Estimating Link Travel Time with Explicitly Considering Vehicle Delay at Intersections

Aichong SunEmail: asun@pagnet.org

Tel: (520) 792-1093

Content Outline

I. Current Status of VDF in Travel Demand

Model

II. VDF Estimation

III. VDF Validation

IV. VDF Implementation

V. Conclusions

Current Status of VDF in Travel Demand Model

Link-Based VDFs

The Bureau of Public Roads (BPR) Function

C

VTT f *1*0

Conical Volume-Delay Function

22

12

112)(

)(*

22

2

0

C

V

C

V

C

Vf

C

VfTT f

Free-Flow-Travel-Time and Capacity are typically determined by link-class/area-type lookup table without considering the intersecting streets

Could change

Stay same

Get built or upgraded

Current Status of VDF in Travel Demand Model

VDF Considering Intersection Delay

Logit-based Volume Delay Function

Israel Institute of Transportation Planning & Research

HCM Intersection Delay Function

Other functions (good discussion on TMIP 3/6/08-3/17/08)

Common Issues

over-sophisticated with the intension of thoroughly characterizing traffic dynamics

Computational Burden & Data Requirement

Function are not convex in natureNo convergence for traffic assignment procedure

Current Status of VDF in Travel Demand Model

PAG’s Travel Demand Model

Use only BPR functions until very recently

BPR functions are not calibrated with local data

Travel demand model is not calibrated against travel speed/time

Traffic is not routed appropriately

Overestimate average travel speed

VDF Estimation

Study Design - Foundamental Thoughts

The VDF should be:

Well Behaved – reaction to the changes of travel demand, traffic controls and cross-streets

Simple – computation time

Convex – model convergence

Least Data Demanding - implementation

Data Collected must cover whole range of congestion

VDF Estimation

Study Design – Data Collection Method

Floating-Car method with portable GPS devices

Two major arterial corridors were selected

Corridor Name

Area Type Length

(Mile)

# of Lanes # of Signalized Intersections

Broadway Blvd

Central Urban

7 6(4) 18

Ina Rd Suburban 4 4 9

Survey Duration

3 weekdays (Mar. 3 – 6, 2008), 12 hours a day (6:00AM – 6:00PM)

Data collected from Broadway Blvd to estimate the model; data collected from Ina Rd to validate the model

VDF Estimation

Collected Data

GPS 1(2)-Sec Vehicle Location Data

VDF Estimation

Collected Data

Distance between signalized intersections

Posted speed limits

Lane Configuration for each street segment between intersections

15-min interval traffic counts between major intersections

Collected concurrently at 7 locations on Broadway Blvd and 3 locations on Ina Rd

Signal phasing/timing/coordination information

Collected from jurisdictions

VDF Estimation

VDF Model Form

c

gS

VcP

VTT

C

Cf

cg

C

i

i

ti

slf

il

*

**1**

2**1* 1

2

0

ft - Percentage of through traffic

P - Traffic Progression Adjustment Factor iill,,, - Coefficients

C s

C i

- Segment capacity

- Intersection Approach Capacity for through traffic

cg - signal g/c ratio for through traffic

0T - midblock free-flow travel time, NCHRP 387

Signal Delay (NCHRP 387)

BPR function

Adjustment based on

congestion

c - Signal Cycle Length

VDF Estimation

Nature of the function form

Convex (when Beta’s >= 1)

)()()(21xxxF ff

Convex ConvexConvex

c

gS

VcP

VTT

C

Cf

cg

C

i

i

ti

slf

il

*

**1**

2**1* 1

2

0

g/c ratio

Midblock congestion Intersection congestion

Sensitive to Signal Timing & Congestion

VDF Estimation

Parameters Capacity

Mid-block

- HCM approach

- (Linkclass, AreaType) lookup Table

Intersection

- Saturation rate 1800/1900 vehicle/hr/lane (HCM)

- Signal g/c ratio

14*88.0 SS pf

12*79.0 SS pf

5SS pf

Speed

NCHRP Report 387

High-speed facilities (>= 50 mph)

Low-speed facilities (< 50 mph)

Or

VDF Estimation

Parameters

Through Traffic Percentage (70%-90%)

Traffic Progression Adjustment Factor

- HCM 2000 (0 – 2.256)

- NCHRP Report 387

Condition Progression Adjustment Factor

Uncoordinated Traffic Actuated Signals 0.9

Uncoordinated Fixed Time Signals 1.0

Coordinated Signals with Unfavorable Progression

1.2

Coordinated Signals with Favorable Progression

0.9

Coordinated Signals with Highly Favorable Progression

0.6

VDF Estimation

Model Estimation – Prepare Dataset

Identify the floating car locations and arrival times immediately after the intersections to compute travel time and travel distance for each run

Build the dataset with one record for each pair of identified travel distance and travel time between two neighboring intersections

Append the following data to each record in the dataset

Traffic CountsStreet Segment CapacityFree-Flow-SpeedSignal Cycle LengthSignal g/c RatioSignal Traffic Progression Adjustment FactorIntersection Saturation Rate

VDF Estimation

Model Estimation – Regression

Nonlinear regression Often no global optimum…

Regression Methods

- Enumeration Method (Least Square) Specify range & increment for each parameter Enumerate the combinations of possible values for each parameter Compute MSE for each combination of parameter values Save 50 combinations of the parameter values that result in the least MSE

- Statistical Analysis Software (SPSS, SAS) Verify the parameters estimated from Enumeration Method Report statistical significance for estimated parameters

VDF Estimation

Model Estimation – Results

Enumeration Method

Best_Alpha1 Best_Beta1 Best_Alpha2 Best_Beta2 Best_MSE

1.9 1.9 2.1 2.4 464.9736023

1.7 1.8 2.1 2.4 464.97755

1.6 1.7 2.1 2.5 465.0029037

2 2 2.1 2.3 465.0132826

1.8 1.8 2 2.4 465.0143812

2 1.9 2 2.4 465.0149071

1.8 1.8 2.1 2.5 465.0155575

1.8 1.9 2.1 2.3 465.0163662

2.1 2 2.1 2.4 465.0249737

1.9 1.9 2 2.3 465.0272314

2.1 2 2 2.3 465.0363844

… … … … …

VDF Estimation

Model Estimation – Results

Statistical Analysis Software (SPSS & SAS)

Both Methods reported very similar parameter estimates

Parameter Estimate Std. Error

95% Confidence Interval

Lower Bound Upper Bound

a1 1.835 (1.9) .890 .089 3.581

b1 1.858 (1.9) .535 .809 2.907

a2 2.073 (2.1) .213 1.655 2.491

b2 2.392 (2.4) .475 1.460 3.324

Parameter Estimates

R2 = 0.38

VDF Validation

Ina Rd Data

Apply the parameters estimated from Broadway Blvd data to Ina Rd

Corridor Name Average I-I Travel Time (Sec)

RMSE

(Sec)

% RMSE

Broadway Blvd 53 21.5 40%

Ina Rd 67 27.8

(26.9)

41.5%

(40.2%)

VDF Validation

Average Regional Travel Speed

  ParkwayMajor Arterial

Minor Arterial

Frontage Road

Average

SPEED 51.0 45.5 46.8 45.3 46.1

BPR – FFS from NCHRP Report 387

BPR – FFS from PAG Model Speed Lookup Table

New VDF – FFS from NCHRP Report 387

  ParkwayMajor Arterial

Minor Arterial

Frontage Road

Average

SPEED 36.9 32.0 35.7 29.5 33.5

  ParkwayMajor Arterial

Minor Arterial

Frontage Road

Average

SPEED 51.0 45.5 46.8 45.3 40.9

VDF Validation

Travel Times of Individual Routes

Route Travel Time (min) Travel Distance

(mile)

Actual Number of Signalized

Intersections

Modeled number of Signalized

Intersections

Reported Model Estimated

(BPR)

Model Estimated (New VDF)

1 35 17 31 12 26 24

2 11 6 10 4 9 6

3 30 14 25 9 21 25

4 21 13 19.5 9 17 15

5 40 19 31 13 23 22

N

W

E

NE

N

VDF Implementation

New VDF is made with C codes and compiled as the modeling software DLL

OUE Assignment is used to replace standard UE assignment for faster convergence

FAQs

Q: Posted Speed Limits for future year networkA: Use the average of the present similar facilities in terms of link class and area type

Q: Cycle Length, g/c Ratio, Progression Adjustment Factor for future year networkA: Categorize the intersection in terms of the facility type of intersecting streets, area type and so on

Conclusions

Empirical Model

Provide some insights into the traffic dynamics, but not as much as HCM traffic flow/congestion models

Report more precise vehicle travel time/speed

Reasonably sensitive to intersection configuration

Turning traffic may experience further delay that is not captured by the VDF

Further study with more samples is necessary (in plan)

Other function forms should be investigated

Questions, Comments Or Suggestions?

Aichong SunEmail: asun@pagnet.org

Kosok ChaeEmail: kchae@pagnet.orgTel: (520) 792-1093