600 feet downstream of the queued vehicle's initial
queuing point to a point 1000 feet from the initial queuing point. Data were initially divided
by 200 feet increments so this analysis combined all data partions greater than and including
600 feet from the initial queuing point. This was done since fewer data were collected at
increasing distances from the data collection location. Additionally, at some point along a
signalized link, it is expected that vehicle activity will become more homogenous. The
272
distance variable was included to test whether distance was in important factor in influencing
vehicle activity. The final regression tree model results are presented in Table B-32 and
Figure B-32. As shown the only significant variables roadway grade.
Table: B-32: Trimmed IPS120 Model Results for Queued Passenger Cars From 600 Feet from Stopping Point to 1000 Feet Downstream Regression tree: tree(formula = PKE120 ~ QUEUE + Distance + DOWNSTREAM + PerTrucks + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsAccelP600Clean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 3) Variables actually used in tree construction: [1] "GRADE" Number of terminal nodes: 2 Residual mean deviance: 90.55 = 1992 / 22 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -15.67 -1.999 -1.999 -1.573e-016 -0.07944 20.03
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Figure B-32: Trimmed IPS120 Model for Queued Passenger Cars 600 Feet From Stopping Point to 1000 Feet Downstream
B.1.5.5 Activity for Queue Vehicles From Initial Stopping Point Upstream
200 Feet (DECEL) After data collected from the stopping point forward for queue
vehicles were analyzed for various distances, deceleration activity that occurred previous to
the vehicle's queuing position was analyzed. The first deceleration data partion was a
distance of 200 feet upstream of the vehicle's queuing position. The final regression tree
model results are presented in Table B-33 and Figure B-33. As shown, the only significant
variable was roadway grade.
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Table B-33: Trimmed IPS120 Model for Queued Passenger Cars 200 Feet Before up to Stopping Point Regression tree: tree(formula = PKE120 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsDecelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 3) Variables actually used in tree construction: [1] "GRADE" Number of terminal nodes: 2 Residual mean deviance: 0.06023 = 18.97 / 315 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -0.08625 3.643e-017 3.643e-017 7.864e-018 3.643e-017 3.354
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Figure B-33: Trimmed IPS120 Model for Queued Passenger Cars 200 Feet Before up to Stopping Point
B.1.5.6 Activity for Queue Vehicles From 200 Feet Upstream of the Initial
Stopping Point to a 400 Feet Upstream (DECELNEG200) The next deceleration data
partion was activity that covering from 200 to 400 feet upstream of the vehicle's queuing
position. No activity was noted for inertial power surrogate over 120 mph2/s, so no models
are presented.
B.1.5.7 Activity for Queue Vehicles From 400 Feet Upstream of the Initial
Stopping Point to a 600 Feet Upstream (DECELNEG400) The next deceleration data
partion was activity that encompassed a distance of 400 feet upstream of the vehicle's
276
queuing position to a point 600 feet upstream from the queued vehicle's initial queuing point.
No model is presented since no activity over 120 mph2/s was observed.
B.1.5.8 "THRU" Vehicles at All locations
Vehicles not stopped at the intersection were analyzed separately since their vehicle
activity traces are expected to somewhat different in the vicinity to the signalized intersection.
Data were partitioned into 200-foot segments as for queued vehicles. However all data
partions were included in a single analysis for "THRU" vehicles and distance was included as
a variables to test whether the location from the stopline affects vehicle activity. Including
midblock data the distances ranged from 2,000 feet before the intersection stopbar to 1,200
past the intersection stopbar. Data models are presented in Table B-34 and Figure B-34,
which show link per lane volume and distance from the upstream intersection as predictor
variables.
Table B-34: Trimmed IPS120 Model for "THRU" Vehicles for All Locations Regression tree: tree(formula = PKE120 ~ Distance + VOLUME + PER.TRUCKS + LINKDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = CarsThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = PKEthru.snip4, nodes = 4) Variables actually used in tree construction: [1] "Distance" "VOLUME" Number of terminal nodes: 3 Residual mean deviance: 38.99 = 22460 / 576 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max.
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-14.02 -2.302 -1.014 4.436e-015 -1.014 85.97
Figure B-34: Trimmed IPS120 Model for "THRU" Vehicles for All Locations B.2 Heavy Trucks
The various models for heavy vehicles were much easier to run. In many cases most
of the models were simple enough that further trimming was not warranted. This is likely due
to the fact that heavy vehicle activity has much less variation to begin with than passenger car
activity. Below is presented the results for each response variable by position partion.
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B.2.1 Percent Activity >= 6.0 mph/s (ACCEL6)
The following sections present the regression tree models for the response variable
of percent activity where acceleration is greater than or equal to 6.0 mph/s. Data are
presented for each data partition.
B.2.1.1 Heavy Vehicle Activity for Queue Vehicles From Stopping Point to 200
Feet Downstream ACCEL Model
This model provides results for heavy vehicles that were stopped at the traffic signal
and includes data for a distance of 200 feet downstream of the vehicle's initial queuing
position. The response variable is the percent of activity where acceleration equals or
exceeds 6 mph/s. Table B-35 provides model results and Figure B-35 shows the final
regression tree model. As shown the distance to the nearest signalized downstream
intersection was the only variable provided by the model.
Table B-35: Trimmed ACC6 Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = ACC6 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = TrucksAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNDIST" Number of terminal nodes: 2 Residual mean deviance: 18.12 = 579.8 / 32 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -5.354 -5.204e-018 -5.204e-018 5.01e-017 -5.204e-018
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19.64
Figure B-35: Trimmed ACC6 Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Downstream
B.2.1.2 Heavy Vehicle Activity for Queue Vehicles From 200 feet From
Stopping Point to 800 Feet Downstream (ACCELPLUS200 to ACCELPLUS600)
This model provides results for heavy vehicles that were stopped at the traffic signal and
includes data for a distance from a point 200 feet downstream of the vehicle's initial queuing
position to a position 800 feet from the initial stopping point. The response variable is the
percent of activity where acceleration equals or exceeds 6 mph/s for the indicated position.
280
Data partions were combined so distance from the initial stopping point was also included as
an independent variable. Table B-36 provides model results and Figure B-36 shows the
final regression tree model. The explanatory variable is downstream per lane volume.
Table B-36: Trimmed ACC6 Model Results for Queued Heavy Vehicles From 200 to 800 Feet From the Initial Stopping Point Regression tree: tree(formula = ACC6 ~ Position + QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = trucksAccelPlusClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 10.07 = 342.5 / 34 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -2.856 -5.2e-18 -5.2e-18 -1.3e-16 -5.2e-18 17.13
Figure B-36: Trimmed ACC6 Model Results for Queued Heavy
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Vehicles From 200 to 800 Feet From the Initial Stopping Point B.2.1.3 Heavy Vehicle Activity for Queue Vehicles From 200 feet Before to
Queuing Point Stopping Point (DECEL)
No model is presented for percent of activity greater or equal to 6.0 mph/s since no
activity in this acceleration range was noted in any of the datasets.
B.2.1.4 Heavy Vehicle Activity for Queue Vehicles From 200 feet up to All Prior
Upstream Positions (DECELNEG200 to DECELNEG400)
Datasets included activity from a point 200 feet above the initial queuing location to
any point upstream of that position. Data include activity from 200 feet to 600 feet
upstream. No model is presented for percent of activity greater or equal to 6.0 mph/s since
no activity in this acceleration range was noted in any of the datasets.
B.2.1.5 Heavy Vehicle Activity for "THRU" Vehicles for All Positions
This model provides results for heavy vehicles that were not stopped at the traffic
signal and includes data for all distances before and after the stopbar including midblock.
The response variable is the percent of activity where acceleration equals or exceeds 6
mph/s for the indicated position. Predictor variables tested, also included distance from the
intersection stopbar since all data partions were included. The final predictor variable is
percent trucks with results shown in Table B-37 provides model results and Figure B-37
shows the final regression tree model.
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Table B-37: Trimmed ACC6 Model Results for "Thru" Heavy Vehicles Regression tree: tree(formula = ACC6 ~ Distance + QUEUE + Volume + PER.TRUCKS + Linkdistance + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 3) Variables actually used in tree construction: [1] "PER.TRUCKS" Number of terminal nodes: 2 Residual mean deviance: 16.28 = 1676 / 103 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -3.647 -0.1419 -0.1419 2.876e-016 -0.1419 29.67
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Figure A2-37: Trimmed ACC6 Model Results for "Thru" Heavy Vehicles B.2.2 Percent Activity >= 3.0 mph/s (ACCEL3) The following sections present the regression tree models for the response variable
of percent activity where acceleration is greater than or equal to 3.0 mph/s. Data are
presented for each data partion.
B.2.2.1 Heavy Vehicle Activity for Queue Vehicles From Stopping Point to
200 Feet Downstream (ACCEL) This model provides results for heavy vehicles that
were stopped at the traffic signal and includes data for a distance of 200 feet downstream of
the vehicle's initial queuing position. The response variable is the percent of activity where
acceleration equals or exceeds 3 mph/s for the indicated position. Table B-38 provides
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model results and Figure B-38 shows the final regression tree model. As shown the distance
to the nearest signalized downstream intersection and roadway grade are the only variables
provided by the model.
Table B-38: Trimmed ACC3 Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = ACC3 ~ QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 6) Variables actually used in tree construction: [1] "DOWNDIST" "GRADE" Number of terminal nodes: 3 Residual mean deviance: 180.4 = 5591 / 31 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -22.49 -8.137 –2.496 1.306e-015 8.991 30.13
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Figure B-38: Trimmed ACC3 Model Results for Queued Heavy Vehicles From Stopping Point to 20 Feet Downstream
B.2.2.2 Heavy Vehicle Activity for Queue Vehicles From 200 feet From
Stopping Point to 800 Feet Downstream (ACCELPLUS200 to ACCELPLUS600)
This model provides results for heavy vehicles that were stopped at the traffic signal and
includes data for a distance from a point 200 feet downstream of the vehicle's initial queuing
position to a position 800 feet from the initial stopping point. Distance from the queuing
position was also included as a predictor variable. The response variable is the percent of
activity where acceleration equals or exceeds 3.0 mph/s for the indicated position. Table B-
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39 provides model results and Figure B-39 shows the final regression tree model. The
explanatory variable is roadway grade with an RMD of 144.7.
Table B-39: Trimmed ACC3 Model Results for Queued Heavy Vehicles From 200 to 800 Feet From the Initial Stopping Point Regression tree: tree(formula = ACC3 ~ Position + QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = trucksAccelPlusClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "GRADE" Number of terminal nodes: 2 Residual mean deviance: 144.7 = 4921 / 34 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -24.44 -1.921 -1.921 6.908e-016 -1.921 35.55
Figure B-39: Trimmed ACC3 Model Results for Queued Heavy Vehicles From
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200 to 800 Feet Downstream From the Initial Stopping Point
B.2.2.3 Heavy Vehicle Activity for Queue Vehicles From 200 feet Before to
Queuing Point Stopping Point (DECEL) No model is presented for percent of activity
greater or equal to 3.0 mph/s since no activity in this acceleration range was noted in any of
the datasets.
B.2.2.4 Heavy Vehicle Activity for Queue Vehicles From 200 feet up to All
Prior Upstream Positions (DECELNEG200 to DECELNEG400) Datasets included
activity from a point 200 feet above the initial queuing location to any point upstream of that
position. Data include activity from 200 feet to 600 feet upstream. Distance from the initial
queuing point was also included as a variable since the model included various data partions.
No model is presented for percent of activity greater or equal to 3.0 mph/s since no activity
in this acceleration range was noted in any of the datasets.
B.2.2.5 Heavy Vehicle Activity for "THRU" Vehicles for All Positions
This model provides results for heavy vehicles that were not stopped at the traffic signal and
includes data for all distances before and after the stopbar including midblock. Distance was
also included as an independent variable. In place of upstream and downstream volume, link
volume for the vehicle's positions was substituted. A variable for the link distance was also
used in place of upstream and downstream distances. The response variable is the percent
of activity where acceleration equals or exceeds 3 mph/s for the indicated position.
Response variables also included distance from the intersection stopbar. Table B-40
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provides model results and Figure B-40 shows the final regression tree model. The only
variable used in the final model is link posted speed limit.
Table B-40: Trimmed ACC3 Model Results for "Thru" Heavy Vehicles Regression tree: tree(formula = ACC3 ~ Distance + Volume + PER.TRUCKS + Linkdistance + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "SPEEDLIMIT" Number of terminal nodes: 2 Residual mean deviance: 28.86 = 2972 / 103 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -2.966 -2.966 -0.8579 -6.725e-016 -0.8579 30.35
Figure B-40: Trimmed ACC3 Model Results for "Thru" Heavy Vehicles
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B.2.3 Percent Activity <= -2.0 mph/s (DECEL2)
The following sections present the regression tree models for the response variable
of percent activity where acceleration is less than or equal to -2.0 mph/s. Data are
presented for each data partion.
B.2.3.1 Heavy Vehicle Activity for Queue Vehicles From Stopping Point to
200 Feet Downstream (ACCEL) This model provides results for heavy vehicles that
were stopped at the traffic signal and includes data for a distance of 200 feet downstream of
the vehicle's initial queuing position. The response variable is the percent of activity where
acceleration is less than or equals -2 mph/s for the indicated position. Table B-41 provides
model results and Figure B-41 shows the final regression tree model. As shown, queue
position and grade were the most influential variables provided by the model.
Table B-41: Trimmed DECEL2 Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Downstream Regression tree: tree(formula = Decel2 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "QUEUE" "GRADE" Number of terminal nodes: 3 Residual mean deviance: 4.695 = 145.6 / 31 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -2.194 -1.68 -3.469e-018 2.582e-017 -3.469e-018
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6.64
Figure B-41: Trimmed DECEL2 Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Downstream
B.2.3.2 Heavy Vehicle Activity for Queue Vehicles From 200 feet From Stopping
Point to 800 Feet Downstream (ACCELPLUS200 to ACCELPLUS600)
This model provides results for heavy vehicles that were stopped at the traffic signal
and includes data for a distance from a point 200 feet downstream of the vehicle's initial
queuing position to a position 800 feet from the initial stopping point. The response variable
is the percent of activity where acceleration is less than or equal to -2.0 mph/s for the
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indicated position. The distance from the intersection stopline was also included as an
independent variable since not all data were from the same data partion. Table B-42
provides model results and Figure B-42 shows the final regression tree model. The single
explanatory variable is downstream per lane volume.
Table B-42: Trimmed DECEL2 Model Results for Queued Heavy Vehicles From 200 Downstream to 800 Feet From the Initial Stopping Point Regression tree: tree(formula = Decel2 ~ Position + QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = trucksAccelPlusClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 2) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 370.2 = 12590 / 34 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -20.3 -3.495 -3.495 2.837e-015 -3.495 79.69
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Figure B-42: Trimmed DECEL2 Model Results for Queued Heavy Vehicles From 200 to 800 Feet Downstream From the Initial Stopping Point B.2.3.3 Heavy Vehicle Activity for Queue Vehicles From 200 feet Before to
Queuing Point Stopping Point (DECEL)
This model provides results for heavy vehicles that were stopped at the traffic signal
and includes data for a distance from a point 200 feet upstream of the vehicle's initial queuing
position to the initial queuing point. The response variable is the percent of activity where
acceleration is less than or equal to -2.0 mph/s for the indicated position. Table B-43
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provides model results and Figure B-43 shows the final regression tree model. The single
explanatory variable selected by the model is queue position.
Table B-43: Trimmed DECEL2 Model Results for Queued Heavy Vehicles From 200 Feet Upstream to the Initial Stopping Point Regression tree: tree(formula = Decel2 ~ QUEUE + UPSTREAM + PER.TRUCKS + UPDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksDecelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "QUEUE" Number of terminal nodes: 2 Residual mean deviance: 573.2 = 6878 / 12 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -46.98 -16.3 9.362 1.523e-015 13.82 28.7
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Figure B-43: Trimmed DECEL2 Model Results for Queued Heavy Vehicles From 200 Feet Upstream to the Initial Stopping Point
B.2.3.4 Heavy Vehicle Activity for Queue Vehicles From 200 feet up to All
Prior Upstream Positions (DECELNEG200 to DECELNEG400) Datasets included
activity from a point 200 feet above the initial queuing location to any point upstream of that
position. Data include activity from 200 feet to 600 feet upstream. Distance from the initial
queuing position was also included as an independent variable. Queue position is the only
final model. As noted the model fit was rather poor with an overall deviance of 1526. The
results are shown in Table B-44 and Figure B-44.
Table B-44: Trimmed DECEL2 Model Results for Queued Heavy Vehicles From 200 Feet Upstream to Higher Upstream Positions Regression tree: Tree(formula = Decel2 ~ Position + QUEUE + UPSTREAM + PER.TRUCKS + UPDIST + GRADE + SPEEDLIMIT, data = TrucksDecelPlusClean, na.action = na.omit, mincut = 3, minsize = 6, mindev = 0.1) Variables actually used in tree construction: [1] "QUEUE" Number of terminal nodes: 3 Residual mean deviance: 1526 = 10680 / 7 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -39.99 -31.55 1.19 1.421e-015 22.85 60
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Figure B-44: Trimmed DECEL2 Model Results for Queued Heavy Vehicles from 200 Feet Upstream to Higher Upstream Positions
B.2.3.4 Heavy Vehicle Activity for "THRU" Vehicles for All Positions This
model provides results for heavy vehicles that were not stopped at the traffic signal and
includes data for all distances before and after the stopbar including midblock. The
response variable is the percent of activity where acceleration is <= -2 mph/s for the
indicated position. Response variables also included distance from the intersection stopbar.
Table B-45 provides model results and Figure B-45 shows the final regression tree model.
Predictor variables used in the final model include location and link volume. Location was
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split by industrial and suburban on the left side of the split and CBD and commercial on the
right side of the split.
Table B-45: Trimmed DECEL2 Model Results for "Thru" Heavy Vehicles Regression tree: tree(formula = Decel2 ~ Distance + Volume + PER.TRUCKS + DIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = d2truckstrhu.snip3, nodes = 7) Variables actually used in tree construction: [1] "LOCATION" "Volume" Number of terminal nodes: 4 Residual mean deviance: 310.1 = 31320 / 101 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -30.8 -4.666 -4.666 5.684e-015 4.414 80.05
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Figure B-45: Trimmed DECEL2 Model Results for "Thru" Heavy Vehicles B.2.4 Average Speed (AVG-SPD)
The following sections present the regression tree models for the response variable
of average speed. Data are presented for each data partion.
B.2.4.1 Heavy Vehicle Activity for Queue Vehicles From Stopping Point to
200 Feet Downstream (ACCEL) This model provides results for heavy vehicles that
were stopped at the traffic signal and includes data for a distance of 200 feet downstream of
the vehicle's initial queuing position. The response variable is average speed for the
indicated position. Table B-46 provides model results and Figure B-46 shows the final
regression tree model. As shown, queue position and distance to the nearest downstream
signalized intersection were the most influential variables provided by the model.
Table B-46: Trimmed AVG_SPD Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Upstream Regression tree: snip.tree(tree = tspdaccel.snip2, nodes = 7) tree(formula = SPEED ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + WIDTH + NO.LANES + LOCATION, data = TrucksAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNDIST" "QUEUE" Number of terminal nodes: 3 Residual mean deviance: 14.74 = 456.9 / 31 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -7.343 -2.289 -0.45 1.045e-015 1.755 9.757
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Figure B-46: Trimmed AVG_SPD Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Downstream
B.2.4.2 Heavy Vehicle Activity for Queue Vehicles From 200 feet From
Stopping Point to 800 Feet Downstream (ACCELPLUS200 to ACCELPLUS600)
This model provides results for heavy vehicles that were stopped at the traffic signal and
includes data for a distance from a point 200 feet downstream of the vehicle's initial queuing
position to a position 800 feet from the initial stopping point. The response variable is
average speed (mph) for the indicated position. The distance from the intersection stopline
was also included as an independent variable since not data were from the same data
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partion. Table B-47 provides model results and Figure B-47 shows the final regression tree
model. The explanatory variables are posted link speed limit, percent heavy vehicles, and
queue position.
Table B-47: Trimmed AVG_SPD Model Results for Queued Heavy Vehicles From 200 to 800 Feet From the Initial Stopping Point Regression tree: tree(formula = SPEED ~ Position + QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = trucksAccelPlusClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 4) Variables actually used in tree construction: [1] "SPEEDLIMIT" "PER.TRUCKS" Number of terminal nodes: 4 Residual mean deviance: 30.12 = 963.9 / 32 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -16.68 -2.312 0.4707 1.135e-015 2.621 11.42
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Figure B-47: Trimmed AVG_SPD Model Results for Queued Heavy Vehicles From 200 to 800 Feet From the Initial Stopping Point
B.2.4.3 Heavy Vehicle Activity for Queue Vehicles From 200 feet Before to
Queuing Point Stopping Point (DECEL) This model provides results for heavy vehicles
that were stopped at the traffic signal and includes data for a distance from a point 200 feet
upstream of the vehicle's initial queuing position to the initial queuing point. The response
variable is average speed for the indicated position. Table B-48 provides model results and
Figure B-48 shows the final regression tree model. The single explanatory variable selected
by the model is roadway grade.
Table B-48: Trimmed AVG_SPD Model Results for Queued Heavy Vehicles From 200 Feet Upstream to the Initial Stopping Point Regression tree: tree(formula = SPEED ~ QUEUE + UPSTREAM +
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PER.TRUCKS + UPDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksDecelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "GRADE" Number of terminal nodes: 2 Residual mean deviance: 19.11 = 210.3 / 11 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -6.45 -3.05 0.34 8.199e-016 2.35 6.05
Figure B-48: Trimmed AVG_SPD Model Results for Queued Heavy Vehicles From 200 Feet Upstream to the Initial Stopping Point
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B.2.4.4 Heavy Vehicle Activity for Queue Vehicles From 200 feet up to All
Prior Upstream Positions (DECELNEG200 to DECELNEG400) Datasets included
activity from a point 200 feet above the initial queuing location to any point upstream of that
position. Data include activity from 200 feet to 600 feet upstream. Distance from the initial
queuing position was also included as an independent variable. Upstream per lane volume is
the only final model variable. Results are given in Table B-49 and Figure B-49.
Table B-49: Trimmed AVG_SPD Model Results for Queued Heavy Vehicles From 200 Feet Upstream to Higher Upstream Positions Regression tree: tree(formula = SPEED ~ Position + QUEUE + UPSTREAM + PER.TRUCKS + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH, data = TrucksDecelPlusClean, na.action = na.omit, mincut = 3, minsize = 6, mindev = 0.1) Variables actually used in tree construction: [1] "UPSTREAM" Number of terminal nodes: 3 Residual mean deviance: 33.89 = 237.3 / 7 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -7.433 -3.381 -0.4833 2.487e-015 2.569 9.067
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Figure B-49: Trimmed AVG_SPD Model Results for Queued Heavy Vehicles From 200 Feet Upstream to Higher Upstream Positions
B.2.4.5 Heavy Vehicle Activity for "THRU" Vehicles for All
Positions This model provides results for heavy vehicles that were not stopped at
the traffic signal and includes data for all distances before and after the stopbar
including midblock. The response variable is average speed (mph) for the indicated
position. Response variables also included distance from the intersection stopbar.
Table B-50 provides model results and Figure B-50 shows the final regression tree
model. The predictor variables given by the model are posted link speed limit and
link per lane volume.
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Table B-50: Trimmed AVG_SPD Model Results for "Thru" Heavy Vehicles Regression tree: Regression tree: tree(formula = SPEED ~ Volume + PER.TRUCKS + Linkdistance + GRADE + SPEEDLIMIT + NO.LANES, data = TrucksThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = last.tree, nodes = 2) Variables actually used in tree construction: [1] "SPEEDLIMIT" Number of terminal nodes: 2 Residual mean deviance: 69.93 = 7343 / 105 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -20.01 -4.966 0.3877 -7.139e-015 5.531 24.09
Figure B-50: Trimmed AVG_SPD Model Results for "Thru" Heavy Vehicles
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B.2.5 Percent Activity Where Inertial Power Surrogate >- 120 mph2/s (IPS120)
The following sections present the regression tree models for the response variable
of percent activity where inertial power surrogate exceeds or equals 120.0 mph2/s. Data are
presented for each data partion.
B.2.5.1 Heavy Vehicle Activity for Queue Vehicles From Stopping Point to
200 Feet Downstream (ACCEL) This model provides results for heavy vehicles that
were stopped at the traffic signal and includes data for a distance of 200 feet downstream of
the vehicle's initial queuing position. The response variable is the percent of activity where
inertial power surrogate is greater than or equal to 120 mph2/s for the indicated position.
Table B-51 provides model results and Figure B-51 shows the final regression tree model.
As shown, distance to the nearest downstream signalized intersection was the most influential
variable provided by the model.
Table B-51: Trimmed IPS120 Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Upstream Regression tree: tree(formula = PKE120 ~ QUEUE + UPSTREAM + DOWNSTREAM + PER.TRUCKS + UPDIST + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksAccelClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNDIST" Number of terminal nodes: 2 Residual mean deviance: 65.54 = 2097 / 32
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Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -8.926 -5.204e-018 -5.204e-018 1.546e-016 -5.204e-018 41.06
Figure B-51: Trimmed IPS120 Model Results for Queued Heavy Vehicles From Stopping Point to 200 Feet Upstream
B.2.5.2 Heavy Vehicle Activity for Queue Vehicles From 200 feet From
Stopping Point to 800 Feet Downstream (ACCELPLUS200 to ACCELPLUS600)
This model provides results for heavy vehicles that were stopped at the traffic signal
and includes data for a distance from a point 200 feet downstream of the vehicle's initial
queuing position to a position 800 feet from the initial stopping point. The response variable
is the percent of activity where inertial power surrogate is greater than or equal to 120
307
mph2/s for the indicated position. The distance from the intersection stopline was also
included as an independent variable since data were not all from the same data partion.
Table B-52 provides model results and Figure B-52 shows the final regression tree model.
The explanatory variable is downstream per lane volume.
Table B-52: Trimmed IPS120 Model Results for Queued Heavy Vehicles From 200 to 800 Feet From the Initial Stopping Point Regression tree: tree(formula = PKE120 ~ Position + QUEUE + DOWNSTREAM + PER.TRUCKS + DOWNDIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = trucksAccelPlusClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) Variables actually used in tree construction: [1] "DOWNSTREAM" Number of terminal nodes: 2 Residual mean deviance: 10.07 = 342.5 / 34 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -2.856 -5.204e-018 -5.204e-018 -1.364e-016 -5.204e-018 17.13
308
Figure B-52: Trimmed IPS120 Model Results for Queued Heavy Vehicles From 200 to 800 Feet From the Initial Stopping Point B.2.5.3 Heavy Vehicle Activity for Queue Vehicles From 200 feet Before to
Queuing Point Stopping Point (DECEL)
No observations of activity exceeding 120 mph2/s were observed in the datasets for
heavy vehicles that were stopped at the traffic signal and includes data for a distance from a
point 200 feet upstream of the vehicle's initial queuing position to the initial queuing point.
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B.2.5.4 Heavy Vehicle Activity for Queue Vehicles From 200 feet up to All
Prior Upstream Positions (DECELNEG200 to DECELNEG400) No activity for
inertial power surrogate greater than or equal to 120 mph2/s was observed for any of the
datasets for heavy vehicles that stopped at the signalized intersection for a distance from 200
feet upstream of the initial queuing position to all other recorded distances upstream of this
point.
B.2.5.5 Heavy Vehicle Activity for "THRU" Vehicles for All Positions
This model provides results for heavy vehicles that were not stopped at the traffic signal and
includes data for all distances before and after the stopbar including midblock. The
response variable is the percent of activity where inertial power surrogate is greater than or
equal to 120 mph2/s for the indicated position. Response variables also included distance
from the intersection stopbar. Table B-53 provides model results and Figure B-53 shows
the final regression tree model. The single variable used in the final model roadway grade.
Table B-53: Trimmed IPS120 Model Results for "Thru" Heavy Vehicles Regression tree: tree(formula = PKE120 ~ Distance + Volume + PER.TRUCKS + DIST + GRADE + SPEEDLIMIT + NO.LANES + WIDTH + LOCATION, data = TrucksThruClean, na.action = na.omit, mincut = 5, minsize = 10, mindev = 0.1) snip.tree(tree = pketrucksthru.snip3, nodes = 2) Variables actually used in tree construction: [1] "GRADE" Number of terminal nodes: 2 Residual mean deviance: 28.54 = 2939 / 103 Distribution of residuals: Min. 1st Qu. Median Mean 3rd Qu. Max. -4.998 -0.7684 -0.7684 –1.866e-015 -0.7684 28.32
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Figure B-53: Trimmed IPS120 Model Results for "Thru" Heavy Vehicles
