TRAVEL TIME PREDICTION MODEL FOR REGIONAL BUS TRANSIT · 2014. 2. 19. · ii Travel Time Prediction Model for Regional Bus Transit Andrew Chun Kit Wong Master of Applied Science Department

TRAVEL TIME PREDICTION MODEL FOR REGIONAL BUS TRANSIT

by

Andrew Chun Kit Wong

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Department of Civil Engineering University of Toronto

© Copyright by Andrew Chun Kit Wong 2009

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Travel Time Prediction Model for Regional Bus Transit

Andrew Chun Kit Wong

Master of Applied Science

Department of Civil Engineering University of Toronto

2009

Abstract

Over the past decade, the popularity of regional bus services has grown in large North American

cities owing to more people living in suburban areas and commuting to the Central Business

District to work every day. Estimating journey time for regional buses is challenging because of

the low frequencies and long commuting distances that typically characterize such services. This

research project developed a mathematical model to estimate regional bus travel time using

artificial neural networks (ANN). ANN outperformed other forecasting methods, namely

historical average and linear regression, by an average of 35 and 26 seconds respectively. The

ANN results showed, however, overestimation by 40% to 60%, which can lead to travellers

missing the bus. An operational strategy is integrated into the model to minimize stakeholders’

costs when the model’s forecast time is later than the scheduled bus departure time. This

operational strategy should be varied as the commuting distance decreases.

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Acknowledgments

I would like to express my sincere gratitude to Dr. Amer Shalaby and Dr. Baher Abdulhai for

their supervision during the studies of my master of applied science degree. Their guidance and

constant inspiration throughout my graduate studies are very much appreciated.

I would also like to give many thanks to my professors in the Transportation Group, fellow

graduate students and administration staff at the ITS Centre and Testbed, including but not

limited to Asmus Georgi, Bilal Farooq, Bryce Sharman, Dr. Eric Miller, Dr. Matthew Roorda,

Farhad Shahla, Hossam Abd El-Gawad, Karen Woo, Marcus Williams, Mahmoud Osman,

Michael Hain, Rinaldo Cavalcante, Wen Xie, Wenli Gao, Yang Hao Jiang, Yasmin Shalaby, and

more, for their help and support during my research.

Thanks to the Greater Toronto Transit Authority – GO Transit and the Ministry of Transportation

of Ontario for providing variable GO buses’ GPS data and loop detectors data for this research

project.

Special thanks to Cally Cheung for her assistance in proofreading my thesis. Last but not least, I

would like to express my appreciation to my family, Cally Cheung, and my dear friends for their

continuous encouragement throughout my graduate studies.

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Table of Contents

Acknowledgments.......................................................................................................................... iii

Table of Contents........................................................................................................................... iv

List of Tables ............................................................................................................................... viii

List of Figures ............................................................................................................................... xii

List of Appendices ....................................................................................................................... xiv

Chapter 1 Introduction .................................................................................................................... 1

1 Introduction ................................................................................................................................ 1

1.1 Research Background ......................................................................................................... 1

1.2 Thesis Objectives ................................................................................................................ 4

1.3 Thesis Scope ....................................................................................................................... 5

1.4 Thesis Organization ............................................................................................................ 5

Chapter 2 Literature Review........................................................................................................... 7

2 Literature Review....................................................................................................................... 7

2.1 Univariate Models............................................................................................................... 7

2.2 Multivariate Models............................................................................................................ 8

2.2.1 Regression Models.................................................................................................. 8

2.2.2 Kalman Filtering Models ...................................................................................... 10

2.3 Artificial Neural Networks ............................................................................................... 12

2.4 Other Forecasting Models................................................................................................. 14

Chapter 3 Data .............................................................................................................................. 17

3 Data .......................................................................................................................................... 17

3.1 Data Collection ................................................................................................................. 17

3.1.1 Bus Schedules ....................................................................................................... 17

v

3.1.2 Global Positioning System (GPS) Data of Bus Locations.................................... 17

3.1.3 Loop Detector Data............................................................................................... 18

3.1.4 Incident Reports .................................................................................................... 21

3.1.5 Historical Daily Weather Conditions.................................................................... 21

Chapter 4 Travel Time Computation and Descriptive Analysis ................................................... 24

4 Travel Time Computation and Descriptive Analysis............................................................... 24

4.1 Regional Bus Journey Time Computation........................................................................ 24

4.1.1 Checkpoint Identification...................................................................................... 24

4.1.2 Procedure of Computing Bus Travel Time........................................................... 27

4.2 Regional Bus Journey Time Performance Analysis ......................................................... 31

4.2.1 Gardiner Expressway Eastbound Route................................................................ 33

4.2.2 Gardiner Expressway Westbound Route .............................................................. 34

4.2.3 Lakeshore Boulevard Eastbound Route................................................................ 35

4.2.4 Lakeshore Boulevard Westbound Route .............................................................. 35

4.3 Limitations ........................................................................................................................ 36

Chapter 5 Artificial Neural Network ............................................................................................ 41

5 Artificial Neural Network ........................................................................................................ 41

5.1 Theoretical Background.................................................................................................... 41

5.1.1 Basic Unit of Artificial Neural Network: Neuron................................................. 41

5.1.2 Selection of Artificial Neural Network Model ..................................................... 42

5.1.3 Advantages and Disadvantages of Artificial Neural Network.............................. 42

5.1.4 Artificial Neural Network’s Transfer Function .................................................... 45

5.1.5 Feedforward Neural Network vs. Feedbackward Neural Network ...................... 46

5.1.6 Artificial Neural Network Training Techniques................................................... 46

5.1.6.1 Supervised Learning Techniques ........................................................... 46

5.1.6.2 Unsupervised Learning Techniques ....................................................... 47

vi

5.1.7 Multilayer Feedforward Perceptron with Backpropagation ................................. 47

5.1.8 Input Component Simplification Techniques ....................................................... 51

5.1.8.1 Sensitivity Analysis ................................................................................ 51

5.1.8.2 Principal Component Analysis ............................................................... 53

5.1.9 Over Fit Training Data Avoidance ....................................................................... 53

5.1.10 Performance Measures.......................................................................................... 54

5.2 Artificial Neural Network Calibrations ............................................................................ 54

5.2.1 Sensitivity Analysis .............................................................................................. 55

5.2.2 Direction-Based Models ....................................................................................... 56

5.2.3 Location-Based Models ........................................................................................ 59

5.3 Direction-Based Models vs. Location-Based Models ...................................................... 61

Chapter 6 Alternative Approaches’ Calibrations and Evaluations ............................................... 63

6 Alternative Approaches’ Calibrations and Evaluations ........................................................... 63

6.1 Historical Average Models ............................................................................................... 63

6.1.1 Model Calibrations and Evaluations..................................................................... 63

6.2 Linear Regression Models ................................................................................................ 65

6.2.1 Statistical Significance of the Parameter Estimates.............................................. 66

6.2.2 Goodness-of-Fit .................................................................................................... 66

6.2.3 Rationale for the Variables Selection Process ...................................................... 66

6.2.4 Model Calibrations and Evaluations..................................................................... 66

6.3 Forecasting Model Evaluations......................................................................................... 71

6.4 Additional Checkpoints’ Artificial Neural Networks Calibration .................................... 73

Chapter 7 Operational Strategy..................................................................................................... 78

7 Operational Strategy................................................................................................................. 78

7.1 Background ....................................................................................................................... 78

7.2 Operational Strategy Alternatives Calibrations and Analysis .......................................... 79

vii

7.3 Graphical User Interface Design....................................................................................... 86

Chapter 8 Thesis Conclusions and Recommendations ................................................................. 88

8 Thesis Conclusions and Recommendations ............................................................................. 88

8.1 Conclusions....................................................................................................................... 88

8.2 Recommendations............................................................................................................. 90

References..................................................................................................................................... 93

viii

List of Tables

Table 1-1: Benefits to Transit Related Users and Associated Individuals..................................... 3

Table 1-2: Benefits to GO Transit ................................................................................................. 3

Table 1-3: Benefits to Other Users ................................................................................................ 4

Table 3-1: Summary of Data Types and Resources...................................................................... 17

Table 3-2: Summary of Loop Detectors along the Freeways and Lakeshore Boulevard ............ 19

Table 4-1: Number of Checkpoints on by Route Segment .......................................................... 25

Table 4-2: Coordinates of the Checkpoints along the Gardiner Expressway, Eastbound ........... 25

Table 4-3: Coordinates of the Checkpoints along the Gardiner Expressway, Westbound.......... 25

Table 4-4: Coordinates of the Checkpoints along Lakeshore Boulevard, Eastbound ................. 26

Table 4-5: Coordinates of the Checkpoints along the Lakeshore Boulevard, Westbound .......... 26

Table 4-6: Gardiner Expressway Eastbound Route’s Distances from the Origin of Square One

Bus Terminal................................................................................................................................. 30

Table 4-7: Gardiner Expressway Westbound Route’s Distances from the Origin of Union GO

Bus Terminal................................................................................................................................. 30

Table 4-8: Lakeshore Boulevard Eastbound Route’s Distances from the Origin of Square One

Bus Terminal................................................................................................................................. 30

Table 4-9: Lakeshore Boulevard Westbound Route’s Distances from the Origin of Union GO

Bus Terminal................................................................................................................................. 31

Table 4-10: List of Bus Travel Time-Distance Figures ............................................................... 33

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Table 4-11: Data Sources............................................................................................................. 36

Table 4-12: Gardiner Expressway Eastbound Route Sample Summary ..................................... 39

Table 4-13: Gardiner Expressway Westbound Route Sample Summary .................................... 39

Table 5-1: Sensitivity Significance Summary of Input Factors................................................... 56

Table 5-2: ANN Structure Summary of Direction-Based Models (Gardiner Expressway

Eastbound Route).......................................................................................................................... 57

Table 5-3: Direction-Based ANN Alternatives Performance Assessment (Gardiner Expressway

Eastbound Route).......................................................................................................................... 58


Westbound Route) ........................................................................................................................ 58

Table 5-5: Direction-Based ANN Alternatives Performance Assessment (Gardiner Expressway

Westbound Route) ........................................................................................................................ 59

Table 5-6: ANN Structure Summary of Location-Based Models (Gardiner Expressway

Eastbound Route).......................................................................................................................... 59

Table 5-7: Location-Based ANN Structure Summary (Gardiner Expressway Westbound Route)

....................................................................................................................................................... 60

Table 5-8: Direction- and Location-Based ANN Alternatives Performance Assessment

(Gardiner Expressway Eastbound Route) ..................................................................................... 61


(Gardiner Expressway Westbound Route).................................................................................... 61

Table 6-1: Historical Average Model Alternatives Performance Assessment (Gardiner

Expressway Eastbound Route) ..................................................................................................... 64

Table 6-2: Historical Average Model Alternative Performance Assessment (Gardiner

Expressway Westbound Route) .................................................................................................... 65

x

Table 6-3: Explanatory Variables used for RE-DE ..................................................................... 67

Table 6-4: Explanatory Variables used for RE-LSE.................................................................... 68

Table 6-5: Explanatory Variables used for RE-LCE ................................................................... 68

Table 6-6: Explanatory Variables used for RE-LDE................................................................... 68

Table 6-7: Explanatory Variables used for RE-DW .................................................................... 69

Table 6-8: Explanatory Variables used for RE-LSW .................................................................. 69

Table 6-9: Explanatory Variables used for RE-LCW.................................................................. 69

Table 6-10: Explanatory Variables used for RE-LDW................................................................ 70

Table 6-11: Regression Models Performance Assessment (Gardiner Expressway Eastbound

Route)............................................................................................................................................ 70

Table 6-12: Regression Models Performance Assessment (Gardiner Expressway Westbound

Route)............................................................................................................................................ 70

Table 6-13: Summary of Configurations of Each Model Type (Gardiner Expressway Eastbound

Route)............................................................................................................................................ 72

Table 6-14: Summary of Configurations of Each Model Type (Gardiner Expressway Westbound

Route)............................................................................................................................................ 72

Table 6-15: Alternative Modelling Approaches Performance Assessment (Gardiner Expressway

Eastbound Route).......................................................................................................................... 72

Table 6-16: Alternative Modelling Approaches Performance Assessment (Gardiner Expressway

Westbound Route) ........................................................................................................................ 73

Table 6-17: ANN Structure Summary at Dufferin Street Checkpoint......................................... 74

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Table 6-18: ANN Structure Summary at Highway 427/QEW Checkpoint ................................. 74

Table 6-19: ANN Performance Assessment at Dufferin Street Checkpoint (Gardiner Expressway

Eastbound Route).......................................................................................................................... 75

Table 6-20: ANN Performance Assessment at Highway 427/QEW Checkpoint (Gardiner

Expressway Westbound Route) .................................................................................................... 75

Table 7-1: Overestimation vs. Underestimation (Gardiner Expressway Eastbound Route) ....... 78

Table 7-2: Overestimation vs. Underestimation (Gardiner Expressway Westbound Route) ...... 78

Table 7-3: Bus Stakeholders’ Wait Time with Different Bus Operational Strategies................. 81

Table 7-4: Wait Time Summary for Gardiner Expressway Eastbound Route............................. 82

Table 7-5: Wait Time Summary for Gardiner Expressway Westbound Route ........................... 83

Table 7-6: Ratio of Time Cost Monetary Value Comparison Summary (Option_2 vs. Option_1)

....................................................................................................................................................... 86

Table 7-7: Ratio of Time Cost Monetary Value Comparison Summary (Option_3 vs. Option_1)

....................................................................................................................................................... 86

xii

List of Figures

Figure 1-1: Study Route and Bus Stop Locations Map ................................................................. 5

Figure 3-1: Transportation Agencies’ Jurisdiction Area ............................................................. 18

Figure 3-2: Toronto West Freeway Network............................................................................... 19

Figure 4-1: Location of Checkpoints along the Gardiner Expressway and Lakeshore Boulevard

Eastbound...................................................................................................................................... 27

Figure 4-2: Location of Checkpoints along the Gardiner Expressway and Lakeshore Boulevard

Westbound .................................................................................................................................... 27

Figure 4-3: Checkpoint and Bus Departure Time Determination using a 300-metre Checkpoint

Buffer ............................................................................................................................................ 28

Figure 4-4: Example of Missing Checkpoint Departure Time .................................................... 29

Figure 4-5: Bus Travel Time Updating Locations....................................................................... 38

Figure 5-1: Typical Artificial Neuron Configuration .................................................................. 41

Figure 5-2: Typical Transfer Function Structures ....................................................................... 45

Figure 5-3: Typical Multilayer Feedforward Network ................................................................ 47

Figure 6-1: Historical Average Approach Options...................................................................... 64

Figure 6-2: Prediction Error Trend for the ANN Approach (Destination Union GO Bus

Terminal)....................................................................................................................................... 76

Figure 6-3: Prediction Error Trend for the ANN Approach (Destination Square One Bus

Terminal)....................................................................................................................................... 76

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Figure 6-4: Prediction Error Trend for the ANN Approach (Destination Cooksville GO Station)

....................................................................................................................................................... 77

Figure 6-5: Prediction Error Trend for the ANN Approach (Destination Dixie GO Station) ..... 77

Figure 7-1: Case when Estimated Arrival Time is earlier than the Scheduled Time .................. 79

Figure 7-2: Bus Operational Strategy Flow Chart ....................................................................... 81

Figure 7-3: Cost Comparison for Different Origin and Destination Pairs................................... 85

Figure 7-4: Basic Design of the Graphical User Interface........................................................... 87

Figure 7-5: Travel Time Broadcasting Results ............................................................................ 87

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List of Appendices

Appendix A: Historical Buses’ Travel Time Performances ........................................................ 98

Appendix B: Programming Syntax for Artificial Neural Network Training............................. 114

Appendix C: Historical Travel Time Summary......................................................................... 116

Appendix D: Input Variables Lists ............................................................................................ 135

Appendix E: Regression Model – Gardiner Expressway Eastbound Route .............................. 138

Appendix F: Regression Model – Gardiner Expressway Westbound Route............................. 140

Appendix G: Programming Syntax for Geographical User Inferfaces ...................................... 142

1

Chapter 1 Introduction

1 Introduction

1.1 Research Background Many people live in suburban areas surrounding large cities in North America and commute to

the central business district (CBD) to work every day. Regional transit services are usually

available between the CBD and its suburban areas, and they typically travel along freeways and

arterials. One such example is GO Transit, which serves the Greater Toronto Area (GTA). GO

Transit provides train and bus services between Toronto’s CBD and various suburban areas such

as Mississauga and Oshawa, carrying approximately 35,000 passengers on a typical weekday

(GO Transit 2008a). This study focuses on the bus services provided by GO Transit. The

average commuting distance per bus ride is about 40 kilometres, with an average headway of 45

to 60 minutes. Since 2003, the annual ridership of GO Transit buses has increased by 19% (GO

Transit 2008a). This ridership increase is mainly because of higher gasoline prices as well as

higher parking rates in the CBD. In addition, starting from July 1, 2006, the federal government

of Canada offers tax credit for public transit passes, which also encourages more regular car

users to take public transport (Government of Canada 2006).

It is expected that regional transit systems will play an increasingly important role as a key

transportation mode for North American residents to commute between suburban areas and the

CBD. Many commuters, however, are still reluctant to take regional transit owing in part to the

relatively long headways of regional buses – approximately 45 to 60 minutes. If a passenger

misses the current bus, he/she would either have to wait a long time for the next bus, or use an

alternate mode of transportation to travel to his/her destination. Passengers are also concerned

about bus delays. Since regional buses run along freeways and arterials with mixed traffic, they

face a high risk of delays owing to traffic signals and congestion. Severe weather conditions and

incident blockages may also cause bus delays. In addition, regional transit schedules are

typically time- and space-constrained, as they operate at limited times of the day with very few

stops along each line. These factors have all contributed to the reluctance of many commuters to

choose regional buses to travel from suburban areas to the CBD.

2

The Intelligent Transportation System (ITS) is a set of methodologies and technologies applied

to transportation. Such methodologies are designed to reduce accidents, save time and money

spent on commuting, and reduce the pollution caused by transportation. Advanced Public

Transport Systems (APTS) include a number of technologies and services to enhance the quality

and efficiency of public transit systems. One such technology is the Advanced Traveller

Information System (ATIS), which assists transit agencies in disseminating transit arrival time

information to travellers through websites, mobile services or Light Emitting Diode (LED)

displays at bus stops, to achieve the goal of reducing travellers’ actual and perceived wait time at

bus stops. Since passengers’ wait time is more costly than passengers’ in-vehicle time,

implementing the ATIS would reduce the cost of delays (Ben Akiva and Lerman 1985).

Through the APTS, public transit agencies can save travellers’ time and money, and encourage

more regular auto users to switch to these regional buses. Transit riders are always interested in

dynamic transit information when bus frequency is fewer than four per hour (Lin and Bertini

2002).

Over the past decade, several researchers have developed predictive models to estimate

travel/arrival time of city bus services with very little attention given to regional bus applications

which have unique and distinct operational characteristics such as long commuting distances,

long headways, and susceptibility to traffic delays on freeways and arterials owing to weather

conditions, road constructions and incidents.

A well-developed bus arrival time prediction model can benefit various stakeholders, particularly

regional bus operators and users, local transit agencies that provide feeder bus services to

regional bus passengers to commute within the suburban communities, government agencies in

the GTA, and industries related to the ITS. Table 1-1 to Table 1-3 provide a summary of such

benefits.

3

Table 1-1: Benefits to Transit Related Users and Associated Individuals

In-Vehicle GO Bus Passengers • Would be informed when the bus will arrive at the final destination • Gain the impression that GO bus services are more reliable • Able to modify their plans immediately if the bus experiences delays owing to traffic

conditions GO Bus Passengers Waiting at Bus Stops

• Receive information on when the next bus will arrive • Able to manage their time more wisely in case of bus delays, e.g. go somewhere to keep

themselves warm if it is very cold or snowing outside, or run an extra errand • Receive other GO Transit information while waiting for the next bus to arrive • Able to choose other modes of transportation if bus delay is severe or if they miss the

current bus Passengers on Local Transit Buses

• Would be notified by a public address system how long they have to wait for the GO bus to arrive if the local transit arrives earlier than scheduled time; different operational strategies can be implemented

Drivers who Pick-up/ Drop-off GO Bus Passengers • Able to save wait time if the bus is delayed; can simply go to the station later • Able to check real-time arrival information through web page and/or other

telecommunication devices • Higher utility to provide carpool services to family and friends • Minimize traffic congestion at passengers’ pick-up/ drop-off facilities • Reduce air pollution created by cars at passengers’ pick-up/ drop-off facilities

Table 1-2: Benefits to GO Transit

GO Transit Managements • Increase ridership • Gain revenue • Raise GO Transit’s reputation • Share information on other GO Transit services at bus stops • Promote sustainability to the general public • Save passengers’ wait time • Save GO bus delay costs • Assist planners in revising bus schedules periodically • Cooperate with other local transit agencies to implement bus holding strategies and local

transit transfer schemes GO Bus Drivers

• Able to inform in-vehicle passengers when the bus will arrive at the destination • Adjust bus running speed when the bus is ahead or behind schedule • Receive bus route guidance information to avoid traffic congestion • Experience less pressure from transit users complaining about bus delays • Prioritize safety while driving without having to worry about when the bus will arrive at

the final destination

4

GO Transit Control Centre Operators • Able to provide assistance to GO bus drivers and in-vehicle passengers • Provide real-time routing guidance to bus drivers

Table 1-3: Benefits to Other Users

Local Transit Agencies • Increase bus ridership • Gain revenue • Experience fewer bus delays owing to car usage reduction on roads • Raise reputation of local public transit • Able to cooperate with GO Transit on implementing bus holding strategies • Assist in managing their own bus schedules

Governments • Minimize car usage on roads; improve congestion problems • Decrease car ownership • Reduce environmental and health impacts caused by air pollution • Promote sustainability to the general public • Create new jobs such as real-time information providers and consultants

General Public • Have more motivation to take GO buses • Experience less traffic on travel between suburban areas and the CBD • Experience fewer environmental and human health problems caused by air and noise

pollution

1.2 Thesis Objectives The objective of this study is to develop a dynamic mathematical model to estimate regional bus

journey time using an Artificial Intelligence (AI) based approach. The research consists of two

parts. The first part develops a model based on the Artificial Neural Network (ANN) approach

to update bus arrival time using real-time Global Positioning System (GPS) coordinates of the

current bus and also real-time highway loop detector data of volume, speed and occupancy. The

second part of the project involves an assessment of the model performance relative to other

prediction approaches, including a historical average model and linear regression model.

Following development and assessment of the final model, an operational strategy is integrated

into the model, which aims at minimizing the costs of misprediction to both transit users and bus

operators.

5

1.3 Thesis Scope The scope of this research is limited to one GO Transit bus route in the GTA, which stretches

between the Square One Bus Terminal in Mississauga (to the west of Toronto) and the Union

GO Bus Terminal in downtown Toronto. Two different bus routing paths in both directions have

been considered. Depending on traffic conditions reported by other drivers or transit control

centre operators, bus drivers can divert from the Gardiner Expressway (the main commuting

corridor) to Lakeshore Boulevard (a parallel arterial). Figure 1-1 shows a map of the study route

and the locations of bus stops. A variety of data sources are used for this research project. They

include historical and real-time loop detector data on roadways, daily weather conditions,

historical and current bus GPS locations, and incident information logged by the traffic control

centre operators, such as the type of incident, incident start and end time, and the number of

lanes blocked.

(Google Inc. 2009)

Figure 1-1: Study Route and Bus Stop Locations Map

1.4 Thesis Organization The thesis is divided into eight chapters. A literature review is presented in Chapter 2. This

review describes past research efforts in developing travel time prediction models for various

transportation modes such as freeway traffic, local buses and school buses. Chapter 3 describes

the data sources used in this research project. Chapter 4 illustrates how the bus travel time is

computed on the basis of the GO buses’ GPS data. Various factors affecting buses’ travel time

and the calibrated model’s limitations are also discussed. In Chapter 5, a brief summary of the

6

theory of artificial neural network (ANN) is provided. Two ANN models – direction-based and

location-based, are calibrated and their estimation performances are evaluated. Chapter 6

presents an assessment the comparative performance of the proposed model relative to other

prediction approaches – historical average and linear regression models. An operational strategy,

which aims to avoid the misprediction problems created by the developed models and to

minimize stakeholders’ wait time costs, is discussed in Chapter 7. The chapter also establishes a

Graphical User Interface (GUI) platform for real-life application. Chapter 8 includes the

conclusions of the thesis and recommendations for improving the calibrated model’s results and

benefits.

7

Chapter 2 Literature Review

2 Literature Review This chapter presents a review of various travel time estimation efforts. The objective of this

task is to investigate various existing methodologies that forecast vehicle and bus travel times

and external factors that may affect the travel time estimation.

Chien et al. (2002) categorized travel time prediction models into three main types: univariate,

multivariate and Artificial Neural Network (ANN). Univariate models are models with results

that are based on historical traffic data. The multivariate model’s travel time forecast is

explained by a mathematical function with respect to a set of independent variables. Lastly, the

ANN is a “black box” system that is built with a non-specified mathematical structure. Of

course, there are other methods developed by other researchers.

The remainder of this chapter is divided into four sub-sections, which describe and discuss the

various techniques used to develop travel time estimation models by past researchers: Section 2.1

– univariate models; Section 2.2 – multivariate models including regression models and Kalman

filtering models; Section 2.3 – Artificial Neural Network with different training techniques; and

Section 2.4 – Other methodologies that have not been discussed.

2.1 Univariate Models Univariate models can be categorized into historical average models and time series models. A

link travel time prediction model for an urban traffic control (UTC) network was designed by

Anderson et al. (1994) using the Autoregressive Integrated Moving Average (ARIMA) approach.

The outcome of the travel time model could assist transit service providers with bus management

and provision of passenger information. Two different models were designed and evaluated by

the authors. The first model was based on information of the previous 11 vehicles passing

through the intersections while the second model was based on the predicted and actual link

travel time of the preceding vehicle (Anderson et al. 1994). Overall, the second model included

much simpler procedures without losing any predictive accuracy. Nevertheless, in the model

calibration, all vehicles including cars, buses and heavy duty vehicles were assumed to

8

decelerate to a complete stop and accelerated to a certain running speed at a constant rate, which

does not reflect the real operations.

Van Arem et al. (1997) utilized on-site loop detectors to collect traffic data and then applied a

linear input-output ARIMA model to predict travel time on freeways in the Netherlands. In this

project, the proposed algorithm was separated into two parts. The first part was intended to

determine if there was traffic congestion. If the freeway was not congested, the travel time

through the freeway link would be determined from the link distance and the free flow speed of

120km/hr. If the roadway was congested, the ARIMA model would then be used to predict the

new traffic volume leaving the link. Van Arem et al. (1997) applied these new traffic volumes to

a mathematical function and estimated the travel delay time. The final travel time was calculated

as the sum of traffic delay and the free flow traffic travel time.

Univariate models usually have a short time lag in the predicted real-time bus journey time

(Patnaik et al. 2004). Moreover, the accuracy of the prediction results changes according to the

variation of the historical average results from previous trips (Smith and Demesky 1995).

2.2 Multivariate Models

2.2.1 Regression Models

Regression modelling is a simple and direct travel time estimation technique. This method has

been applied to estimate traffic travel time along arterials and freeways, and transit travel time

and delay.

Travel time prediction models on multilink streets in the CBD of medium to large cities were

developed by Frechette and Khan (1997), using a Bayesian regression approach. Several video

cameras were used to collect traffic data on streets. Four different types of models were

generated with respect to various street networks. Travel times were estimated based on counts

of turning movements at intersections, average number of signalized intersections per kilometre,

percentage of heavy vehicles on road, and average transit flows on links (Frechette and Khan

1997). When all four models were compared, the one-way street travel time model’s prediction

was found to have the smallest error value. Video camera installation for data collection was

not, however, as dependable as loop detectors. The camera images could be affected by sunlight

and fog, directly impacting the accuracy of the travel time prediction.

9

Abdelfattah and Khan (1998) developed a nonlinear regression model to estimate bus delays.

The bus route was divided into different links in the model. The explanatory variables

considered to affect bus delays included link length, number of bus stops per link, total traffic

density on each link and bus efficiency ratio estimates (Abdelfattah and Khan 1998). Dwell time

and the number of passengers boarding buses, however, which were also relevant factors for bus

delay prediction, were excluded from the model’s calibration process. In addition, bus delay

time was estimated in a link-based format. Therefore, the overall delay experienced by a bus in

reaching its final destination would be the sum of delay estimates for individual links. Thus, the

error of the delay estimation would be propagated downstream of the bus routing path (Chen and

Chien 2001).

Kwon et al. (2000) developed a linear regression model to estimate travel time on a freeway

using flow and occupancy data collected from loop detectors and historical travel time

information collected from probe vehicles. Owing to the limitations of loop detectors such as

technical problems or impacts by weather conditions, some data were lost, and the interpolation

of data from adjacent stations was required. All detectors for the proposed model development

were required to be equally spaced. In real life, however, loop detectors on freeways are usually

spaced irregularly. This caused the proposed model’s results to be unrealistic. The authors

emphasized that simple prediction models such as linear regression models were useful for short-

term forecasts, but long-term travel time prediction required historical data. Final findings were

dependent on the availability of probe vehicles or other similar high-quality data (Juri et al.

2007). This approach would be costly if many probe vehicles were required to collect data along

freeways in order to develop a highly reliable model (Juri et al. 2007). The proposed model

outperformed the ANN with higher accuracy. The ANN model results could be improved,

however, if more combinations of network structures and training methods were applied (Kwon

et al. 2000).

A multivariate linear regression model to estimate bus arrival time between two points along a

route was developed by Patnaik et al. (2004). In order to include the dwell time in the bus delay

estimation, the authors installed an Automatic Passenger Counter (APC) on buses to count the

number of people getting on board and the time taken. The proposed regression model was

explained by attributes of distances between points, average dwell time, number of bus stops

along the path and time periods (Patnaik et al. 2004). Owing to limited wireless

10

telecommunication technology on buses, the APC data could only be downloaded after the bus

had reached the garage or the bus terminal. As a result, the travel time prediction cannot be

updated on a dynamic basis. Furthermore, models were categorized into different time periods

(Patnaik et al. 2004). Bus travel time also depends on traffic congestion conditions and ridership

along the route. Because there are more alighting and boarding passengers during rush hours,

parameters used for each variable during such time periods should be different from those used

during the non-rush hours.

Even though regression models are easy and simple to apply, they suffer from several

limitations, the biggest being that many variables in transportation are highly correlated (Jeong

and Rilett 2004). Moreover, regression models are not capable of estimating dynamic travel

time, and hence the bus arrival time estimates may not be responsive to poor weather conditions

or traffic incidents. Last but not least, regression models are site specific and have to be

recalibrated for various environments (Liu and Ma 2007). This increases the time and costs

needed to implement them.

2.2.2 Kalman Filtering Models

To overcome the weaknesses of univariate and regression models, dynamic algorithms could be

developed to predict bus arrival times (Patnaik et al. 2004). The Kalman filtering model, an

alternative approach to predicting travel time, enables utilizing real-time data to predict up-to-

date bus arrival time.

A study to compare travel time prediction accuracy on buses using the Kalman filtering and the

statistical averaging models was completed by two British researchers, Reinhoudt and Velastin

(2001). Research findings showed that the Kalman filtering model’s overall absolute mean error

was 7% lower than the statistical averaging algorithm (Reinhoudt and Velastin 2001). The

adaptive parameters developed by the Kalman filtering model could respond very quickly to

unforeseeable traffic changes. Hence, the use of this model to estimate travel time could provide

reliable traveller information to users and enhance bus ridership. Recently, the use of AVL

technologies such as GPS devices has grown in popularity. For example, some new buses in

London are already equipped with GPS devices, provided to transit agencies at no extra cost

(Reinhoudt and Velastin 2001). Hence, the infrastructure costs of APTS technologies in public

11

transit would not be as high as one might expect. The GO buses analyzed in this thesis are

mostly equipped with GPS devices as well.

Shalaby and Farhan (2003) used both AVL and APC data to design a bus travel time prediction

model. The proposed model was developed by two Kalman filtering algorithms to predict local

bus run time and dwell time between checkpoints. Dwell time was identified as a major factor

affecting bus schedules (Shalaby and Farhan 2003). The length of dwell time impacted bus

passengers who were already in the bus and travellers who were waiting at bus stops

downstream. Different from other research efforts, the separation of dwell time from run time

could enhance the model’s suitability to capture the effect of lateness or earliness in bus arrivals

(Shalaby and Farhan 2003). Nevertheless, the variation of dwell time at each time-point stop

could reduce the accuracy of travel time estimation (Jeong and Rilett 2004). Furthermore, the

authors compared the proposed model with other forecasting models, including the linear

regression model and the ANN. They demonstrated that the Kalman filtering model provided

better results particularly in the scenarios involving special events and incidents (Shalaby and

Farhan 2003).

A freeway travel time prediction model was proposed by Chien et al. (2003) with the aid of the

Kalman filtering algorithm in South Jersey, NJ. The authors indicated that drivers tend to rely on

their own experiences when deciding which route to take in the absence of traffic condition

information. The aim of the study by Chien et al. (2003) was to divert some drivers to take a less

congested route into Philadelphia, PA, if the travel time along one of the bridges was longer than

a threshold value. The Kalman filtering algorithm was chosen because it could continuously

update the travel time prediction. The model evaluation was only performed, however, with

simulations. In-field application should be tested in order to confirm the performance of the

proposed model.

Vanajakshi et al. (2008) employed buses as probe vehicles to predict short-term travel time in

India with the aid of the Kalman filtering method. GPS devices were installed on three

consecutive buses running along the same route, so that all bus locations could be collected.

Thirty days of peak hour data were collected. The first vehicle’s data were used to estimate the

adaptive Kalman filtering parameters. The second bus was identified as a real-time data provider

to update the new bus location and its travel time. With the data of the first two buses, bus travel

12

time could be estimated and compared with that of the third bus, which was used as a test

vehicle. The proposed model was compared with the historical average method, and the

proposed algorithm outperformed the average approach by 8.4% (Vanajakshi et al. 2008).

During the rush hour, the headway between buses was only approximately 15 minutes, and it

was practicable to update real-time bus schedules using data from the previous bus. Once this

model is applied to bus services during off-peak hours or late evening periods, which typically

involve long headways, the error would increase (Vanajakshi et al. 2008). Hence, the Kalman

filtering approach would demonstrate superior results only when predicting one or two time

periods ahead in the future. It may not be suitable for regional buses because the headways were

always between 45 and 60 minutes. Also, Vanajakshi et al. (2008) planned to apply buses as

probe vehicles to estimate travel time for general traffic along the Indian road network. Stopping

was required for boarding and alighting of bus passengers at bus stops, however, so this method

would not be suitable to represent generic traffic performances.

2.3 Artificial Neural Networks The ANN can model complicated input and output relationships, without specifying the form of

an explicit function. Another advantage of ANN-based models is that they do not require

independencies among input variables (Chen et al. 2007), like regression models. Currently,

there are many methodologies to train ANNs. One of the common training methods is the

backpropagation training approach. This algorithm is responsive to dynamic, non-lagging, and

over-prediction conditions (Smith and Demetsky 1994).

Chien et al. (2002) developed two ANNs (one trained on link-based data and another on stop-

based data) to study which model had the better travel time estimation performance. The stop-

based model had a lower Root Mean Square Error (RMSE) than the link-based model. It also

had a higher capacity to accommodate stochastic conditions at stops further downstream than the

link-based model. Moreover, the stop-based ANN was suitable for scenarios where there were

multiple intersections between stops while the link-based algorithm was more suitable for many

stops with few intersections. Based on the analysis, an enhanced ANN was developed with a

combination of link-based and stop-based data (Chien et al. 2002). The aim of this new ANN

approach was to improve computational efficiency and prediction performance while adapting to

a dynamic environment, without the requirement for retraining. As regards the overall

13

performance, the enhanced ANN was better than the other two without adaptive features. This

project concluded that both AVL and traffic data were key inputs to ensure high levels of

prediction accuracy. Nevertheless, this project was only conducted in a simulated traffic

environment, without being tested on actual traffic data.

Subsequently, Jeong and Rilett (2004) and Chen et al. (2007) used the backpropagation training

method to generate ANNs. Both models were compared with other estimation models, including

historical average and linear regression models, in terms of prediction accuracy. Although

results obtained from the backpropagation training method were reliable, this training method

had shortcomings including long computation time, very slow convergence rate, and arbitrary

problems resulting from the selection of learning and momentum ratios (Hung and Adeli 1994).

In addition, there are several alternative types of neural networks for estimating travel time. Yu

et al. (2006) used a support vector machine (SVM) approach to predict bus arrival time.

Training SVM was equivalent to solving a linearly constrained quadratic programming problem.

The approach provided a unique and global optimal solution (Yu et al. 2006). The training

procedure for this method was faster when compared with the other ANNs. In the research, the

proposed model trained by SVM outperformed the model using backpropagation by

approximately 6% in four different scenarios (Yu et al. 2006). The SVM approach did not have

an over-fitting problem if proper parameters were selected.

Dharia and Adeli (2003) used a counter-propagation neural (CPN) network to estimate freeway

link travel time. This method’s computational time was shorter than that of the backpropagation

neural network algorithm because the CPN algorithm’s training pattern was localized to the

weight of its winning node only (Dharia and Adeli 2003). Furthermore, results obtained by both

CPN and backpropagation had the same level of accuracy.

Overall, the ANN method employed for travel time estimation gave superior results for three to

five time periods into the future (Yu et al. 2006). Most of the models, however, were only tested

in a simulation environment. Also, the ANN model itself lacks transparency (Liu and Ma 2007).

ANNs require a very long training time in order to find the optimum network structure for the

sampling data. If the ANN learns the training data too well, the network memorizes the data and

gives incorrect results (Hung and Adeli 1994). Input variables to the network also depend on the

researchers’ experience and knowledge (Mohamad-Saleh and Hoyle 2008). Even though the

14

variables do not have to be independent of one another, the best input variable candidates should

maintain a correlation between 0.2 and 0.95 (Innamaa 2005). Lastly, an increasing number of

hidden layers could reduce the network’s ability to make a better ANN (Chen et al. 2004).

Hence, one or two hidden layers are usually used when creating a neural network model.

2.4 Other Forecasting Models Some researchers have applied other techniques to predict bus and other vehicle arrival and

travel time. Lin and Zeng (1999) developed four algorithms to determine which combination of

data should be used to forecast bus arrival time in rural areas. In such settings, bus headways

were similar to those of regional buses, which could be as long as one hour throughout the day.

To avoid duplication of segments on bus routes, segments were represented by means of links

and nodes. In the generation of the four proposed models, GPS data of bus locations were

employed to estimate bus delays. As regards the overall prediction accuracy, robustness and

stability among all four algorithms, the one using GPS data of bus locations, bus schedule, delay

between the current and scheduled time at the destination and time stopping at checkpoints was

the best (Lin and Zeng 1999). In addition to the proposed algorithm development, dwell time at

checkpoints was identified as the most significant factor affecting the algorithm’s performance.

Also, as this algorithm did not have a fixed sample time period, the accuracy of the prediction

could be reduced (Chen et al. 2004). Although the final model’s estimation accuracy is high,

there may be the possibility of travel time overestimation. This means that the actual bus arrival

time is earlier than the predicted time, causing bus users who rely on the ATIS to miss the bus

and wait an hour for the next one to arrive. An effective operational strategy must be considered

when an estimation model is implemented, so that fewer people would miss the bus when they

rely on the reported estimated time.

Chung and Shalaby (2007) used GPS location data to develop an expected arrival time system

for school transit. The operation of school buses is similar to that of regional buses in that their

run time and dwell time can be combined because each stop can be assumed to have stable

demand and thus have very little variation of dwell time. Highly reliable school bus arrival time

information would benefit students and their parents. The authors used a combination of the

historical GPS data over the previous seven days and the current day’s operational conditions to

estimate the arrival time of school buses (Chung and Shalaby 2007). The deployment of this

15

model, however, also created errors when the authors estimated the bus arrival time at

downstream stops. The estimation of these downstream stops depended on the prediction from

the first stop. Error at the first stop could be propagated to downstream bus stops. The proposed

model outperformed other common predictive models, including historical average and

regression models. To improve the current model, more analysis of the relationship between

weather conditions and traffic performances was recommended (Chung and Shalaby 2007). An

operational strategy of announcing the school bus expected arrival time three minutes earlier

than the estimated time was developed to avoid overestimation problems. This technique

allowed more than 97% of students to catch the school bus (Chung and Shalaby 2007).

The Kalman filtering and the ANN approaches were combined to develop a model to predict

dynamic bus arrival time (Chen et al. 2004). In this study, the authors separated the model into

two parts. The first part was an ANN using APC data, bus operating time and weather data. The

second part applied the Kalman filtering algorithm to update the arrival time estimate using real-

time bus location information. In some cases, bus operators might skip certain stops if there was

no passenger waiting or if it was a special bus service. The author interpolated the missing data

from the available information at upstream and downstream points by assuming that travel speed

remained constant between the two consecutive time points (Chen et al. 2004). Test runs were

performed to compare results obtained by this enhanced technique with other methods. The

experiments showed that the estimation by the new model outperformed the predictions using the

Kalman filtering and the ANN algorithms individually (Chen et al. 2004). Since, however, the

Kalman filtering algorithm requires information from the previous buses to estimate the current

bus travel time, this may not be applicable for the current research project when frequency of

regional buses is very low. The use of the preceding regional bus to predict the travel time of the

current one is not practical for this research.

Palacharia and Nelson (1999) applied a fuzzy logic and neural network model to estimate

dynamic travel time. Various occupancy and flow data collected by loop detectors were

identified as fuzzy input variables. Through the fuzzy neural network analysis, input variables

were converted into arterial link travel time. The advantage of using a fuzzy logic model was

that it could capture nonlinear relationships between inputs and outputs (Palacharia and Nelson

1999). When results are compared with those of the linear regression analysis, the proposed

16

model has more accurate predictions and higher modelling flexibility. Training the fuzzy neural

network was, however, very time-consuming.

After comparison of the various approaches used in previous research efforts, the ANN seems to

be the most suitable approach to use for this research owing to its dynamic structure, ability to

work with inter-dependent input variables, and facility for handling buses with long headways.

More detailed studies on the ANN are provided in later sections.

17

Chapter 3 Data

3 Data This chapter describes the data used to develop the regional bus arrival time prediction models

and the sources of such data.

3.1 Data Collection In this research project, all relevant data are collected from public and academic institutions.

Table 3-1 summarizes the data obtained for this research and their respective sources.

Table 3-1: Summary of Data Types and Resources

Data Public Agency(ies)/ Academic Institution(s)

Bus Schedule • GO Transit, operated by Greater Toronto Transit Authority

Global Positioning System (GPS) Data of Bus Locations

• GO Transit, operated by Greater Toronto Transit Authority

Freeway Loop Detector Data including Speed, Occupancy and Volume

• Ministry of Transportation of Ontario • City of Toronto • University of Toronto’s ITS Centre and Testbed

Incident Reports • City of Toronto • University of Toronto’s ITS Centre and Testbed

Historical Daily Weather Conditions • Environment Canada

3.1.1 Bus Schedules

The GO Bus schedules used in this study were listed on the GO Transit web page (GO Transit

2008b). GO Transit provides three different schedules to commuters – weekday, Saturday, and

Sunday/holiday. It adjusts bus schedules regularly to meet seasonal demands from customers.

3.1.2 Global Positioning System (GPS) Data of Bus Locations

The GPS data were provided by the regional bus service provider in the Greater Toronto Area,

known as GO Transit, which is operated by the Greater Toronto Transit Authority. A GPS

device installed on each GO bus collects and saves the bus latitude and longitude every minute

along the study route. In addition to the bus location information, the GPS device also collects

the speed of the bus.

18

3.1.3 Loop Detector Data

Along the study routing path in both directions, regional buses travel four road segments, namely

arterial roads in the City of Mississauga, a short section of the Queen Elizabeth Way (QEW), the

Gardiner Expressway and Lakeshore Boulevard. The first two roadway segments and

approximately half of the third roadway segment are fixed along which buses must travel in all

weather and traffic conditions. At some points along the Gardiner Expressway, GO buses may

continue on the Gardiner Expressway or shift to the Lakeshore Boulevard corridor to their

terminal destination depending on traffic conditions as advised by other drivers or control centre

operators.

The road networks are operated by different jurisdictions. Specifically, all arterials in

Mississauga are operated and maintained by the City of Mississauga, the QEW is under the

jurisdiction of the Ministry of Transportation of Ontario (MTO), and the Gardiner Expressway

and Lakeshore Boulevard are under the jurisdiction of the City of Toronto. Figure 3-1 shows

each agency’s jurisdiction route on which regional buses travel.

(Google Inc. 2009)

Figure 3-1: Transportation Agencies’ Jurisdiction Area

The QEW and the Gardiner Expressway are separated by a north-south freeway, Highway 427,

which is also under the jurisdiction of the MTO. Highway 427 and the QEW have posted speed

limits of 100km/hr. The Gardiner Expressway and the Lakeshore Boulevard’s posted speeds are

90km/hr and 60km/hr, respectively. Since all networks are under different jurisdictions, their

19

traffic management centres are also coordinated independently. Figure 3-2 illustrates these

freeway locations on the west side of Toronto.

(Google Inc. 2009)

Figure 3-2: Toronto West Freeway Network

Many loop detectors are imbedded under pavements along the freeways as well as Lakeshore

Boulevard. These loop detectors are separated by a typical distance ranging from 0.6km to

0.8km, or located at an approximate distance of 0.1km before the stop bar at individual

intersections along the Lakeshore Boulevard. Table 3-2 presents the overall number of detectors

used along each section.

Table 3-2: Summary of Loop Detectors along the Freeways and Lakeshore Boulevard

Freeways/ Lakeshore Boulevard

Direction (Eastbound/Westbound)

Number of Detectors Available

Locations

QEW Eastbound 2 • The West Mall • Highway 427

QEW Westbound 2 • The West Mall • Highway 427

20

Freeways/ Lakeshore Boulevard

Direction (Eastbound/Westbound)

Number of Detectors Available

Locations

Gardiner Expressway

Eastbound 9 • Ellis Avenue • Colborne Lodge Road • Parkside Drive • Dowling Avenue • Jameson Avenue • Dunn Avenue • Dufferin Street • Strachan Avenue • Spadina Avenue

Gardiner Expressway

Westbound 6 • Strachan Avenue • Dufferin Street • Dowling Avenue • Parkside Drive • Colborne Lodge Road • Ellis Avenue

Lakeshore Boulevard

Eastbound 4 • Windermere Avenue • Parkside Drive • BC Drive • Newfoundland Drive

Lakeshore Boulevard

Westbound 7 • Rees Street • Stadium Road • Ontario Drive • BC Drive • Dowling Avenue • Colborne Lodge Road • Ellis Avenue

In the early 2000s, the City of Toronto agreed to share its traffic-related information such as loop

detector data and incident reports with the University of Toronto’s ITS Centre and Testbed.

Subsequently, the University of Toronto’s ITS Centre and Testbed developed an ITS Centre and

Testbed (ICAT) platform in 2005. This platform is able to transfer and output the traffic

information into a HyperText Markup Language (HTML) format. Only registered and academic

research users are permitted to use this platform. In this research, all data collected by loop

detectors imbedded in the Gardiner Expressway and Lakeshore Boulevard were obtained from

the ICAT platform. Since the QEW loop detector data are not available from the ICAT, they

were obtained from the MTO instead.

21

When a detector is in operation, it collects traffic data every twenty seconds and transfers the

data to the traffic control centre for analysis. Control centre operators use different software

programs developed by transportation departments to determine how the road networks perform

and apply responsive plans to resolve congestion problems such as displaying variable messages

and sending police to scenes of incidents for further intervention. These loop traffic data include

travel speed, volume and occupancy. Occasionally, detectors on freeways are not accessible

owing to technical problems or being powered off.

No traffic information on Mississauga’s arterials could be obtained. Therefore, no loop detector

data at intersections of major arterials are included in this research project. This lack of

Mississauga traffic information may limit the model’s applicability. More discussion on data

limitations impacting the model development can be found in Section 4.3.

3.1.4 Incident Reports

The ICAT platform can display incidents’ information logged by traffic control centre operators.

The operators monitor incidents happening through closed circuit television cameras (CCTV),

which are widely installed on the freeways and Lakeshore Boulevard in Toronto. Once an

incident is detected or reported by individuals, the control centre operators will pan the CCTV

camera to the incident scene to confirm and log the incident information on the server. If the

incident is severe, the operators will report it to emergency departments and tow trucks, so that

they can provide immediate assistance to the road users involved. This action can also ensure

that other road users are safe from the incident.

In general, incident information includes the start and end time of an incident, number of lanes

with blockage, location of the incident and the type of incident, whether collision, disabled

vehicle or road work. Incident information is only available on the Gardiner Expressway and

Lakeshore Boulevard.

3.1.5 Historical Daily Weather Conditions

Some drivers may slow down their vehicles under sudden severe weather conditions such as

snowstorms and thunderstorms. Environment Canada posts daily and hourly historical weather

data since the 1950s on its web page (Environment Canada 2008). The weather data included in

this research are:

22

• Daily Rainfall (mm)

• Daily Snowfall (cm)

• Daily Total Precipitation (mm)

• Daily Accumulated Snow on Ground (cm)

• Hourly Visibility (km)

In addition to the quantitative data, the agency also indicates the hourly weather conditions with

a descriptive term such as “Clear”, “Cloudy” or “Snow”. In order to incorporate these hourly

descriptive terms into the model development, this project used the terms defined by Chung and

Shalaby (2007) to identify bad weather conditions. Bad weather conditions are defined to have

descriptive terms of:

• Freezing Drizzle

• Freezing Rain

• Heavy Rain

• Heavy Snow Showers

• Thunderstorms

• Ice Pellets

• Snow

• Snow Shower

• Blowing Snow

• Snow Grains

• Snow Pellets

23

• Moderate Snow

The rest of the weather description terms are considered to be “Good” weather conditions.

24

Chapter 4 Travel Time Computation and Descriptive Analysis

4 Travel Time Computation and Descriptive Analysis This chapter describes the method used to compute the bus travel time between checkpoints.

The historical bus travel time under various conditions, including time period, day of the week

and weather conditions, is also analyzed. Last, this chapter discusses the data limitations and the

implications for the suitability for the model to predict regional bus transit travel time.

4.1 Regional Bus Journey Time Computation This section describes the regional bus journey time calculation procedure based on data

collected from GPS devices. Three major steps are performed to calculate the bus travel time.

First, checkpoints along the bus route are identified. Second, distances between the bus current

location and the checkpoints are calculated. This distance computation can assist the author to

determine the exact time when the bus departs from checkpoints. Third, when all checkpoint

departure times are obtained, the travel time between checkpoints can be computed.

4.1.1 Checkpoint Identification

Checkpoints are defined as passenger attraction points such as bus stops and other key locations

along the bus travel path, including key loop detectors locations and freeway interchanges. The

exact GPS coordinates of these checkpoints should also be easily obtainable from transit

operators or other recognized sources.

In this research, checkpoint coordinates were provided by GO Transit and the ICAT platform.

Along the study route of this project, regional buses only stop at four major bus stops, which are:

• Square One Bus Terminal, Mississauga

• Cooksville GO Station, Mississauga

• Dixie GO Station, Mississauga

• Union GO Bus Terminal, Toronto

25

In addition to these major stops, loop detectors on freeways and Lakeshore Boulevard listed in

Table 3-2 are also classified as regional bus journey time prediction checkpoints in this study.

Table 4-1 summarizes the overall number of checkpoints on each routing path and Table 4-2 to

Table 4-5 present all checkpoints’ coordinates on the Gardiner Expressway and the Lakeshore

Boulevard corridors. Figure 4-1 and Figure 4-2 illustrate the locations of all checkpoints along

eastbound and westbound directions, respectively.

Table 4-1: Number of Checkpoints on by Route Segment

Route Segment Direction Number of Checkpoints, including Stops and Loop Detector Points

Gardiner Expressway Eastbound 15 Gardiner Expressway Westbound 12 Lakeshore Boulevard Eastboud 8 Lakeshore Boulevard Westbound 11

Table 4-2: Coordinates of the Checkpoints along the Gardiner Expressway, Eastbound

Locations Latitude Longitude Square One Bus Terminal* 43.5934 -79.6419

Cooksville GO Station* 43.5841 -79.6219 Dixie GO Station* 43.6064 -79.5798

The West Mall 43.5979 -79.5675 Highway 427 Interchange 43.6132 -79.5499

Ellis Avenue 43.6373 -79.4647 Colborne Lodge Road 43.6389 -79.4572

Parkside Drive 43.6385 -79.4499 Dowling Avenue 43.6365 -79.4429 Jameson Avenue 43.6335 -79.4358

Dunn Avenue 43.6326 -79.4298 Dufferin Street 43.6346 -79.4223

Strachan Avenue 43.6362 -79.4166 Spadina Avenue 43.6391 -79.3896

Union GO Bus Terminal* 43.6458 -79.3784 *Remark: All loop detector coordinates at GO bus stops are provided by GO Transit; the rest of the checkpoints’ coordinates are obtained from the ICAT platform.

Table 4-3: Coordinates of the Checkpoints along the Gardiner Expressway, Westbound

Locations Latitude Longitude Union GO Bus Terminal* 43.6458 -79.3784

Strachan Avenue 43.6363 -79.4167 Dufferin Street 43.6347 -79.4224

Dowling Avenue 43.6366 -79.4428 Parkside Drive 43.6386 -79.4499

Colborne Lodge Road 43.6390 -79.4573

26

Locations Latitude Longitude Ellis Avenue 43.6375 -79.4648

Highway 427 Interchange 43.6132 -79.5499 The West Mall 43.5979 -79.5675

Dixie GO Station* 43.6064 -79.5798 Cooksville GO Station* 43.5841 -79.6219

Square One Bus Terminal* 43.5934 -79.6419 *Remark: All loop detector coordinates at GO bus stops are provided by GO Transit; the rest of the checkpoints’ coordinates are obtained from the ICAT platform.

Table 4-4: Coordinates of the Checkpoints along Lakeshore Boulevard, Eastbound

Locations Latitude Longitude Square One Bus Terminal* 43.5934 -79.6419

Cooksville GO Station* 43.5841 -79.6219 Dixie GO Station* 43.6064 -79.5798

The West Mall 43.5979 -79.5675 Highway 427 Interchange 43.6132 -79.5499

Windermere Avenue 43.6355 -79.4667 Parkside Drive 43.6382 -79.4556

BC Drive 43.6317 -79.4311 Newfoundland Drive 43.6320 -79.4122

Union GO Bus Terminal* 43.6458 -79.3784 *Remark: All loop detector coordinates at GO bus stops are provided by GO Transit; the rest of the checkpoints’ coordinates are obtained from the ICAT platform.

Table 4-5: Coordinates of the Checkpoints along the Lakeshore Boulevard, Westbound

Location Latitude Longitude Union GO Bus Terminal* 43.6458 -79.3784

Rees Road 43.6396 -79.3886 Stadium Road 43.6360 -79.4012 Ontario Drive 43.6308 -79.4179

BC Drive 43.6322 -79.4303 Dowling Avenue 43.6363 -79.4432

Colborne Lodge Road 43.6384 -79.4568 Ellis Avenue 43.6360 -79.4663

Highway 427 Interchange 43.6132 -79.5499 The West Mall 43.5979 -79.5675

Dixie GO Station* 43.6064 -79.5798 Cooksville GO Station* 43.5841 -79.6219

Square One Bus Terminal* 43.5934 -79.6419 *Remark: All loop detector coordinates at GO bus stops are provided by GO Transit; the rest of the checkpoints’ coordinates are obtained from the ICAT platform.

27

(Google Inc. 2009)

Figure 4-1: Location of Checkpoints along the Gardiner Expressway and Lakeshore

Boulevard Eastbound

(Google Inc. 2009)

Figure 4-2: Location of Checkpoints along the Gardiner Expressway and Lakeshore

Boulevard Westbound

4.1.2 Procedure of Computing Bus Travel Time

Distances between the current bus location and identified checkpoints are computed by the

following equation:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )[ ]r

aababababaD××

++= −

π2360/2sin1sin2cos2cos1sin1cos2cos2cos1cos1coscos 1

28

where D (in km) is a distance between the current bus location and the identified checkpoint. a1,

b1, a2 and b2 (in degrees) are latitudes and longitudes of the two locations, and r (6371.0km) is

the radius of the earth. All calculations are computed with a Macro Program developed in

Microsoft Office Excel 2007.

In the calculation, several criteria are developed to identify the time when the bus departs from

the checkpoint. A 300-metre checkpoint boundary is designed to verify whether the bus has

departed from the checkpoint at the specific time period. In some cases, a bus may be inside the

boundary for several minutes, such as when picking up and dropping off passengers. To

maintain accuracy and consistency, the bus departure time from this checkpoint is determined to

be the time when the calculated distance between the bus and the checkpoint is minimal. Figure

4-3 demonstrates how the above situation occurs. The location of the bus, marked by grey and

black bus symbols, is within the 300-metre boundary circle for more than four minutes. When

the bus is closest to the specific checkpoint, as indicated by the black bus symbol, its respective

time is used as the bus departure time.

Figure 4-3: Checkpoint and Bus Departure Time Determination using a 300-metre

Checkpoint Buffer

29

The above 300-metre checkpoint boundary approach can identify 80% of bus departure times

among all checkpoint locations. The 20% of data that are missing are generally related to

checkpoints located at freeways. Since GPS devices on the buses are only able to collect bus

travel information every minute, assuming that the average speed along freeways is around

90km/hr, it may take less than a minute for the bus to pass several nearby checkpoints. To solve

this problem, a linear interpolation of time measurement is required. Figure 4-4 shows how this

situation could be solved.

Figure 4-4: Example of Missing Checkpoint Departure Time

There are four checkpoints, “#1” to “#4” in the above figure. Using the 300-metre checkpoint

boundary method demonstrated in Figure 4-3, the departure times at Checkpoints #1 and #4 are

calculated. The bus departure times at Checkpoints #2 and #3 are missing, however, owing to

the location of checkpoints and the limitation of the GPS device. In order to determine the bus

departure time at Checkpoints #2 and #3, it is assumed that travel speed of the bus along Link 1-

2, Link 2-3 and Link 3-4 is the same. The departure times at Checkpoints #2 and #3 are then

computed using the distance between checkpoints and the departure time at Checkpoint #1 and

#4 with the equations below:

1)14(2 DTZYX

XDTDTDT +++

×−=

1)14(3 DTZYX

YXDTDTDT +++

+×−=

where DT1,DT2, DT3, and DT4 are bus departure times at Checkpoints #1, #2, #3 and #4. X, Y,

and Z (in km) are distances between Checkpoints #1 and #2, #2 and #3, and #3 and #4,

representatively.

#1 #2 #3 #4

X km Y km Z km

30

Table 4-6 to Table 4-9 summarize the distances between checkpoints along the Gardiner

Expressway and the Lakeshore Boulevard corridors using ArcGIS 9.2 software.

Table 4-6: Gardiner Expressway Eastbound Route’s Distances from the Origin of Square

One Bus Terminal

Locations Distances from Square One Bus Terminal (km) Cooksville GO Station 4.87

Dixie GO Station 10.47 The West Mall 13.35

Highway 427/QEW 15.57 Ellis Avenue 23.03

Colborne Lodge Road 23.67 Parkside Drive 24.27

Dowling Avenue 24.92 Jameson Avenue 25.59

Dunn Avenue 26.11 Dufferin Street 26.78

Strachan Avenue 27.27 Spadina Avenue 30.62

Union GO Bus Terminal 31.35

Table 4-7: Gardiner Expressway Westbound Route’s Distances from the Origin of Union

GO Bus Terminal

Locations Distance from Union GO Bus Terminal (km) Strachan Avenue 3.72 Dufferin Street 4.22

Dowling Avenue 6.02 Parkside Drive 6.66

Colborne Lodge Road 7.25 Ellis Avenue 7.89

Highway 427/QEW 15.41 The West Mall 17.64

Dixie GO Station 19.72 Cooksville GO Station 25.32

Square One Bus Terminal 30.19

Table 4-8: Lakeshore Boulevard Eastbound Route’s Distances from the Origin of Square

One Bus Terminal

Locations Distance from Square One Bus Terminal (km) Cooksville GO Station 4.87

Dixie GO Station 10.47 The West Mall 13.35

Highway 427/QEW 15.57

31

Locations Distance from Square One Bus Terminal (km) Windermere Avenue 22.87

Parkside Drive 23.83 BC Drive 25.98

Newfoundland Drive 27.57 Union GO Bus Terminal 31.21

Table 4-9: Lakeshore Boulevard Westbound Route’s Distances from the Origin of Union

GO Bus Terminal

Locations Distance from Union GO Bus Terminal (km) Rees Road 1.41

Stadium Road 2.52 Ontario Drive 4.06

BC Drive 5.16 Dowling Avenue 6.32

Colborne Lodge Road 7.46 Ellis Avenue 8.28

Highway 427/QEW 15.64 The West Mall 17.87

Dixie GO Station 19.95 Cooksville GO Station 25.55


After the interpolations are performed, each checkpoint has a corresponding bus departure time.

Based on the differences of these bus departure times, the bus journey time from a checkpoint to

another checkpoint can be calculated.

4.2 Regional Bus Journey Time Performance Analysis This section provides a discussion on how GO buses perform under the influence of various

external factors such as time of day, day of week, and weather conditions. The bus route is

separated into four routing paths:

• Gardiner Expressway Eastbound

• Gardiner Expressway Westbound

• Lakeshore Boulevard Eastbound

• Lakeshore Boulevard Westbound

32

Each survey day is divided into four time periods:

• AM Peak (5:30 a.m. to 10:30 a.m.)

• Off-Peak (10:30 a.m. to 4:00 p.m.)

• PM Peak (4:00 p.m. to 8:00 p.m.)

• Late Evening (8:00 p.m. to 2:00 a.m.)

Moreover, GO buses have different weekday and weekend schedules. The bus travel time

performance is studied for both bus schedules. Finally, bus performance under different weather

conditions is also analyzed.

There is no bus service on the Gardiner Expressway and the Lakeshore Boulevard eastbound

direction between 6:30 a.m. and 8:30 a.m. on weekdays, and no bus service on the Gardiner

Expressway and the Lakeshore Boulevard westbound direction from 4:30 p.m. to 7:00 p.m. on

weekdays. During those time periods, GO Transit provides train services for commuters instead,

to accommodate higher ridership levels as well as to avoid congestion on major roadways.

Time-distance diagrams of bus travel on all routes are prepared for different scenarios. In each

diagram, there are four data lines that represent the different statistical measures, including mean,

median, maximum and ninety-fifth percentile of travel times. In addition, the scheduled bus

travel time data points are also shown in each diagram. Table 4-10 summarizes the time-distance

diagrams provided with respect to the appropriate factor given in Appendix A.

33

Table 4-10: List of Bus Travel Time-Distance Figures

Factors Gardiner

Expressway Eastbound

Gardiner Expressway Westbound

Lakeshore Boulevard Eastbound

Lakeshore Boulevard Westbound

AM Peak Figure A-1 Figure A-9 Figure A-17 Figure A-25 Off Peak Figure A-2 Figure A-10 Figure A-18 Figure A-26 PM Peak Figure A-3 Figure A-11 Figure A-19 Figure A-27

Time Period

Late Evening Figure A-4 Figure A-12 Figure A-20 Figure A-28 Weekday Figure A-5 Figure A-13 Figure A-21 Figure A-29 Day of

the Week Weekend Figure A-6 Figure A-14 Figure A-22 Figure A-30 Good Figure A-7 Figure A-15 Figure A-23 Figure A-31 Weather

Condition Bad Figure A-8 Figure A-16 Figure A-24 N/A* *Remark: No bus travels along the Lakeshore Boulevard westbound direction in bad weather conditions in the study.

4.2.1 Gardiner Expressway Eastbound Route

On the Gardiner Expressway eastbound routing path, Figures A-1 to Figure A-4 in Appendix A

show that GO buses have the shortest median journey time to the Union GO Bus Terminal

during the Late Evening time period; the longest median journey time occurs at the PM Peak

period. These figures also illustrate that throughout the bus route, buses always travel at lower

speeds along arterials at Mississauga and Toronto owing to lower posted speed limits. Analysis

is also performed for the impact of day of week, and Figures A-5 and A-6 indicate that the bus

travel time at weekends is shorter than that on weekdays because fewer vehicles are on roads

during weekends.

No significant impact is found on bus journey time in various weather conditions, as illustrated

in Figures A-7 and A-8. These figures also demonstrate that the bus’s travel speed along

arterials in Mississauga in bad weather conditions is only slightly lower than normal. The bus

can recover its travel time back when travelling along freeways. This situation occurs because

fewer people would drive along freeways when the weather is bad. Furthermore, the frequency

of snow removal on freeways is higher than that of arterials, and hence the impact of snow

accumulation on roads is minimal for the overall bus traffic time. This result is similar to past

research work completed by Daniel et al. (2009), who indicated that snowfall and rainfall

impacts decrease as the average speed on the roadway increases.

34

The weather data for this thesis were collected at the Toronto Pearson Airport weather station,

which is approximately 15km away from the Gardiner Expressway. Weather conditions vary in

the region where the data were collected. This means that the weather described on Environment

Canada’s web page may not be exactly the same as what the GO bus experiences on the Gardiner

Expressway. This also might explain why weather conditions do not show a big impact on bus

travel performance. In addition, weather data provided by Environment Canada’s web page are

mostly daily-based – daily rainfall, daily snowfall and daily accumulated snow on ground, except

for visibility and weather descriptive terms, which are provided hourly. It is very difficult to

apply these daily-based data to studying the bus travel time. Therefore, the impact of weather

conditions on bus travel time is expected to be lower than the impact of traffic data collected

from loop detectors at 20-second intervals.

Also, bus travel time data that lie outside of ninety-fifth percentile area are discarded. This

ensures that results are not affected by extreme maximum cases. This is also why the median of

the data set is more appropriate to use than the mean figure. Mean values would provide biased

results under extreme travel time values.

For this particular route, results show that the scheduled bus journey time is always longer than

the median historical travel time. This causes the bus to wait for a long time at each bus stop

until it can depart at the scheduled time. The extended wait time is costly for bus operators and

passengers.

4.2.2 Gardiner Expressway Westbound Route

For the Gardiner Expressway westbound route, Figures A-9 to A-12 illustrate that GO buses take

a longer time to travel during Off-Peak and PM Peak periods. Since very few vehicles travel

outbound to the suburban area during the AM Peak and Late Evening periods, congestion rarely

happens and buses would not experience any delays. Bus travel performance does not show too

much difference with respect to the day of week and weather condition. Similar behaviour is

also observed along the Gardiner Expressway eastbound route. For this route though, bus

scheduled time matches well with the historical median travel time, showing that westbound

buses regularly arrive at major checkpoints on time.

35

As regards the overall bus journey time in both directions, the travel time for the westbound

direction is generally less than the travel time for the eastbound direction during the AM Peak

period. Since fewer road users go to suburbs during the AM Peak period, total travel time along

the westbound direction should be less than that of the eastbound direction. During the Off-Peak

and Late Evening time periods, there is no significant difference in the journey time between

eastbound and westbound directions.

As regards the PM Peak period, one might expect that inbound (eastbound) travel time would be

shorter. Results in Appendix A, however, show that this assumption is incorrect. The eastbound

travel time along Mississauga’s arterials is actually longer than that of the westbound direction,

the reason being that signals tend to favour traffic going towards the suburbs, giving longer green

time phase and thus leading the eastbound traffic to experience longer delays. This extended

delay causes inbound (eastbound) bus travel time to be longer than that of outbound (westbound)

bus trip even though its travel time along freeways is shorter.

4.2.3 Lakeshore Boulevard Eastbound Route

The overall journey time for the Lakeshore Boulevard eastbound route is generally longer than

that of the Gardiner Expressway eastbound route. This could be because of differences of speed

limits on arterials and freeways, as well as delays created by traffic signals and other factors

along arterials such as pedestrian crossings. Among the four service time periods, the longest

bus travel time occurs at the PM Peak period and the shortest at the Late Evening period. Buses

always require longer travel time on weekdays than at weekends. Once again, weather

conditions do not produce noticeable difference in bus performance along the Lakeshore

Boulevard corridor. Finally, the scheduled bus travel time matches better with the actual median

travel time of this Lakeshore Boulevard eastbound route than the Gardiner Expressway

eastbound route.

4.2.4 Lakeshore Boulevard Westbound Route

The Lakeshore Boulevard westbound route’s journey time during the Late Evening time period

is the shortest among all four study periods. Different from the other routes, travel time at

weekends is very similar to travel time on weekdays. As the data set collected does not contain

information of buses travelling along the Lakeshore Boulevard westbound route in bad weather

36

conditions, the impact of the weather variable cannot be studied. Last but not least, the

scheduled bus travel time along this route is shorter than the actual median travel time.

Therefore, if this routing path is chosen, buses are expected to be late in arriving at the final

destination.

4.3 Limitations Limitations of the data obtained impact on the accuracy and utility of the final calibrated model.

These limitations include short study time frames and other issues that are out of the author’s

control such as the wrong incident information provided by traffic control operators and

malfunctioning of loop detectors and GPS devices on buses.

Section 3.1 describes four main types of data that were acquired for the model development.

Only a small subset of data was collected by various agencies at the same time period, however,

and this is presented in Table 4-11. Owing to the limited amount of data provided by the MTO,

the study time period is set to be between 5:30 am and 12:00 noon. In addition, there are very

few buses that travel along the Lakeshore Boulevard corridor during the study period, and hence

the model development for the Lakeshore Boulevard route cannot be done. This research only

focuses on developing a model for both directions, eastbound and westbound, of the Gardiner

Expressway routing path. The analysis segments the eastbound route from different origins

towards a fixed destination, Union GO Bus Terminal; and it segments the westbound route from

a fixed origin to different destinations.

Table 4-11: Data Sources


Data Availability Time Frame

Bus Schedule • Greater Toronto Transit Authority (GO Transit)

All survey days between January and April 2008

Global Positioning System Bus Data

• Greater Toronto Transit Authority (GO Transit)

All survey days between January and April 2008

Loop Detector Data • Ministry of Transportation of Ontario

5:30 a.m. – 12:00 noon. Specifically 37 full days between January and April 2008*

Loop Detector Data • City of Toronto • University of Toronto’s ITS

Centre and Testbed

37 full days between January and April 2008*

37


Data Availability Time Frame

Incident Reports • City of Toronto • University of Toronto’s ITS

Centre and Testbed

37 full days between January and April 2008*

Historical Daily Weather Conditions • Environment Canada All survey days between

January and April 2008 * These survey dates are January 9 to January 18, 2008/ February 8 to February 10, 2008/ March 27 to March 31, 2008/ April 1 to April 16, 2008 and April 28 to April 30, 2008.

On the other hand, weather data are mainly daily-based except for information related to

visibility and descriptive weather information. Owing to this aggregation of data, it is assumed

that all bus samples running on the same day experience the same amount of snowfall or rainfall,

but different visibility, depending on the time of travel. This lack of variation in the weather data

would be expected to decrease the impact of weather conditions on bus travel time.

The travel time between intermediate checkpoints such as “Square One Bus Terminal-to-

Cooksville GO Station” and “Cooksville GO Station-to-Dixie GO Station”, which involves the

use of arterials alone, is not estimated in this research. Since the objective of this research is to

benefit passengers who are taking regional transit to commute between the CBD and the

suburban areas, it is assumed that no passenger would take regional buses for suburban travel

between intermediate points owing to the lack of schedule flexibility and high bus fare. In

addition, since no traffic and incident information can be obtained from the City of Mississauga,

the ability to estimate travel time between intermediate stops is limited.

The final model for the Gardiner Expressway eastbound route can predict the travel time from

the Square One Bus Terminal to Union GO Bus Terminal, from Cooksville GO Station to Union

GO Bus Terminal, and from Dixie GO Station to Union GO Bus Terminal. The estimation of

these travel times is made each time the bus departs from a major bus stop. Once the bus leaves

the last station, Dixie GO Station before the final stop, there is no additional midpoint in

between. This long distance can increase the risk of inaccurate prediction results. Accordingly,

an additional checkpoint is added, so that the bus arrival time at Union GO Bus Terminal can be

updated. The historical bus time-distance diagrams in Appendix A show that buses usually run

at a steady speed along the freeway from Dixie Road to Dufferin Street, and then slow down

until they arrive at the Union GO Bus Terminal. The checkpoint of Dufferin Street is

approximately 6.5km away from the Union GO Bus Terminal with travel time of around eight

38

minutes. The observed change in behaviour of the bus and the central location of Dufferin Street

make it a desirable checkpoint candidate to use between Dixie GO Station and the Union GO

Bus Terminal. This update aims at providing more accurate bus arrival information results.

A similar problem is experienced at the Gardiner Expressway westbound route. When the bus

departs from Union GO Bus Terminal, bus journey times to different destinations, Dixie GO

Station, Cooksville GO Station and Square One Bus Terminal, are predicted using the calibrated

model. Since traffic conditions on freeways vary every second, it is important to rerun the model

with updated data after the bus has travelled for awhile. The freeway interchange at Highway

427 and the QEW is defined as an additional checkpoint for updating bus travel time along the

westbound routing path. Table 4-5 gives a graphical presentation of all these checkpoint

locations.

(Google Inc. 2009)

Figure 4-5: Bus Travel Time Updating Locations

In order to ensure all estimates made at every stop are independent, bus travel time samples are

separated with respect to the major checkpoint locations. This means that data for each bus trip

are separated into multiple segments of origin and destination pairs. For example, along the

Gardiner Expressway eastbound route, “Bus Trip #1” leaves Square One Bus Terminal at 6:50

a.m., departs from Cooksville GO Station at 7:05 a.m., leaves Dixie GO Station at 7:15 a.m.,

passes Dufferin Street at 7:32 a.m., and finally arrives at Union GO Bus Terminal at 7:40 a.m.

The travel time to the Union GO Bus Terminal is separated by stop origin, resulting in the

following travel time segments: 50 minutes from the Square One Bus Terminal, 35 minutes from

39

the Cooksville GO station, 25 minutes from the Dixie GO Station and eight minutes from the

checkpoint of Dufferin Street.

Among all sample trips, approximately half of them have an incomplete set of loop detector data.

A complete set of loop detector data means that all downstream loop detectors are available

when the bus departs from one of the major stops. There should be eleven and eight sets of loop

detector data along the eastbound and westbound routing paths, respectively. Missing data

happen occasionally owing to malfunction or other operational problems of the loop detectors at

a certain time period. Although these samples are not suitable for model development, they are

still categorized as historical journey time samples, and the data can be used to treat historical

bus time as an explanatory variable for further model development. The rest of the sample trips

with a complete set of loop data are used for model calibration and model testing. Table 4-12

and Table 4-13 summarize the number of sample sets along the two study paths.

Table 4-12: Gardiner Expressway Eastbound Route Sample Summary

Route Complete Loop Data Set Incomplete Loop Data Set

Origin Destination Model

Development Sample Size

Testing Sample Size

Historical Bus Journey Time Sample Sizes

Square One Bus Terminal

Union GO Bus Terminal 39 38 124

Cooksville GO Station


Dixie GO Station


Dufferin Street Union GO Bus Terminal 49 50 95

Table 4-13: Gardiner Expressway Westbound Route Sample Summary




Testing Sample Size


Union GO Bus Terminal

Square One Bus Terminal 44 46 107


Cooksville GO Station 44 46 107

40




Testing Sample Size



Dixie GO Station 34 16 65

Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW

Dixie GO Station 41 29 50

Both Table 4-12 and Table 4-13 show that sample sizes for model development and testing are

very similar except for trip segment with Dixie GO Station at its origin and destination. This is

because GO Transit does not provide services to Dixie GO Station at weekends, and hence the

availability of a complete loop data set is less than for other sections. Therefore, in the routing

path with Dixie GO Station, two-thirds of the sample trips are allocated for model calibration and

one-third for testing. Other origin and destination pairs will have approximately half of the

sample trips for model calibration and the other half for model testing. This division of trips is

applied to guarantee that all origin and destination pairs have a minimum number of observations

to use for model calibration, ensuring the quality of model performance.

41

Chapter 5 Artificial Neural Network

5 Artificial Neural Network The artificial neural network (ANN) is a “black box” system based on a biological neural

network that captures a complicated input and output relationship, without specifying the explicit

function. It is formed by a number of interconnected artificial neurons attempting to work

together to solve a problem (Beale and Jackson 1990). The neural network iteratively changes

its structure, depending on the number and type of data entering the network, during the training

process. This chapter gives a detailed summary of the theoretical background of ANN and

discusses the most suitable ANN structure to use for estimating bus travel time.

5.1 Theoretical Background

5.1.1 Basic Unit of Artificial Neural Network: Neuron

An artificial neuron receives inputs, sums them together, applies the transfer function, and

produces an output. The value of the output depends on each input’s respective weight and the

transfer function applied in the layer (Demuth et al. 2008). Figure 5-1 shows a typical

configuration of an artificial neuron.

Figure 5-1: Typical Artificial Neuron Configuration

42

5.1.2 Selection of Artificial Neural Network Model

The best ANN structure is the model with the fewest error values. The selection of a suitable

ANN structure depends on the problem’s characteristics (Joseph et al. 1992). These

characteristics are:

• Nature of Inputs

Since some inputs of the regional bus travel time estimation are continuous, only models

that can handle continuous variables are considered.

• Availability of the Desired Outputs

The operational input data, such as traffic data and weather data are available and the

output result, bus travel time, is also known. Hence, the supervised learning approach is

more appropriate for this particular application.

• Linearity

Most transportation-related problems are dynamic and nonlinear such as the event of bus

journey time estimation and the event of estimating number of vehicles approaching a

signalized intersection. This research’s scenario is considered to be dynamic and

nonlinear. The selected model should be capable of dealing with the nonlinearity features

of the bus operations.

• Hidden Layers

An increased number of hidden layers can reduce the network’s ability to make a better

ANN (Chen et al. 2004). Thus, one or two hidden layers are usually used to create a

neural network model.

5.1.3 Advantages and Disadvantages of Artificial Neural Network

ANN models benefit many engineering industries, including the transportation field. The

advantages of this innovative approach include (Demuth et al. 2008, Beale and Jackson 1990):

• Good performance in pattern recognition and forecasting.

43

• Good at interpolation.

• Can detect patterns when inputs are available.

• Capable of resolving complex pattern-recognition tasks, especially nonlinear problem

sets.

• Has fault tolerance, meaning that the model can still function even when some neurons

are out of order.

• Can maintain a very strong parallelism between inputs and outputs.

• Computation time for a calibrated ANN to determine the final result is short.

• Workable with input variables that are dependent. In a transportation system, many

variables are inter-correlated with one another (Jeong and Rilett 2004).

• Responsive to dynamic conditions/ no lagging (Smith and Demetsky 1995).

Although the ANN model has many advantages in engineering applications, several drawbacks

may affect the final model’s outcomes (Demuth et al. 2008, Beale and Jackson 1990). These

shortcomings include:

• “Black box” system – very difficult to understand the actual architecture of the model and

internal mathematical functions.

• Not good at extrapolation.

• Its performance and accuracy depend on numerous factors, including ANN architectures,

training rates, training methodologies, and transfer functions used in different layers. The

training process can be time-consuming.

• Need a large sample size so that there will be enough data for training, validation, and

testing.

44

• No specific guidelines for researchers to follow when determining a suitable neural

network. Researchers need to understand the problem clearly and decide on the most

appropriate algorithm.

• If the neural network learns the training data too well, the network memorizes the data

and gives incorrect results (Hung and Adeli 1994).

• Input variables for the network depend on researchers’ experience and knowledge

(Mohamad-Saleh and Hoyle 2008).

Another drawback not mentioned above is that the network may sometimes return the local

minimum instead of the overall minimum of total error, causing the final result to be incorrect.

Several alternatives (Beale and Jackson 1990) have been designed to minimize this occurrence,

including:

• Lowering the Gain Term

This approach reduces the learning rate, so that the gradient descent method takes smaller

steps towards the final solution. This can give deeper minima without wild oscillation.

Since the learning rate is slower, the time for training will be longer.

• Momentum Term

This technique introduces an extra term into the weight adaptation equation. The use of

this method is to increase the chance of overshooting the local minima and to speed up

the convergence. This approach can also use previous weights to readjust for a new set

of weights.

• Addition of Noise

This method is to get the system out of the local minimum, so that new local minima can

be found. The absolute minimum of the error values can be obtained by comparing all

the local minima.

45

5.1.4 Artificial Neural Network’s Transfer Function

There are four common types of transfer functions, also named activation functions, including

linear threshold, hard-limit threshold, log-sigmoid threshold and tan-sigmoid threshold functions.

Figure 5-2 shows the structures of these transfer functions. When input variables enter each

hidden and output layer, all elements are combined with respect to their weights, and then

converted into an output value using a corresponding transfer function.

Figure 5-2a: Linear Transfer Function

Figure 5-2b: Hard-limit Transfer Function

Figure 5-2c: Log-sigmoid Transfer Function

Figure 5-2d: Tan-sigmoid Transfer Function

(Demuth et al. 2008)

Figure 5-2: Typical Transfer Function Structures

Among the four functions, log-sigmoid and tan-sigmoid are nonlinear. Outputs from their

transformations depend on the frequency power of inputs, rather than the frequency values

themselves (Beale and Jackson 1990). These two nonlinear functions can also ensure that

enough information is available in the neurons of earlier layers, meaning that errors created at

46

later layers will be lower. On the other hand, if linear transfer functions are used at all layers,

these layers can be combined into one single layer, speeding up the training process (Beale and

Jackson 1990). As for the hard-limit function, the neuron output can only be zero or one, and

therefore is more suitable to engineering problems related to pattern classification. For the

current project, log-sigmoid, tan-sigmoid, and linear transfer functions can be used, while the

hard-limit function is not appropriate.

5.1.5 Feedforward Neural Network vs. Feedbackward Neural Network

Feedforward and feedbackward are the two major architectures of neural networks. One of the

key differences between these two architectures is the data signal transmission (Farhan 2002). In

the feedforward network, its input data pass through the model neuron to produce an output

using the corresponding transfer function, and this can only be done in one direction. In the

feedbackward network, the signal can travel in all directions and provide responses to its layer or

other layers at an early stage.

5.1.6 Artificial Neural Network Training Techniques

Artificial Neural Network training methods can be divided into two main categories, supervised

and unsupervised, according to the availability of actual observed results in the sample sets used

in training (Beale and Jackson 1990). Different types of ANNs using these two learning

techniques and their examples are discussed in the following section.

5.1.6.1 Supervised Learning Techniques

In the supervised learning technique, a set of training samples with inputs and outputs are given.

Through the use of this technique, an ANN can be calibrated with a developed function aiming

to match the input and output pair. Examples of neural networks using the supervised learning

rule are:

• Multilayer Feedforward with Backpropagation

• Probabilistic Neural Networks

• Time Delay Neural Networks

47

5.1.6.2 Unsupervised Learning Techniques

Opposite to the supervised learning technique, knowledge will not be learnt through the

unsupervised learning process. Instead, unsupervised neural networks develop a routine to group

certain input data together with common features. Next, the weights are adjusted using

neurobiological principles such as competitive learning, so that similar characteristics of input

components will end up producing specific types of outcomes (Farhan 2002). Examples of

unsupervised learning techniques include:

• Kohonen Self-Organizing Network

• Adaptive Resonance Theory

• Fuzzy Adaptive Resonance Theory

5.1.7 Multilayer Feedforward Perceptron with Backpropagation

The multilayer feedforward with backpropagation network was applied in this research. In

general, the multilayer feedforward network consists of three different layers – input layer,

output layer, and hidden layer (Beale and Jackson 1990). While there can only be one input and

one output layer, there can be a number of hidden layers. Figure 5-3 presents an example of a

typical multilayer feedforward network.

Figure 5-3: Typical Multilayer Feedforward Network

48

The way this network works is that, first, I1, I2, , Ii enters the neurons in the hidden layer, HL1,

HL2, , HLj. Next, these elements are summed with certain weight values, depending on each

input’s sensitivity power (Demuth et al. 2008). The more sensitive the output is to the input

element, the higher its weight. Through the transfer function of each neuron, HLj, an output is

calculated. This then becomes the new input for the neurons in output layer, OL1, OL2, , OLk.

Repeat the previous steps with these new input values, and a final output would be produced. A

similar approach is used for networks with more than one hidden layer.

Backpropagation learning algorithm is a common learning rule for the multilayer feedforward

network. First, the ANN structure needs to be developed. This involves setting up the number

of hidden layers, the number of neurons in each layer, the transfer function applied in each layer,

and more. The next step is the actual learning procedure to update weight values between layers.

The following shows a simple example of the calibration taking place in the ANN structure. All

transfer functions used in the example below are log-sigmoid functions.

Hidden Layer – Part 1 (inputs are sent to the hidden layer and then fed through a transfer

function to give a new output)

)(11

jj tXj

iiijj

eY

IwX

−−+=

= ∑

where Xj is the weighted sum of inputs to the jth hidden-neuron, Yj is the output at the jth hidden-

neuron, wij is the weight of the ith input to the jth hidden-neuron, Ii is the ith input, and tj is the bias

adjustment for the jth hidden-neuron.

Output Layer – Part 2 (results from its transfer function are fed to the output layer to obtain a

final estimation)

)(11

kk tXk

jjjkk

eY

YwX

−−+=

= ∑

49

where Xk is the weighted sum of inputs to the kth output-neuron, Yk is the result of the kth output-

neuron, wjk is the weight of the jth hidden-neuron result to the kth output-neuron, Yj is the output

at the jth hidden-neuron, and tk is the bias adjustment for the kth output-neuron.

Once the ANN’s weights are initialized, the training process runs by iteratively adjusting the

weight values to minimize the error function. The simplest way to demonstrate backpropagation

is to use the gradient descent method (Demuth et al. 2008). In this approach, the derivative of

the error values, E, with respect to inputs, weights, and outputs of each layer is computed.

Output Layer

jkjk

kkkk

kkk

YXE

wE

YYYE

XE

OYYE

∂∂

=∂∂

−∂∂

=∂∂

−=∂∂

)1(

where Xk is the weighted sum of inputs to the kth output-neuron, Yk is the result of the kth output-

neuron, wjk is the weight of the jth hidden-neuron result to the kth output-neuron, Ok is the actual

observed result from the training sample, and Yj is the result of the jth hidden-neuron (which also

serves as an input to different output-neurons).

Hidden Layer

ijij

jjjj

kjk

kj

IXE

wE

YYYE

XE

wXE

YE

∂∂

=∂∂

−∂∂

=∂∂

∂∂

=∂∂ ∑

)1(

where Xj is the weighted sum of inputs, I1, I2, , Ii, to the jth hidden-neuron, and wij is the weight

of the ith input to the jth hidden-neuron. Yj, wjk, and Xk are defined as above.

Next, the weight on each input element is revised with the following equation:

50

wEcww∂∂

−='

where c is the learning rate of the ANN, and w is the weight of wij and wjk as defined above.

All weight values are updated continuously until the error function tends to zero. Mean Square

Error (MSE) is a common function used for assessing multilayer feedforward network

performance (Demuth et al. 2008). MSE is a function of the average square of the difference

between actual output and target output. Its function is shown as follows:

[ ]2

1)()(1 ∑

=

−=Q

kkOkY

NMSE

where N is the total number of training sample sets, Y(k) is the target value for the output of the

kth neuron in the output layer, and O(k) is the actual output of the kth neuron in the output layer.

The training time of the gradient descent method may, however, be lengthy in some practical

problems. Hence, a faster numerical optimization technique, the Levenberg-Marquardt

algorithm, is adopted in this research to speed up the weight determination process. The

drawback of this technique is that it requires more computer memory storage during the training

(Demuth et al. 2008). The new weight adjustment calculation is presented in the following

equation:

[ ] eJIJJww TT 1' −+−= μ

where w is a vector of the current weights and biases, J is the Jacobian matrix that contains the

first derivatives of the network errors with respect to the weights and biases, μ is a scalar

parameter, I is the identity matrix, and e is a vector of network errors.

In conclusion, the training process using the backpropagation learning method that incorporates

the Levenberg-Marquardt algorithm to update input weights in each layer is summarized as

follows:

51

1. Present inputs and compute the desired output in a pre-set ANN structure with a fixed

number of hidden layers, learning rate, transfer function of each layer and number of

neurons in each layer, etc.

2. If the resulting output is very close to the desired output, i.e. with a very low error, the

network training ends. If not, the training goes backwards with the weight adjustment.

3. The weights are continually updated using the Levenberg-Marquardt algorithm as

illustrated in the previous equation until the best ANN structure is formed with the least

MSE value.

4. Finally, the new determined weights are input back into the ANN for further analysis and

training.

5.1.8 Input Component Simplification Techniques

Some major criticisms of the ANN are that the training process is time-consuming and the model

nature is very complex, as discussed previously in Section 2.3. Two common techniques,

sensitivity analysis and principal component analysis, can be used to improve these weaknesses

and are described in the section below.

5.1.8.1 Sensitivity Analysis

The significance identification of each input parameter can assist researchers to simplify an

engineering problem. This can lead to a smaller network, faster training process and more

accurate estimation. Sensitivity analysis (Engelbrecht et al. 1995, Sung 1998, Zurada et al.

1994) is a tool to assess the significance of each input parameter with respect to each training

sample set. Input parameters that are highly significant are kept for the ANN training. The

following equations demonstrate the calculation of the sensitivity, Sik, of a trained multilayer

feedforward neural network output, Ok, with respect to its input, Ii, on each training sample:

52

∑

∑

=

=

=

∂∂

=

∂∂

=

J

jijjjkkik

i

iJ

jikkik

i

kik

wYwOS

IY

wOS

IO

S

1

''

1

'

where Ok’ is the derivative of the transfer function used in the kth output-neuron, Yj

’ is the

derivative of the transfer function used in the jth hidden-neuron, wjk is the weight of the jth

hidden-neuron result to the kth output-neuron, and wij is the weight of the ith input to the jth

hidden-neuron.

To simplify the above equation, the sensitivity value can be expressed as:

IJ wYwOS ''=

where wJ is the weight matrix between the hidden and output layers and wI is the weight matrix

between the input and hidden layers. O’ and Y’ are diagonal matrices of the output and hidden

layers.

Different input parameters have various sensitivity values with respect to each sample’s output.

Combining all training samples, the overall sensitivity measure for output, Ok, with respect to

input, Ii, is the absolute value of the average sensitivity matrix, which is defined as:

∑=

=N

nikik NSaverageS

1/)(

where N is the total number of the training sample sets.

If an additional hidden layer is added into the network, each input’s sensitivity value with respect

to each output is expanded to:

ILJ wZwYwOS '''=

where wJ is the weight matrix between the second hidden and output layers, wL is the weight

matrix between the first and the second hidden layers and wI is the weight matrix between the

53

input and first hidden layer. O’, Y’, and Z’ are diagonal matrices of the output layer, the second

hidden layer, and the first hidden layer.

5.1.8.2 Principal Component Analysis

The principal component analysis is another effective technique that can reduce the dimension of

the input vectors (Mohamad-Saleh and Hoyle 2008). This method orthogonalizes the

components of the input vectors, so that all vectors are uncorrelated with one another (Demuth et

al. 2008). Then the resulting orthogonal components are rearranged, bringing the vector with a

larger variation to be higher on the list. The components that contribute less than a certain

percentage to the total variation in the data set are eliminated from the ANN training. This

reduces the number of input variables needed for the training process.

With the aid of MATLAB’s Neural Network Toolbox, the principal component analysis is

demonstrated to generate a transformation matrix (Demuth et al. 2008). The use of this

transformation matrix is to reduce the dimension of input vectors, so that the ANN training

process can be done faster. Once the final ANN structure is defined, all input vectors of test

samples should be normalized with zero mean and unity variance, and then multiplied by the

transformation matrix before proceeding to the simulation stage (Demuth et al. 2008) to forecast

the bus journey time.

5.1.9 Over Fit Training Data Avoidance

To avoid the problem of data over fitting, a MATLAB technique called “Early Stopping” could

be employed during the neural network training process (Demuth et al. 2008). The training data

should be separated into two sets – a training set and a validation set. The training dataset is

used to capture the relationships between inputs and outputs by adjusting weights and bias

factors. The validation dataset is applied to monitor the performance of the training process

(Demuth et al. 2008). The validation error is supposed to be decreasing during the initial stage

of the network training. The error increasing over iterations is a signal that the network is

experiencing over fitting problem. At that point, the training process should stop immediately.

54

5.1.10 Performance Measures

In the past, many forms of performance measures have been used to evaluate bus travel time

prediction models, including Mean Absolute Error (MAE) (Chung and Shalaby 2008), Mean

Relative Error (MRE), Root Square Relative Error (RSRE) (Farhan and Shalaby 2003), Absolute

Percent Error (Jeong and Rilett 2005) and Root Mean Square Error (RMSE) (Chen et al. 2005).

Through an extensive analysis, RMSE is chosen to be the performance measure in this research

project because of its sensitivity to occasional large errors. The squaring process gives

disproportionate weight to very large outliers, and hence disfavouring any large estimation

errors. It is noted that regional bus users dislike long wait time, especially when these bus

headways are already very long. The travel time estimation model that has the smallest RMSE

value would also have the smallest probability of passengers having to wait for an extremely

long time. The RMSE function is shown as follows:

( ) NYYRMSEN

iactualipredictedi /

1

2∑=

−=

where N is the total number of the testing sample trips, Ypredictedi is the estimated bus travel time,

and Yactuali is the actual bus travel time.

5.2 Artificial Neural Network Calibrations Two types of ANN models are presented in this section – the direction-based model and the

location-based model. The direction-based model defines all origin and destination pairs along

the same routing path, such as “Square One Bus Terminal-to-Union GO Bus Terminal” and

“Cooksville GO Station-to-Union GO Bus Terminal” using the same ANN structures. Although

this method is time saving, the performance of the model cannot be accurately determined. For

example, suppose two direction-based models, A and B, both have four origin and destination

pairs, with RMSEs of 50 seconds. Model A has RMSEs of 40, 60, 55, and 45 seconds

respectively for each origin and destination pair. The individual RMSEs are very consistent.

Therefore, the overall RMSE of 50 seconds represents the performance of this model very well.

On the other hand, the values for Model B are 5, 95, 80, and 20 seconds. In this case, the overall

RMSE of 50 seconds is misleading.

55

The location-based model is defined as a model with every origin and destination pair having a

distinct network structure to estimate bus journey time. The accuracy of this type of model is

expected to be higher than the direction-based model. However, the calibration time of this

model is very lengthy. Moreover, the number of training samples available to calibrate location-

based models is a lot fewer than that of direction-based models, as seen in Table 4-12 and Table

4-13 in Section 4.3. This may also affect the capability of pattern recognition.

The first part of this section introduces four types of direction-based models using two

simplifying techniques – sensitivity analysis and principal component analysis. These models’

performances are evaluated based on the Gardiner Expressway eastbound route. Next, the best

two direction-based models are further assessed with the Gardiner Expressway westbound route.

The goal of this additional assessment is to ensure that the model performs well on both routes.

The second part of this section evaluates the predicting performance of the direction-based and

location-based models for each origin and destination pair, and determines which ANN structural

configuration gives the best results.

In the neural network structure development, 70% of the modelling sample trips are assigned for

network training and the rest are used for model validation. For the validation sample set, a tool

from MATLAB, called “Early Stopping” technique, is used to avoid ANNs from over fitting the

training data (Demuth et al. 2008). In the training process, a total of 48 variables are used as

input vectors to predict bus travel time. The dimensions of the input vector matrix therefore are

quite big. This increases the training time and impacts the model prediction accuracy.

Sensitivity analysis and principal component analysis are used to reduce the size of the input

matrix. The full syntax of the ANN training process is presented in Appendix B.

5.2.1 Sensitivity Analysis

Sensitivity analysis is completed before the ANN training process starts. Table 5-1 presents the

sensitivity significance summary of the top 20 variables. The ranking summary illustrated in

Table 5-1 is based on the sensitivity values relative to the most significant factor, traffic volume

data, collected by loop detectors at Parkside Drive.

56

Table 5-1: Sensitivity Significance Summary of Input Factors

Rank Variable Relative to the

Most Significant Variable

Rank Variable Relative to the

Most Significant Variable

1 Parkside_Volume 1.00 11 Spadina_Volume 0.78

2 Colborne Lodge_Occupancy 0.99 12 Dufferin_Speed 0.76

3 Jameson Exit_Occupancy 0.97 13 Parkside_Speed 0.73

4 Ellis_Occupancy 0.95 14 Historical Bus Travel Time 0.73

5 Total Snowfall 0.94 15 Spadina_Speed 0.70

6 Bus Current Speed captured by GPS

Devices 0.93 16 Dixie/QEW_Volume 0.70

7 Lanes Affected by Incidents 0.84 17 Jameson Exit_Volume 0.69

8 Strachan_Occupancy 0.80 18 Dunn_Volume 0.69

9 Colborne Lodge_Speed 0.79 19 Incident Start Time 0.69

10 Dowling_Speed 0.79 20 Dufferin_Occupancy 0.66

5.2.2 Direction-Based Models

Four alternative configurations of the direction-based models are developed. These models

include different number of input components and input simplification techniques. These four

options are:

• Option 1 – ANN with principal component analysis technique (ANN-PCA). A total of

48 variables are input into the neural network structure. Through the transformation

matrix created by the principal component analysis, the actual input matrix used for the

neural network training can be reduced to 28 input variables. Once the final ANN

structure is developed, all input vectors should be normalized with zero mean and unity

variance, and then multiplied by the obtained transformation matrix before proceeding to

the model simulation (Demuth et al. 2008).

• Option 2 – ANN with sensitivity analysis technique (ANN-S1). The top fifteen sensitive

variables are included in this network, as illustrated in Table 5-1. Among these variables,

some are loop detector data such as “Parkside_Volume” and “Colborne

57

Lodge_Occupancy”. Using “Parkside_Volume” as an example, the loop detector at

Parkside Drive also collects speed and occupancy in addition to volume data. These

additional data are also included in the input components. This increases the total

number of input variables to 28.

• Option 3 – ANN with sensitivity analysis technique (ANN-S2). The top 20 most

significant variables are included in this network, as seen in Table 5-1. Similarly to the

ANN-S1, other relevant loop data are also gathered for use as network input variables.

Thus, there is a total of 35 variables predicting the bus journey time.

• Option 4 – ANN with “Do Nothing” option (ANN-DN). No simplification technique is

used with this network. All 48 input variables are included in the network training.

In each ANN option, 1240 trials of ANN structures are developed and their respective RMSEs

are examined. Table 5-2 presents the best ANN structure for each option. Table 5-3 illustrates

the evaluation summary among these four options of direction-based models.


Eastbound Route)

ANN Structure ANN-PCA ANN-S1 ANN-S2 ANN-DN Number of Inputs 48 28 35 48 Number of Hidden Layers 2 2 2 2 Number of Neurons (1st Hidden Layer) 8 10 1 18

Number of Neurons (2nd Hidden Layer) 1 1 5 9

Transfer Function (1st Hidden Layer) Tan-sigmoid Tan-sigmoid Log-sigmoid Log-sigmoid

Transfer Function (2nd Hidden Layer) Linear Log-sigmoid Tan-sigmoid Tan-sigmoid

Transfer Function (Output Layer) Tan-sigmoid Linear Linear Linear Training Rate 0.005 0.005 0.005 0.005

58

Table 5-3: Direction-Based ANN Alternatives Performance Assessment (Gardiner

Expressway Eastbound Route)

RMSE (seconds) Origin Destination ANN-PCA ANN-S1 ANN-S2 ANN-DN Square One Bus

Terminal Union GO Bus

Terminal 562 532 595 443


Union GO Bus Terminal 230 266 266 268

Dixie GO Station Union GO Bus Terminal 162 194 211 216

Average 318 331 357 309

Results in Table 5-3 illustrate that the ANN-PCA and the ANN-DN have smaller RMSEs than

the ANN-S1 and the ANN-S2. These results also indicate that removing input variables using

the sensitivity analysis technique reduces estimation accuracy. The RMSE difference between

the ANN-PCA and the ANN-DN is negligible, being only nine seconds, and can be ignored. The

ANN using principal component analysis reduces the training process time while maintaining the

same level of accuracy as the ANN without any simplification technique. Further analysis using

the Gardiner Expressway westbound routing path is demonstrated to confirm the ANN-PCA is

more suitable for the bus journey time forecast.

In the westbound direction, there are 39 input variables owing to fewer loop detectors imbedded

along westbound freeway lanes. The ANN structures of the ANN-PCA and the ANN-DN for the

westbound routing path are summarized in Table 5-4. Table 5-5 illustrates the RMSE after bus

travel time simulations of each origin and destination pair.


Westbound Route)

ANN Structure ANN-PCA ANN-DN Number of Inputs 39 39 Number of Hidden Layers 1 2 Number of Neurons (1st Hidden Layer) 11 20 Number of Neurons (2nd Hidden Layer) N/A 1 Transfer Function (1st Hidden Layer) Linear Tan-sigmoid Transfer Function (2nd Hidden Layer) N/A Linear Transfer Function (Output Layer) Linear Tan-sigmoid Training Rate 0.05 0.005

59

Table 5-5: Direction-Based ANN Alternatives Performance Assessment (Gardiner

Expressway Westbound Route)

RMSE (seconds) Origin Destination ANN-PCA ANN-DN Union GO Bus Terminal Square One Bus Terminal 179 210 Union GO Bus Terminal Cooksville GO Station 168 219 Union GO Bus Terminal Dixie GO Station 187 258

Average 178 229

Table 5-5 shows that the ANN-PCA has lower RMSEs than the ANN-DN for all origin and

destination pairs in the westbound route by an average of 51 seconds. Therefore, it can be

concluded that the ANN with principal component analysis is the best direction-based ANN

configuration among the ones tested in this study to predict regional transit journey time.

5.2.3 Location-Based Models

The location-based models for all origin and destination pairs are calibrated. The number of

training sample trips for the location-based models is obviously smaller than that of the

direction-based models. In the location-based model, no simplification technique is used

because the number of input variables is larger than the number of training sample trips, and

hence only the “Do Nothing” option is demonstrated in each origin and destination pair (Demuth

et al. 2008). The ANN structures of all origin-destination pairs are presented in Table 5-6 and

Table 5-7.

Table 5-6: ANN Structure Summary of Location-Based Models (Gardiner Expressway

Eastbound Route)

Origin Destination Origin Destination Origin Destination

ANN Structure Square One Bus Terminal

Union GO Bus

Terminal

Cooksville GO

Station

Union GO Bus

Terminal

Dixie GO

Station

Union GO Bus

Terminal ANN Name ANN-SE ANN-CE ANN-DE Number of Inputs 48 48 48

Number of Hidden Layers 2 2 2

Number of Neurons (1st Hidden Layer)

20 20 16

60


ANN Structure Square One Bus Terminal

Union GO Bus

Terminal

Cooksville GO

Station

Union GO Bus

Terminal

Dixie GO

Station

Union GO Bus

Terminal Number of Neurons (2nd Hidden Layer)

10 1 8

Transfer Function (1st Hidden Layer)

Log-sigmoid Tan-sigmoid Tan-sigmoid

Transfer Function (2nd Hidden Layer)

Tan-sigmoid Tan-sigmoid Log-sigmoid

Transfer Function (Output Layer)

Linear Tan-sigmoid Linear

Training Rate 0.005 0.005 0.005

Table 5-7: Location-Based ANN Structure Summary (Gardiner Expressway Westbound

Route)


ANN Structure Union GO Bus Terminal

Square One Bus

Terminal




Dixie GO Station

ANN Name ANN-SW ANN-CW ANN-DW Number of Inputs 48 48 48

Number of Hidden Layers 2 2 2


20 10 8

Number of Neurons (2nd Hidden Layer)

1 3 1


Log-sigmoid Tan-sigmoid Linear


Tan-sigmoid Tan-sigmoid Tan-sigmoid


Linear Tan-sigmoid Tan-sigmoid

Training Rate 0.005 0.005 0.005

61

5.3 Direction-Based Models vs. Location-Based Models After calibration is completed for both direction- and location-based ANNs, their performance

measures are combined and evaluated, as shown in Table 5-8 and Table 5-9.


(Gardiner Expressway Eastbound Route)

RMSE (seconds) Origin Destination Direction-Based Location-Based


Union GO Bus Terminal 562 519

Cooksville GO Station Union GO Bus Terminal 230 240

Dixie GO Station Union GO Bus Terminal 162 149

Average 318 303


(Gardiner Expressway Westbound Route)

RMSE (seconds) Origin Destination

Direction-Based Location-Based Union GO Bus

Terminal Square One Bus

Terminal 179 157

Union GO Bus Terminal Cooksville GO Station 168 175

Union GO Bus Terminal Dixie GO Station 187 168

Average 178 167

Results in both Table 5-8 and Table 5-9 demonstrate that the location-based ANNs have lower

average RMSEs than the direction-based ANNs for all origin and destination pairs of the

eastbound and westbound routes by 15 and 11 seconds respectively. Although the location-

based model has higher RMSEs on two origin and destination pairs (Eastbound – “Cooksville

GO Station-to-Union GO Bus Terminal” and westbound – “Union GO Bus Terminal-to-

Cooksville GO Station”), the differences are relatively small, being only ten seconds, and hence

can be neglected.

In conclusion, the location-based model is preferable for forecasting bus journey time between a

chosen origin and destination pair. Although their calibration process may take longer, location-

62

based models can ensure that transit providers offer a high quality of bus journey time

estimation.

63

Chapter 6 Alternative Approaches’ Calibrations and

Evaluations 6 Alternative Approaches’ Calibrations and Evaluations In order to evaluate the applicability of calibrated ANNs, ANNs are compared with two other

travel time forecasting approaches – historical average and linear regression. The sections below

briefly introduce the alternative approaches, how these models are calibrated, and their

performance against the ANNs using the testing samples defined in Section 4.3. Similar to the

previous section, the Root Mean Square Error (RMSE) is used as the performance measure for

evaluation.

6.1 Historical Average Models Historical average is a traditional approach to estimate bus journey time using data from the past.

This method uses the median of all historical data to predict the journey time of the next regional

bus under different scenarios. The median, which describes the data point that separates the

upper half of the samples from the lower half, is selected as predicted time. Using the median

instead of the mean can minimize the impact of extremely large or small values in the data set

(outliers).

6.1.1 Model Calibrations and Evaluations

In the model calibration process, four configurations with different combinations of historical

data inputs are tested, including:

• Option 1 (HAE1/ HAW1) – Day of the week (weekday or weekend)

• Option 2 (HAE2/ HAW2) – Day of the week, bus operating hour (5, 6, 7, 8, 9, 10 or 11

a.m.)

• Option 3 (HAE3/ HAW3) – Day of the week, bus operating hour, weather condition

(good or bad condition)

64

• Option 4 (HAE4/ HAW4) – Day of the week, bus operating hour, weather condition,

incident information (road works, collisions, disabled vehicles or unknown)

These four options are illustrated in Figure 6-1. The historical average approach is origin- and

destination-specific, meaning that the result would be different for each origin and destination

pair. A summary of historical travel time for these four options is illustrated in Appendix C.

Figure 6-1: Historical Average Approach Options

Table 6-1 and Table 6-2 summarize the performance evaluation results among the four options in

forecasting eastbound and westbound transit journey times along the Gardiner Expressway.

These tables show that each origin and destination pair has its own best configuration. The

options HAE1, HAE2 and HAE3 all have very similar RMSEs. HAE4 has exceptionally high

RMSEs because the delay time caused by incidents on freeways varies greatly, even when the

incident type is the same. For example, a disabled vehicle would require more time to be

removed on a freeway without a shoulder lane than one with a shoulder lane. No individual

option of historical average approach can be determined to be the best for all origin and

destination pairs.

Table 6-1: Historical Average Model Alternatives Performance Assessment (Gardiner


RMSE (seconds) Origin Destination HAE1 HAE2 HAE3 HAE4 Square One Bus


Terminal 591 579 623 1040


Union GO Bus Terminal 286 276 285 531

Dixie GO Station Union GO Bus Terminal 219 258 218 540

Average 366 371 375 704

65

Table 6-2: Historical Average Model Alternative Performance Assessment (Gardiner


RMSE (seconds) Origin Destination HAW1 HAW2 HAW3 HAW4* Union GO Bus


Terminal 190 169 171 N/A


Cooksville GO Station 181 176 201 N/A

Union GO Bus Terminal Dixie GO Station 190 223 201 N/A

Average 187 189 191 N/A *Remark: No incident data were found in the modelling and testing samples. HAW4 has exactly the same results as HAW3.

6.2 Linear Regression Models The second alternative to estimate bus travel time along the Gardiner Expressway corridor is the

linear regression approach. Again, two types of linear regression models are generated –

direction-based and location-based. Their details are discussed in Section 5.2.

The general linear regression model can be expressed as

εβ += ),( iixfY

where Y is the bus journey time forecast, xi is the vector of values of the independent variables,

βi is the vector of corresponding estimated parameters for xi, and ε is an error standing for the

discrepancy between the true value of Y and the value actually measured.

When a linear regression model is calibrated, several statistical analysis methods have to be

performed to confirm that the explanatory variable is in fact suitable for the generated model.

These methods include:

• Statistical significance of the parameter estimates

• Goodness-of-fit

• Rationale for the variables selection process

66

All linear model generations in this section are completed using Microsoft Office Excel 2007’s

Data Analysis tool.

6.2.1 Statistical Significance of the Parameter Estimates

In the regression function, each parameter’s t-statistical value is applied. From these values, the

author can decide whether the parameter estimates for each variable should be zero. To validate

the result, a 90% confidence level of t-statistics test is applied. If the parameter’s t-value is

larger than the threshold of 1.65, it is determined to be not zero. Thus, its value should be set to

the estimated value calculated by the regression function in Microsoft Office Excel 2007.

6.2.2 Goodness-of-Fit

In general, if the coefficient of determination, R2, is close to one, the model can be classified as a

“best-fit” model. R2 coefficient is defined as the ratio of explained variance to the total sum of

explained and unexplained variances, illustrated by the following equation:

∑∑

−

−= 2

22

)()''(

MmMm

R

where m is the actual value of the data point, M is the average value of the data point, m’ is the

estimated value of the data point, and M’ is the average estimated value of the data point using

the linear regression equation.

6.2.3 Rationale for the Variables Selection Process

Explanatory variables used to estimate bus travel time should be independent of one another.

Correlation analysis can insure the independencies among variables. If the absolute value of

correlation is close to one, the two variables are highly correlated. Since many transportation

variables are highly correlated with one another, it is important to insure the independencies of

all explanatory variables (Jeong and Rilett 2004).

6.2.4 Model Calibrations and Evaluations

Direction-based and location-based models with respect to various origin and destination pairs

are calibrated. The explanatory variables applied to the model generation include:

67

• Historical average variable that summarizes different factors such as day of week and

daily bus operating hour

• Variables for weather conditions such as amount of rainfall, amount of snowfall and

snow accumulated on ground

• Incident information, such as the type of incident and the number of lanes blocked

• Loop detector data from detector stations along the route at the time the bus departs from

the major stops

There is a total of 48 variables altogether for the model calibration, as illustrated in Appendix D.

All explanatory variables in each of the following linear regression models are 90% statistically

significant and independent of each other, as seen from the correlation analysis. Furthermore,

these models’ R2 are usually higher than 0.60. Lastly, all variables can be intuitively explained

in terms of why they would affect the model’s results. The equations below include the final

calculated parameters for direction- and location-based models. Their respective explanatory

variables are presented in Table 6-3 to Table 6-10, and their statistical analysis results can be

found in Appendices E and F for both directions.

Gardiner Expressway Eastbound

Direction-Based Model (RE-DE)

)_(29.6)_(20.0)(96.042.1481 SpeedSpadinaVolumeEllisHistY ×−×−×+=

Table 6-3: Explanatory Variables used for RE-DE

Variables Description(s) Y Bus journey time in seconds

Hist Variable of historical data summarized by day of the week and daily bus operating hour

Ellis_Volume Variable of hourly volume at Ellis Avenue loop detectors at the time when the bus departs from any eastbound major stop

Spadina_Speed Variable of speed at Spadina Avenue loop detectors at the time when the bus departs from any eastbound major stop

68

Location-Based Model – Square One Bus Terminal to Union GO Bus Terminal (RE-LSE)

)_(08.0)_(56.7)_(90.144)_(35.048.1744

VolumeJamesonSpeedParksideIncTypeDayHistY

×+×−×+×+=

Table 6-4: Explanatory Variables used for RE-LSE


Hist_Day Variable of historical data summarized by day of the week Type_Inc Variable of incident type, where collisions = 1, disabled vehicles = 2,

road works = 3, unknowns = 4, otherwise = 0 Parkside_Speed Variable of traffic speed collected at Parkside Drive loop detectors when

the bus departs from Square One Bus Terminal Jameson_Volume Variable of traffic volume collected at Jameson Avenue loop detectors

when the bus departs from Square One Bus Terminal

Location-Based Model – from Cooksville GO Station to Union GO Bus Terminal (RE-LCE)

)_(25.0)_(00.157.1159 VolumeEllisDayHistY ×−×+=

Table 6-5: Explanatory Variables used for RE-LCE


Hist_Day Variable of historical data summarized by day of the week Ellis_Volume Variable of traffic volume collected at Ellis Avenue loop detectors when

the bus departs from Cooksville GO Station

Location-Based Model – from Dixie GO Station to Union GO Bus Terminal (RE-LDE)

)_(41.5)_(51.3)_(10.55)(323.046.1607

SpeedEllisSpeedSpadinaGroundSnowHistY

×−×−×+×+=

Table 6-6: Explanatory Variables used for RE-LDE


Hist Variable of historical data summarized by day of the week and bus operating hour

Snow_Ground Variable of the amount of snow accumulated on ground in centimetres Spadina_Speed Variable of traffic speed collected at Spadina Avenue loop detectors

when the bus departs from Dixie GO Station

69

Variables Description(s) Ellis_Volume Variable of traffic volume collected at Ellis Avenue loop detectors when

the bus departs from Dixie GO Station

Gardiner Expressway Westbound

Direction-Based Model (RE-DW):

)_(47.8)2(23.269)1(29.465)(60.061.1179 SpeedDowlingLocLocHistY ×−×+×+×+=

Table 6-7: Explanatory Variables used for RE-DW



Loc1 Dummy variable for estimating bus travel time from Union GO Bus Terminal to Square One Bus Terminal

Loc2 Dummy variable for estimating bus journey time from Union GO Bus Terminal to Cooksville GO Station

Dowling_Speed Variable of traffic speed collected at Dowling Avenue loop detectors when the bus departs from Union GO Bus Terminal

Location-Based Model – from Union GO Bus Terminal to Square One Bus Terminal (RE-LSW)

)_(69.0)(69.014.1267 SpeedDowlingHistY ×−×+=

Table 6-8: Explanatory Variables used for RE-LSW



Dowling_Speed Variable of traffic speed collected at Dowling Avenue loop detectors when the bus departs from Union GO Bus Terminal

Location-Based Model – from Union GO Bus Terminal to Cooksville GO Station (RE-LCW)

)_(99.8)(552.036.1586 SpeedDowlingHistY ×−×+=

Table 6-9: Explanatory Variables used for RE-LCW



70

Variables Description(s) Dowling_Speed Variable of traffic speed collected at Dowling Avenue loop detectors

when the bus departs from Union GO Bus Terminal

Location-Based Model – from Union GO Bus Terminal to Dixie GO Station (RE-LDW)

)_(75.11)_(12.0)(98.043.1594 SpeedColborneVolumeStrachanHistY ×−×−×+=

Table 6-10: Explanatory Variables used for RE-LDW



Strachan_Volume Variable of traffic volume collected at Strachan Avenue loop detectors when the bus departs from Union GO Bus Terminal

Colborne_Speed Variable of traffic speed collected at Colborne Lodge Road loop detectors when the bus departs from Union GO Bus Terminal

After all parameters of the equations are finalized, test samples are applied to the above

generated models and their estimation performances are summarized in Table 6-11 and Table

6-12.

Table 6-11: Regression Models Performance Assessment (Gardiner Expressway

Eastbound Route)

RMSE (seconds) Origin Destination Direction-Based

Model Location-Based

Model Square One Bus


Terminal 516 571


Union GO Bus Terminal 284 244

Dixie GO Station Union GO Bus Terminal 253 185

Average 351 333

Table 6-12: Regression Models Performance Assessment (Gardiner Expressway

Westbound Route)



Model Union GO Bus


Terminal 159 175

71



Model Union GO Bus

Terminal Cooksville GO

Station 182 177

Union GO Bus Terminal Dixie GO Station 293 246

Average 211 199

Both tables show that the overall performance of the location-based model is slightly better than

that of the direction-based model. This should not be surprising, because the location-based

regression model is specifically calibrated for each origin-destination pair. As seen in the table

of the Gardiner Expressway eastbound route, the direction-based model is more accurate only

when estimating “Square One Bus Terminal-to-Union GO Bus Terminal”. Higher RMSE

values, however, are observed for other origin and destination pairs compared with the location-

based model. Average RMSEs of location-based models are eighteen and twelve seconds less

than those of the direction-based models in respect of both eastbound and westbound routing

paths, respectively. One possible explanation for the unexpected inferiority of the location-based

model for the “Square One Bus Terminal-to-Union GO Bus Terminal” model is the fact that a

good portion of this journey is on surface streets in Mississauga, for which travel time variability

is high and loop detector data is not available. Hence, it seems that when the bus journey is

mostly on a freeway, location based models perform better and vice versa. On average, though,

the location based models outperform the direction based models. Therefore, the author uses

location-based model for further evaluation in this research.

6.3 Forecasting Model Evaluations In this section, performance of all three modelling approaches is compared. Through the above

assessment, location-based models are concluded to be a better forecasting methodology to

predict transit journey time, and are therefore selected as the method to be used in all

comparisons below. Table 6-13 and Table 6-14 give a summary of the configurations of each

model type used in the model evaluation section. The final performance assessments are found

in Table 6-15 and Table 6-16.

72

Table 6-13: Summary of Configurations of Each Model Type (Gardiner Expressway

Eastbound Route)

Alternative Modelling Approaches Origin Destination Historical

Average Regression ANN


Union GO Bus Terminal HAE2 RE-LSE ANN-SE


Union GO Bus Terminal HAE2 RE-LCE ANN-CE

Dixie GO Station Union GO Bus Terminal HAE3 RE-LDE ANN-DE

Table 6-14: Summary of Configurations of Each Model Type (Gardiner Expressway

Westbound Route)

Alternative Modelling Approaches Origin Destination Historical



Square One Bus Terminal HAW2 RE-LSW ANN-SW


Cooksville GO Station HAW2 RE-LCW ANN-CW

Union GO Bus Terminal Dixie GO Station HAW3 RE-LDW ANN-DW

Table 6-15: Alternative Modelling Approaches Performance Assessment (Gardiner


RMSE (seconds) Origin Destination Historical






Dixie GO Station Union GO Bus Terminal 218 185 149

Average 358 333 303

73

Table 6-16: Alternative Modelling Approaches Performance Assessment (Gardiner


RMSE (seconds) Origin Destination Historical






Union GO Bus Terminal Dixie GO Station 201 246 168

Average 182 199 167

Table 6-15 and Table 6-16 demonstrate that the ANNs always outperform other estimation

approaches. In the eastbound direction, the ANNs’ overall average RMSE is smaller than those

of historical average and linear regression models by 55 and 30 seconds. In the westbound

direction, the differences become 15 and 32 seconds, respectively.

The ANN model is able to generalize more complicated input variables together and predict bus

journey time with the smallest error values. In addition, the ANN model combines all the

variables together in determining bus journey time, which is more inclusive than the other two

approaches with model versions that focus only on a few significant variables but omit the other

ones that may still contribute slightly to the bus journey time. The ANN model also captures

nonlinear correlation in between the inputs and outputs. Furthermore, the ANN model is

comprised of real-time traffic data, which in theory should outperform the historical average

approach (Chien et al. 2002). Lastly, the ANN can include inter-correlated explanatory variables

for the bus travel time prediction, but linear regression models cannot (Chen et al. 2007).

6.4 Additional Checkpoints’ Artificial Neural Networks Calibration As mentioned in Section 4.3, Dufferin Street and Highway 427/QEW are chosen as checkpoints

in between bus stops for updating the bus journey time. This section incorporates these

checkpoints into the location-based ANNs and evaluates whether the addition of these

checkpoints improves the bus journey time estimation.

Through 1240 trials of ANN structures, Table 6-17 and Table 6-18 summarize the final ANN

structures that are applied to eastbound and westbound routes respectively.

74

Table 6-17: ANN Structure Summary at Dufferin Street Checkpoint

Origin Destination ANN Structure Dufferin Street Union GO Bus

Terminal ANN Name ANN–DuE Number of Inputs 48 Number of Hidden Layers 2 Number of Neurons (1st Hidden Layer) 7 Number of Neurons (2nd Hidden Layer) 4 Transfer Function (1st Hidden Layer) Tan-sigmoid Transfer Function (2nd Hidden Layer) Linear Transfer Function (Output Layer) Tan-sigmoid Training Rate 0.005

Table 6-18: ANN Structure Summary at Highway 427/QEW Checkpoint

Origin Destination Origin Destination Origin DestinationANN

Structure Highway 427/QEW

Square One Bus

Terminal

Highway 427/QEW


Highway 427/QEW

Dixie GO Station

ANN Name ANN-SQW ANN-CQW ANN-DQW Number of Inputs 48 48 48

Number of Hidden Layers

2 2 2


18 2 5

Number of Neurons (2nd Hidden Layer)

3 1 2


Tan-sigmoid Log-sigmoid Tan-sigmoid


Log-sigmoid Tan-sigmoid Tan-sigmoid

75

Origin Destination Origin Destination Origin DestinationANN

Structure Highway 427/QEW

Square One Bus

Terminal

Highway 427/QEW


Highway 427/QEW

Dixie GO Station


Linear Linear Tan-sigmoid

Training Rate 0.005 0.005 0.005

Subsequently, RMSEs for both eastbound and westbound routing paths are calculated and their

respective results are summarized in the Table 6-19 and Table 6-20.

Table 6-19: ANN Performance Assessment at Dufferin Street Checkpoint (Gardiner


Origin Destination RMSE (seconds)

Dufferin Street Union GO Bus Terminal 82

Table 6-20: ANN Performance Assessment at Highway 427/QEW Checkpoint (Gardiner


Origin Destination RMSE (seconds)

Highway 427/ QEW Square One Bus Terminal 151 Highway 427/ QEW Cooksville GO Station 139 Highway 427/ QEW Dixe GO Station 76

Figure 6-2 shows the prediction error comparison with respect to different checkpoints along the

Gardiner Expressway eastbound route. Figure 6-3 to Figure 6-5 illustrate the RMSEs of the bus

journey time along the westbound route. It can be seen that the RMSE gradually decreases as the

distance in between the origin and destination pair reduces. All these diagrams prove that

dynamic bus journey time updates can reduce errors and can provide more useful information to

assist transit users in planning their trips. For example, in the eastbound direction using the

ANN, RMSE for predication made at Dufferin Street is 437 seconds less than when the

prediction was made at the first bus stop, Square One Bus Terminal.

76

0

100

200

300

400

500

600

Square One Cooksville Dixie Dufferin

Major Checkpoint Location

Root M

ean Square Error (s)

Figure 6-2: Prediction Error Trend for the ANN Approach (Destination Union GO Bus

Terminal)

0

20

40

60

80

100

120

140

160

180

200

Union QEW/427


Root M


Figure 6-3: Prediction Error Trend for the ANN Approach (Destination Square One Bus

Terminal)

77

020406080

100120140160180200

Union QEW/427


Root M


Figure 6-4: Prediction Error Trend for the ANN Approach (Destination Cooksville GO

Station)

020406080

100120140160180200

Union QEW/427


Root M


Figure 6-5: Prediction Error Trend for the ANN Approach (Destination Dixie GO Station)

78

Chapter 7 Operational Strategy

7 Operational Strategy

7.1 Background A bus travel time prediction model aims to benefit two major stakeholders – bus operators and

passengers. From a bus operator’s perspective, the system should satisfy the passengers by

minimizing their wait times, and hence maintain the ridership and revenue levels. Also, the

operator can save costs such as fuel and driver wages incurred during the bus idle time at the bus

stop. Similarly, passengers can use the bus arrival time information to optimize their travel plans

and minimize their wait time. Therefore, the reliability of the model is very important to the

operator and passengers alike. As far as possible, the prediction model should not overestimate

or underestimate the bus arrival time. The less the variance or the margin of error, the better the

system’s performance will be.

Table 7-1 and Table 7-2 present the percentage of testing samples that are overestimated and

underestimated by the proposed location-based ANNs. Overestimation is defined as the bus

arriving earlier than the model’s estimation result and underestimation means that the bus arrived

later than the forecast result.

Table 7-1: Overestimation vs. Underestimation (Gardiner Expressway Eastbound Route)

Overestimation (%) Underestimation (%) Origin/ Destination Union GO Bus Terminal Union GO Bus Terminal Square One Bus Terminal 51.4% 48.7%

Cooksville GO Station 57.1% 42.9% Dixie GO Station 45.0% 55.0% Dufferin Street 51.0% 49.0%

Table 7-2: Overestimation vs. Underestimation (Gardiner Expressway Westbound Route)

Overestimation (%) Underestimation (%) Origin/

Destination Dixie GO

Station

Cooksville GO

Station


Dixie GO

Station

Cooksville GO

Station


Union GO Bus Terminal 75.0% 52.3% 43.2% 25.0% 47.7% 56.8%

79

Overestimation (%) Underestimation (%) Origin/

Destination Dixie GO

Station

Cooksville GO

Station


Dixie GO

Station

Cooksville GO

Station


Highway 427/ QEW 59.0% 49.0% 60.8% 41.0% 51.0% 39.2%

Both tables indicate that approximately 40% to 60% of testing samples are overestimated, which

means that if commuters follow the predicted times, there is about a 50% chance of them missing

the bus. Such risks should be mitigated by applying a proper operational strategy in announcing

bus estimation times.

7.2 Operational Strategy Alternatives Calibrations and Analysis This section introduces an operating strategy that will be incorporated into the bus travel time

prediction model to reduce the overall costs for both the bus operators and the passengers.

Currently, no GO bus driver is permitted to depart from the bus stop earlier than the scheduled

time. Therefore, if the predicted system is implemented, in the case when the estimated arrival

time is earlier than the scheduled time, the scheduled time will be disseminated to the general

public through different telecommunications media. If the bus arrives early, it will be idle and

only permitted to leave at the scheduled time. This way, there is no chance that any passenger

would miss the bus that arrives and departs earlier than the schedule. If it turns out that the bus

actually arrives at the stop later than the scheduled time, passengers waiting at the bus stop will

wait for a few more minutes for the bus to arrive, which is less risky compared to missing the

bus. Figure 7-1 illustrates how above cases would happen.

Figure 7-1: Case when Estimated Arrival Time is earlier than the Scheduled Time

80

In the case when the estimated arrival time is later than the scheduled time, a more detailed

analysis is required to determine the most optimal operational strategy as follows:

• Option_1 (Hold and Wait) – If the estimated time is later than the scheduled time, the

estimated time becomes the new scheduled time. The bus would have to follow the new

scheduled time regardless of when it actually arrives at the station.

• Option_2 (No Idling) – The estimated arrival time is later than the scheduled time. The

estimated time is broadcast but not used as the new schedule. Buses that arrive after the

original scheduled time but before the broadcast time may leave the bus stop without

idling.

• Option_3 (Without ATIS) – Only the regular scheduled time is displayed to travellers, i.e.

the public is not aware of the estimated time. Late arrival buses depart from bus stops

after picking up and dropping off passengers. This option is added to determine whether

ATIS is worth implementing.

In general, different stakeholders value wait time differently. When the bus arrives between the

original scheduled and the predicted late time, passengers on the bus and the bus driver

experience an additional wait time until the new schedule passes, if Option_1 is implemented. If

Option_2 is chosen, had the bus arrived earlier than the estimated time, passengers at the bus

stop would miss the bus. Under Option_3 runs, passengers at bus stops would experience wait

time equalling the bus’s delay time.

Figure 7-2 gives a flow chart of the operational strategies working under different scenarios.

Table 7-3 demonstrates the wait time calculation equations under different scenarios using the

three strategies.

81

Figure 7-2: Bus Operational Strategy Flow Chart

Table 7-3: Bus Stakeholders’ Wait Time with Different Bus Operational Strategies

Cases Options Broadcasting Information

Critical Stakeholders Wait Time Equations, Wait

#1 N/A Scheduled Time

Bus operator, in-bus travellers ActSchWait −=

#2 N/A Scheduled

Time Bus operator, in-

bus travellers ActSchWait −=

#3 N/A Scheduled Time

Passengers waiting at bus

stops SchActWait −=

#4 Option_1 Predicted Time Bus operator, in-bus travellers ActEstWait −=

#4 Option_2 Predicted Time

Bus operator, in-bus travellers,

passengers waiting at bus

stops

Bus operator, in-vehicle travellers: ActScht −=

Passengers waiting at bus stops:

EstNextBusArrWait −=

#4 Option_3 Scheduled Time

Bus operator, in-bus travellers ActSchWait −=

#5 Option_1 Predicted Time Bus operator, in-bus travellers ActEstWait −=

#5 Option_2 Predicted TimePassengers

waiting at bus stops

EstNextBusArrWait −=

82

Cases Options Broadcasting Information

Critical Stakeholders Wait Time Equations, Wait






EstActWait −=



EstActWait −=




Remark: Act is the actual bus arrival time, Sch is the scheduled bus arrival time, Est is the estimated bus arrival time (from the model), NextBusArr is the next bus arrival time, and Wait is the bus stakeholders’ wait time.

Using the flow chart in Figure 7-2 and wait time equations in Table 7-3, each scenario’s wait

times with the different strategies are computed. Results for routing paths in both directions are

summarized in Table 7-4 and Table 7-5. In both tables, several options’ maximum wait times

are left blank owing to the lack of bus samples occurring for the specific origin and destination

pair. In general, Option_2’s average wait times are always the highest among all origin and

destination pairs because many commuters who rely on the estimated time would miss the bus

and have to wait for the next one. No significant difference can be found between results for

Option_1 and Option_3.

Table 7-4: Wait Time Summary for Gardiner Expressway Eastbound Route

Average Wait Time (Maximum Wait Time) (seconds) Option_1 Option_2 Option_3 Origin Destination

B_DT* P_BS* B_DT* P_BS* B_DT* P_BS* Square

One Bus Terminal

Union GO Bus

Terminal

103 (184) 0 (0) 0 (0) 1789

(1814) 120

(180) 1 (1)

Cooks- ville GO Station

Union GO Bus

Terminal 99 (309) 172

(188) 0 (0) 1400 (1951) 60 (180) 248

(361)

Dixie GO Station

Union GO Bus

Terminal 83 (N/A) 164

(N/A) 0 (N/A) 1823 (N/A) 60 (N/A) 240

(N/A)

Average 101 (192) 86 (117) 0 (0) 1595

(1863) 90 (140) 125 (201)

*Remark: B_DT represents “Bus operator and in-bus travellers” and P_BS represents “Passengers waiting at bus stops”.

83

Table 7-5: Wait Time Summary for Gardiner Expressway Westbound Route

Average Wait Time (Maximum Wait Time) (seconds) Option_1 Option_2 Option_3 Origin Destination

B_DT* P_BS* B_DT* P_BS* B_DT* P_BS* Union

GO Bus Terminal

Square One Bus

Terminal

157 (200) 77 (-) 0 (0) 1061

(1566) 0 (0) 100 (121)



152 (320)

138 (441) 0 (0) 735

(2013) 359

(826) 90 (120)


Dixie GO Station 36 (97) 198

(640) 0 (0) 1256 (1875) 0 (0) 249

(900)

Average 115 (205)

138 (386) 0 (0) 1018

(1818) 120

(275) 146

(380) *Remark: B_DT represents “Bus driver and in-bus travellers” and P_BS represents “Passengers waiting at bus stops”.

To have a better comparison with respect to costs incurred from waiting, an analysis is conducted

using monetary values to represent wait time. Several assumptions are made for this evaluation:

• First, an hour of a traveller’s wait time costs is the same as a person’s minimum hourly

wage – $8.75 in the GTA (Ministry of Labour 2008), or fifteen cents per minute.

• Second, it is assumed that 60% of the bus’s total operation costs (fuel, maintenance and

wages) come from driver wages. If a GO bus driver is paid $25 per hour, the bus

operation cost will be around $25/60%, or $41.67 per hour, and therefore, 70 cents per

minute.

The number of passengers on the bus and passengers waiting at the bus stop also contribute to

differences in the overall costs. The following equations demonstrate the mathematical

calculations of each option’s costs under all scenarios.

Costs for bus operator and in-bus passengers, CostP

WaitPCost P ×+×= )3600/67.413600/75.8(

where P is the number of in-vehicle passengers (ranging from 0 to 30) and Wait is a variable

defined in Table 7-3.

84

Costs for passengers standing at the bus stop, CostT

WaitTCost T ××= 3600/75.8

where T is the number of commuters waiting at the bus stop (ranging from 0 to 10) and Wait is a

variable defined in Table 7-3.

Overall Costs, CostTot

TPTot CostCostCost +=

Figure 7-3 presents stakeholders’ total cost summary with respect to the number of passengers on

the bus and the number of passengers waiting at the bus stop. This figure assists the transit

provider to determine which alternative strategy is more worthwhile to implement when there are

certain number of passengers on the bus and waiting at bus stops downstream.

Figure 7-3a: Cost Comparison for the Origin and Destination Pair, “Square One Bus Terminal-to-Union GO Bus Terminal”

Figure 7-3b: Cost Comparison for the Origin and Destination Pair, “Cooksville GO Station-

to-Union GO Bus Terminal”

85

Figure 7-3c: Cost Comparison for the Origin and Destination Pair, “Dixie GO Station-to-

Union GO Bus Terminal”

Figure 7-3d: Cost Comparison for the Origin and Destination Pair, “Union GO Bus

Terminal-to-Square One Bus Terminal”

Figure 7-3e: Cost Comparison for the Origin and Destination Pair, “Union GO Bus Terminal-to-Cooksville GO Station”

Figure 7-3f: Cost Comparison for the Origin and Destination Pair, “Union GO Bus

Terminal-to-Dixie GO Station” *Remark: Red dots represent the ratio of overall costs of Option_2 to Option_1; Blue dots represent the ratio of overall costs of Option_3 to Option_1.

Figure 7-3: Cost Comparison for Different Origin and Destination Pairs

Table 7-6 and Table 7-7 show the average cost comparison summary for the three options, using

Option_1, the Hold and Wait strategy, as the reference point. Using the example of the

eastbound direction, results indicate that Option_2 costs an average of fourteen times more than

Option_1 for all origin and destination estimation pairs. When the author compares Option_1

and Option_3, Option_3’s average costs are 1.23 times those of Option_1, except for the origin

and destination pair of Square One Bus Terminal and Union GO Bus Terminal. This indicates

86

that operational strategies should be determined on a case by case basis for each origin and

destination pair. Similar results are seen in the westbound direction. As the commuting distance

decreases though, the ANN estimation becomes more accurate, as illustrated in Figure 6-2 to

Figure 6-5 in Section 6.4. In this case, implementing Option_1, the Hold and Wait strategy, is

appropriate because it lowers the costs of bus delays incurred by stakeholders the most.

Table 7-6: Ratio of Time Cost Monetary Value Comparison Summary (Option_2 vs.

Option_1)

Origin/ Destination Square One Bus Terminal


Dixie GO Station



Cooksville GO Station 25.17

Dixie GO Station 6.76 Union GO Bus

Terminal 2.95 4.56 83.65

Table 7-7: Ratio of Time Cost Monetary Value Comparison Summary (Option_3 vs.

Option_1)

Origin/ Destination Square One Bus Terminal


Dixie GO Station



Cooksville GO Station 1.52

Dixie GO Station 1.58 Union GO Bus

Terminal 0.52 2.89 26.93

7.3 Graphical User Interface Design Once the operational strategy is developed, a complete bus forecasting model is ready for

implementation. In order to combine all analysis and calculations into one single system, a

Graphical User Interface (GUI) platform is introduced to make this application more user-

friendly. This GUI also integrates all estimation procedures and operational strategies, and

provides the upcoming bus status information to transit operators and passengers.

In the GUI design, it is assumed that all data are available from various sources and they are

already in the pre-set format required by the application. The GUI is developed using Visual

87

Basic for Microsoft Office Excel 2007. A screenshot of the GUI is shown in Figure 7-4. Once

all data are input into the program, the total travel time to the destination is estimated by the

location-based ANN. Afterwards, the final broadcast time schedule using a suitable operational

strategy is disseminated to transit users, as illustrated in Figure 7-5. The full syntax of the GUI

design can be found in Appendix G.

Figure 7-4: Basic Design of the Graphical User Interface

Figure 7-5: Travel Time Broadcasting Results

88

Chapter 8 Thesis Conclusions and Recommendations

8 Thesis Conclusions and Recommendations

8.1 Conclusions In large North American cities, many individuals commute from the suburbs to work in the CBD

every day. This large population shift has triggered an increase of regional transit services. In

Toronto, GO Transit, a regional transit provider, serves more than 35,000 passengers per day

(GO Transit 2008a). The ridership is expected to increase even more in the near future owing to

the higher oil prices and parking fares. Even though this travel option has attractive advantages,

its low frequency necessitates more stringent reliability requirements for commuter transit to be

attractive. APTS can encourage more people to take public transit. The regional bus travel time

estimation model is an APTS technique that can promote regional bus services and benefit many

stakeholders such as transit providers and users.

Very few researches have addressed regional transit’s journey time estimation. This is mainly

because of the lack of data and the complex interactions amongst numerous factors related to

traffic conditions, weather conditions, transit terminal locations and so on. Regional transit lines

usually run long distances along freeways and major arterials. Their travel time is always

affected by congestion on freeways and arterials as well as traffic signals. Moreover, it is very

difficult to use the bus ahead as a reference bus to estimate travel time owing to the long

headway between bus services. Hence, the aim of this research project is to develop an ANN to

dynamically predict the arrival time of the regional bus at its destination. GO bus data are used

in this study.

The data used in this research are obtained from different public and academic organizations.

They include: loop detector data on freeways from the ICAT system at the University of Toronto

and from the MTO, weather information from Environment Canada, incident reports from the

ICAT, and bus trajectories from GPS devices installed on individual GO buses. The study time

period is from 5:30 a.m. to 12:00 noon. The study path is a major route between Square One Bus

Terminal and Union GO Bus Terminal, running along major arterials in Mississauga before it

89

gets to the Gardiner Expressway travelling towards downtown Toronto. Buses usually stop at

two intermediate points – Cooksville GO Station and Dixie GO Station. In the eastbound

direction, each bus run is separated into three sample sets – “Square One Bus Terminal-to-Union

GO Bus Terminal”, “Cooksville GO Station-to-Union GO Bus Terminal”, and “Dixie GO

Station-to-Union GO Bus Terminal”. Similar sampling formats are used in the westbound

direction, which are “Union-GO Bus Terminal-to-Square One Bus Terminal”, “Union GO Bus

Terminal-to-Cooksville GO Station” and “Union GO Bus Terminal-to-Dixie GO Station”. Each

sample set contains a complete set of input variables. Travel times to the final destination are

estimated when the bus departs from each of these major stops. These sample sets are divided

into two parts, one for model calibration and the other for model testing.

In the eastbound direction, when the bus departs from the last suburban bus stop, Dixie GO

Station, the bus runs for more than 20km of freeway to the destination, Union GO Bus Terminal.

An additional checkpoint which is not a bus stop, Dufferin Street, is added to provide more

accurate estimation. Similarly, an extra checkpoint at Highway 427/QEW is chosen for the

westbound routing path.

The multilayer feedforward neural network with backpropagation training is used for prediction.

The ANN structure formation depends on the nature of inputs, the availability of the desired

outputs, the nonlinearity and the number of hidden layers. The ANN training process may over-

fit training samples in some cases. To avoid this problem, 30% of the data is reserved for

validation. Also, two ANN simplification techniques, sensitivity analysis and principal

component analysis, are applied to reduce the input components size. These methods can

minimize the ANN training time and improve the travel time prediction accuracy.

In the model calibration, two types of ANN models are studied, direction-based and location-

based models. Direction-based models use one ANN structure for all origin and destination pairs

along the same route. Location-based models are, on the other hand, location-specific, such that

each origin and destination pair has its own ANN structure. Root Mean Square Error (RMSE) is

used to assess the estimation accuracy of the models. The evaluation of the ANN structure

format proved that the location-based ANNs are more accurate than the direction-based ANNs

by an average of thirteen seconds. Nevertheless, the calibration of location-based models is

time-consuming.

90

The calibrated location-specific ANNs are then compared with two other modelling approaches –

historical average models and linear regression models. In the historical average approach, each

origin and destination pair requires a specific type of historical average configuration. The linear

regression model development is similar to that of ANNs. Results of the linear regression model

also demonstrate that location-based models outperform direction-based models. When all

modelling approaches and configurations are compared together, the location-based version of

the ANN gives the smallest RMSE. The analysis also indicates that RMSE goes down as the bus

location is closer to the destination, which is expected. Using the eastbound route as an example,

at Square One Bus Terminal, the RMSE for the prediction is 519 seconds; at Dufferin Street, a

closer checkpoint to the destination, the RMSE is only 82 seconds.

Although ANNs perform very well in bus journey time estimation, overestimation of arrival time

sometimes occurs. An operational strategy needs to be incorporated to minimize stakeholders’

costs. Three scenarios are analyzed to determine which would result in the least overall cost for

all stakeholders at every origin and destination pair. To perform the cost analysis, passenger

wait times are transformed into monetary values. Results show that the optimal strategy varies

depending on the location and the specific situation. As the commuting distance decreases,

however, the proposed strategy of using the estimated time as the new scheduled time should be

implemented.

Finally, since implementation of this system in real life is the final goal of this project, a GUI

platform has been designed. This platform incorporates the operational strategy and provides

passengers information on the next bus arrival time in a user-friendly way.

8.2 Recommendations The study period for this project was limited to January to April, 2008 between 5:30 a.m. and

12:00 noon owing to data availability limitations. The lack of more extensive data makes the

resulting model applicable only to the period of the analysis. It is not known at this stage

whether the models are transferable to other times of the year. Factors such as different time of

day and seasonal periods would always impact on vehicles’ run time on roads. In order to

deploy the proposed model, more traffic data from other time periods should be gathered, so that

the ANN models can capture a larger variety of travel time patterns during the training process.

91

In addition, this project only focuses on predicting bus journey time along the Gardiner

Expressway corridor in the eastbound direction. More bus travel information is needed along

other corridors, including the parallel path on Lakeshore Boulevard. The combination of the two

corridors’ forecasting results could provide route guidance for GO bus drivers.

Future research on regional bus transit should also put more focus on the arterial component of

the journey to better predict bus arrival times. Signal timing plans and loop detector data from

the City of Mississauga, for instance, could improve bus journey time prediction along arterials.

Another suggestion for future research would be obtaining pre-aggregate weather information

from Environment Canada, related to the hourly rainfall and snowfall information. Hourly

information on snow accumulated on freeways and highway run-off may also be useful for travel

time estimation. Conditions of road surfaces tend to affect travel speeds more than the actual

weather (Daniel et al. 2009).

All data sources used in the research are collected separately from various sources, such as traffic

data from the ICAT and the MTO, and weather information from Environment Canada.

Currently, there is no common database available to obtain all the required information at the

same time and input them into the ANN for bus travel time estimation. It is suggested that all

agencies should work together in developing a centre-to-centre data transfer system with

common computational language standards, so that traveller information can be gathered more

easily.

Traffic reports from bus drivers would be another source of input that can be considered in

further studies. Currently, bus drivers report road conditions to the traffic control centre and

other bus drivers. If such messages are added to the model, the model’s reliability could

increase, especially when there are malfunctions of loop detectors. In addition, this project only

used Route 21, Square One Bus Terminal to Union GO Bus Terminal, as the study route. In

order to confirm the benefits and accuracy of this model, another bus route with similar

characteristics should be analyzed to insure that a location-based ANN model is the best

technique to use.

A bus-holding operational strategy is incorporated with the prediction model. More detailed

study should be performed to find the best operational strategy to implement under different

92

circumstances. These circumstances could be location-related (determined by the bus’s current

location) or customer-related (determined by a certain type or number of passengers waiting at

bus stops downstream or sitting on the bus). Finally, additional design work on the GUI is

required. A timer should be set in the GUI, so that the bus’s location and other detectors’

information can be input into the system automatically and travel time will update once the bus

reaches the major checkpoints. In this case, no more manual input would be required.

93

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98

Appendix A: Historical Buses’ Travel Time Performances

0

30

60

90

120

150

0 5 10 15 20 25 30 35

Distance from Square One Bus Terminal (km)

Travel Tim

e (m

in)

Mean

Median

Max

95th Percenti le

Schedule

Figure A-1: Time Space Diagram – AM Peak Period (Gardiner Expressway Eastbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percenti le

Schedule

Figure A-2: Time Space Diagram – Off-Peak Period (Gardiner Expressway Eastbound Route)

99

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-3: Time Space Diagram – PM Peak Period (Gardiner Expressway Eastbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-4: Time Space Diagram – Late Evening Period (Gardiner Expressway Eastbound

Route)

100

0

30

60

90

120

150

0 5 10 15 20 25 30 35

Distance from Square One GO Bus Terminal (km)

Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-5: Time Space Diagram – Weekday (Gardiner Expressway Eastbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-6: Time Space Diagram – Weekend (Gardiner Expressway Eastbound Route)

101

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-7: Time Space Diagram – Good Weather Conditions (Gardiner Expressway

Eastbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-8: Time Space Diagram – Bad Weather Conditions (Gardiner Expressway Eastbound

Route)

102

0

30

60

90

120

150

180

210

0 5 10 15 20 25 30 35

Distance from Union GO Bus Terminal (km)

Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-9: Time Space Diagram – AM Peak Period (Gardiner Expressway Westbound Route)

0

30

60

90

120

150

180

210

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-10: Time-space Diagram – Off-Peak Period (Gardiner Expressway Westbound Route)

103

0

30

60

90

120

150

180

210

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-11: Time-space Diagram – PM Peak Period (Gardiner Expressway Westbound Route)

0

30

60

90

120

150

180

210

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-12: Time-Space Diagram – Late Evening Period (Gardiner Expressway Westbound

Route)

104

0

30

60

90

120

150

180

210

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-13: Time-Space Diagram – Weekday (Gardiner Expressway Westbound Route)

0

30

60

90

120

150

180

210

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-14: Time-Space Diagram – Weekend (Gardiner Expressway Westbound Route)

105

0

30

60

90

120

150

180

210

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-15: Time Space Diagram – Good Weather Conditions (Gardiner Expressway

Westbound Route)

0

30

60

90

120

150

180

210

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-16: Time Space Diagram – Bad Weather Conditions (Gardiner Expressway

Westbound Route)

106

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-17: Time Space Diagram – AM Peak Period (Lakeshore Boulevard Eastbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-18: Time Space Diagram – Off-Peak Period (Lakeshore Boulevard Eastbound Route)

107

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-19: Time Space Diagram – PM Peak Period (Lakeshore Boulevard Eastbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-20: Time Space Diagram – Late Evening Peak Period (Lakeshore Boulevard

Eastbound Route)

108

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-21: Time Space Diagram – Weekday (Lakeshore Boulevard Eastbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-22: Time Space Diagram – Weekend (Lakeshore Boulevard Eastbound Route)

109

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-23: Time Space Diagram – Good Weather Conditions (Lakeshore Boulevard

Eastbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-24: Time Space Diagram – Bad Weather Conditions (Lakeshore Boulevard Eastbound

Route)

110

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-25: Time Space Diagram – AM Peak Period (Lakeshore Boulevard Westbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-26: Time Space Diagram – Off-Peak Period (Lakeshore Boulevard Westbound Route)

111

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-27: Time Space Diagram – PM Peak Period (Lakeshore Boulevard Westbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-28: Time Space Diagram – Late Evening Period (Lakeshore Boulevard Westbound

Route)

112

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Tim

e (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-29: Time Space Diagram – Weekday (Lakeshore Boulevard Westbound Route)

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Time (min)

Mean

Median

Max

95th Percenti le

Schedule

Figure A-30: Time Space Diagram – Weekend (Lakeshore Boulevard Westbound Route)

113

0

30

60

90

120

150

0 5 10 15 20 25 30 35


Travel Time (m

in)

Mean

Median

Max

95th Percentile

Schedule

Figure A-31: Time Space Diagram – Good Weather Condition (Lakeshore Boulevard

Westbound Route)

114

Appendix B: Programming Syntax for Artificial Neural Network Training

% Inputting training and testing samples into MATLAB with Principal Component Analysis (Only applicable for direction-based model) load Miss_Model_Data.txt; inputs = Miss_Model_Data; load Miss_Model_Target.txt; targets = Miss_Model_Target; load Miss_Test_Data.txt; Test = Miss_Test_Data; load Miss_Test_Target.txt; Final = Miss_Test_Target; %Perform Principal Component Analysis [pn, stdp] = mapstd(inputs); [ptrans, transMat] = processpca(pn, 0.01); %Determine the size of input components for ANN Training after Principal component analysis [R,Q] =size(ptrans); % Create Network, depends on the proposed network structure for training numHiddenNeurons = 1; % Adjust as desired %numHiddenNuerons2 = 7; % Adjust as desired net = newfit(ptrans,targets, numHiddenNeurons, {'tansig' 'tansig'}, 'trainlm'); net.trainParam.lr = 0.05; % Learning Rate net.divideParam.trainRatio = 70/100; % Adjust as desired for training net.divideParam.valRatio = 30/100; % Adjust as desired for validation net.divideParam.testRatio = 0/100; % Adjust as desired % Train and Apply Network [net,tr] = train(net,ptrans,targets); outputs = sim(net,ptrans); % Plot and study the network prerformance during training process plotperf(tr) plotfit(net,inputs,targets) plotregression(targets,outputs) %save the network with a new network name net_1 = net; % Simulate testing samples pnewn = mapstd('apply', Test,stdp); pnewtrans = processpca('apply', pnewn,transMat);

115

Result_1= sim(net_1,pnewtrans); % Inputting training and testing samples into MATLAB with no simplification Technique (Applicable for both direction-based and location base models) load Cooksville_Model_Data.txt; inputs = Cooksville_Model_Data; load Cooksville_Model_Target.txt; targets = Cooksville_Model_Target; load Cooksville_Test_Data.txt; Test = Cooksville_Test_Data; load Cooksville_Test_Target.txt; Final = Cooksville_Test_Target; % Create Network, depends on the proposed network structure for training numHiddenNeurons = 20 ;% Adjust as desired %numHiddenNuerons2 = 10 ; net = newfit(inputs,targets, numHiddenNeurons, {'logsig' 'purelin'}, 'trainlm'); net.trainParam.lr = 0.05; % Learning Rate net.divideParam.trainRatio = 70/100; % Adjust as desired for training net.divideParam.valRatio = 30/100; % Adjust as desired for validation net.divideParam.testRatio = 0/100; % Adjust as desired % Train and Apply Network [net,tr] = train(net,inputs,targets); outputs = sim(net,inputs);

116

Appendix C: Historical Travel Time Summary Table B-1: HAE1 – Gardiner Expressway Eastbound Route

Origin Destination Day of the Week Bus Journey Time (s) Square One Bus


Terminal Weekday 2461


Union GO Bus Terminal Weekend 1681


Union GO Bus Terminal Weekday 2101


Union GO Bus Terminal Weekend 1440

Dixie GO Station Union GO Bus Terminal Weekday 1320

Dufferin Street Union GO Bus Terminal Weekday 439

Dufferin Street Union GO Bus Terminal Weekend 347

Table B-2: HAE2 – Gardiner Expressway Eastbound Route

Origin Destination Day of the Week

Operating Hour

Bus Journey Time (s)


Union GO Bus Terminal Weekday 5 am 2461








Union GO Bus Terminal Weekend 6 am 1621













117


Operating Hour


















Dixie GO Station Union GO Bus Terminal Weekday 5 am 1080




Dufferin Street Union GO Bus Terminal Weekday 6 am 345




Dufferin Street Union GO Bus Terminal Weekend 6 am 331






118



Operating Hour

Weather Condition



Union GO Bus Terminal Weekday 5 am Good 2100


Union GO Bus Terminal Weekday 5 am Bad 2131








Union GO Bus Terminal Weekday 10am Bad 2613




Union GO Bus Terminal Weekend 6 am Good 1621




Union GO Bus Terminal Weekend 7 am Bad 2041























119


Operating Hour

Weather Condition







Union GO Bus Terminal Weekend 7 am Bad 1560









Dixie GO station


Dixie GO station


Dixie GO station


Dixie GO station


Dixie GO station


Dixie GO station


Dufferin Street Union GO Bus Terminal Weekday 6am Good 345

Dufferin Street Union GO Bus Terminal Weekday 9 am Good 510



Dufferin Street Union GO Bus Terminal Weekend 6 am Good 331





120


Operating Hour

Weather Condition



Dufferin Street Union GO Bus Terminal Weekday 6 am Bad 345




Dufferin Street Union GO Bus Terminal Weekend 6 am Bad 331








Operating Hour

Weather Condition Incidents Bus Journey

Time (s) Square One

Bus Terminal

Union GO Bus

Terminal Weekday 5 am Good N/A 2100

Square One Bus

Terminal

Union GO Bus

Terminal Weekday 5 am Bad N/A 2131

Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus

Terminal Weekday 9 am Good Roadwork 2589

Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus


121


Operating Hour


Time (s) Square One

Bus Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus

Terminal Weekday 10 am Good Unknown 2701

Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus

Terminal Weekend 6 am Good N/A 1621

Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus

Terminal Weekend 7 am Bad N/A 2041

Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus


Square One Bus

Terminal

Union GO Bus



Union GO Bus



Union GO Bus


122


Operating Hour


Time (s)


Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus



Union GO Bus


123


Operating Hour


Time (s)


Union GO Bus



Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dixie GO Station

Union GO Bus


Dufferin Street

Union GO Bus

Terminal Weekday 6am Good N/A 345

Dufferin Street

Union GO Bus


124


Operating Hour


Time (s)

Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


125


Operating Hour


Time (s)

Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Dufferin Street

Union GO Bus


Table B-5: HAW1 – Gardiner Expressway Westbound Route

Origin Destination Day of the Week Bus Journey Time (s) Union GO Bus


Terminal Weekday 2340


Square One Bus Terminal Weekend 1740


Cooksville GO Station Weekday 1981


Cooksville GO Station Weekend 1381

Union GO Bus Terminal Dixie GO

Station

Dixie GO Station Weekday 1081

Highway 427/ QEW Square One Bus Terminal Weekday 1523

Highway 427/ QEW Square One Bus Terminal Weekend 907

Highway 427/ QEW Cooksville GO Station Weekday 1141

Highway 427/ QEW Cooksville GO Station Weekend 546

Highway 427/ QEW Dixie GO Station Weekday 271



Operating Hour



Square One Bus Terminal Weekday 5 am 3495





126


Operating Hour











Square One Bus Terminal Weekend 7 am 1591










Cooksville GO Station Weekday 5 am 3255














Cooksville GO Station Weekend 7 am 1171










Dixie GO Station Weekday 5 am 2475

127


Operating Hour














Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


128


Operating Hour


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW




Operating Hour

Weather Condition



Square One Bus Terminal Weekday 5 am Good 3495




Square One Bus Terminal Weekday 7am Good 2701


Square One Bus Terminal Weekday 7am Bad 2761




Square One Bus Terminal Weekday 8 am Bad 2581




Square One Bus Terminal Weekday 9am Bad 2340

129


Operating Hour

Weather Condition











Square One Bus Terminal Weekend 7 am Good 1471


Square One Bus Terminal Weekend 7 am Bad 1710


















Cooksville GO Station Weekday 5 am Good 3255




Cooksville GO Station Weekday 7am Good 2251


Cooksville GO Station Weekday 7am Bad 2341




Cooksville GO Station Weekday 8 am Bad 2190




Cooksville GO Station Weekday 9am Bad 1980

130


Operating Hour

Weather Condition











Cooksville GO Station Weekend 7 am Good 1171


Cooksville GO Station Weekend 7 am Bad 1260


















Dixie GO Station Weekday 5 am Good 2475




Dixie GO Station Weekday 7am Good 1261


Dixie GO Station Weekday 7am Bad 1200




Dixie GO Station Weekday 8 am Bad 1410




Dixie GO Station Weekday 9am Bad 1200

131


Operating Hour

Weather Condition










Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


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Operating Hour

Weather Condition


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


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Highway 427/ QEW


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Operating Hour

Weather Condition


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


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Highway 427/ QEW


Highway 427/ QEW


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Operating Hour

Weather Condition


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW

Dixie GO Station Weekend 6 am Bad 253

Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Highway 427/ QEW


Remark: HAW4 of the Gardiner Expressway westbound route has exactly the same results as HAW3 because no incident occurred in both modelling and historical samples.

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Appendix D: Input Variables Lists Variables Description(s)

Loc Variable of the origin location, i, where the regional bus departs or ends (Square One Bus Terminal = 1, Cooksville GO Station = 2, Dixie GO Station = 3)

Type_Inc Variable of the type of incident happened at downstream when the regional bus starts (Collisions = 1, Disabled Vehicles = 2, Road Works = 3, Unknowns = 4)

Start_Inc Variable of the incident starting hour while the bus operates End_Inc Variable of the incident ending hour while the bus operates

Lanes_Aff Variable of the number of lanes affected by incidents at downstream while the bus is running (0 lane = 0, 1 lane = 1, 2 lanes = 2, shoulder = 3)

Loc_Inc Variable of the location where the incident happens (1 = Square One Bus Terminal, Cooksville GO Station = 2, …etc)

Rain Variable of daily rainfall in millimetres Snow Variable of daily snowfall in centimetres Precip Variable of daily precipitation in millimetres

Snow_Ground Variable of daily snow accumulated on ground in centimetres Avg_Vis Variable of daily average visibility in kilometres Hr_Vis Variable of hourly visibility in kilometres

Bad_Weather Variable of the weather condition, if bad condition = 1, otherwise = 0 GPS_Speed Variable of the bus travel speed collected by the GPS device

West_Volume Variable of volume at The West Mall loop detectors at the time when the bus departs from a major checkpoint, i

West_Occupancy Variable of occupancy at The West Mall loop detectors at the time when the bus departs from a major checkpoint, i

West_Speed Variable of speed at The West Mall loop detectors at the time when the bus departs from a a major checkpoint, i

QEW_Volume Variable of volume at Highway 427/QEW loop detectors at the time when the bus departs from a major checkpoint, i

QEW_Occupancy Variable of occupancy at Highway 427/QEW loop detectors at the time when the bus departs from a major checkpoint, i

QEW_Speed Variable of speed at Highway 427/QEW loop detectors at the time when the bus departs from a major checkpoint, i

Ellis_Volume Variable of volume at Ellis Avenue loop detectors at the time when the bus departs from a major checkpoint, i

Ellis_Occupancy Variable of occupancy at Ellis Avenue loop detectors at the time when the bus departs from a major checkpoint, i

Ellis_Speed Variable of speed at Ellis Avenue loop detectors at the time when the bus departs from a major checkpoint, i

Colborne_Volume Variable of volume at Colborne Lodge Road loop detectors at the time when the bus departs from a major checkpoint, i

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Variables Description(s) Colborne_Occupancy Variable of occupancy at Colborne Lodge Road loop detectors at the

time when the bus departs from a major checkpoint, i Colborne_Speed Variable of speed at Colborne Lodge Road loop detectors at the time

when the bus departs from a major checkpoint, i Parkside_Volume Variable of volume at Parkside Drive loop detectors at the time when

the bus departs from a major checkpoint, i Parkside_Occupancy Variable of occupancy at Parkside Drive loop detectors at the time when

the bus departs from a major checkpoint, i Parkside_Speed Variable of speed at Parkside Drive loop detectors at the time when the

bus departs from a major checkpoint, i Dowling_Volume Variable of volume at Dowling Avenue loop detectors at the time when

the bus departs from a major checkpoint, i Dowling_Occupancy Variable of occupancy at Dowling Avenue loop detectors at the time

when the bus departs from a major checkpoint, i Dowling_Speed Variable of speed at Dowling Avenue loop detectors at the time when

the bus departs from a major checkpoint, i Jameson_Volume Variable of volume at Jameson Avenue loop detectors at the time when

the bus departs from a major checkpoint, i Jameson_Occupancy Variable of occupancy at Jameson Avenue loop detectors at the time

when the bus departs from a major checkpoint, i Jameson_Speed Variable of speed at Jameson Avenue loop detectors at the time when

the bus departs from a major checkpoint, i Dunn_Volume Variable of volume at Dunn Avenue loop detectors at the time when the

bus departs from a major checkpoint, i Dunn_Occupancy Variable of occupancy at Dunn Avenue loop detectors at the time when

the bus departs from a major checkpoint, i Dunn_Speed Variable of speed at Dunn Avenue loop detectors at the time when the

bus departs from a major checkpoint, i Dufferin_Volume Variable of volume at Dufferin Street loop detectors at the time when

the bus departs from a major checkpoint, i Dufferin_Occupancy Variable of occupancy at Dufferin Street loop detectors at the time when

the bus departs from a major checkpoint, i Dufferin_Speed Variable of speed at Dufferin Street loop detectors at the time when the

bus departs from a major checkpoint, i Strachan_Volume Variable of volume at Strachan Avenue loop detectors at the time when

the bus departs from a major checkpoint, i Strachan_Occupancy Variable of occupancy at Strachan Avenue loop detectors at the time

when the bus departs from a major checkpoint, i Strachan_Speed Variable of speed at Strachan Avenue loop detectors at the time when

the bus departs from a major checkpoint, i Spadina_Volume Variable of volume at Spadina Avenue loop detectors at the time when

the bus departs from a major checkpoint, i Spadina_Occupancy Variable of occupancy at Spadina Avenue loop detectors at the time

when the bus departs from a major checkpoint, i Spadina_Speed Variable of speed at Spadina Avenue loop detectors at the time when the

bus departs from a major checkpoint, i

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Variables Description(s) Loc1 Dummy variable for estimating bus travel time from Union GO Bus

Terminal to Square One Bus Terminal Loc2 Dummy variable for estimating bus journey time from Union GO Bus

Terminal to Cooksville GO Station Historical Variable of historical data summarized by day of the week, daily bus

operating hour and/or weather condition

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Appendix E: Regression Model – Gardiner Expressway Eastbound Route

139

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Appendix F: Regression Model – Gardiner Expressway Westbound Route

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Appendix G: Programming Syntax for Graphical User Interfaces

Public Sub cmdData_Click() Dim LongCurr As Single 'Current Bus Dim LatCurr As Single 'Current Bus Dim LongFix1 As Single 'Square One Dim LatFix1 As Single 'Square One Dim LongFix2 As Single 'Cooksville Dim LatFix2 As Single 'Cooksville Dim LongFix3 As Single 'Dixie Dim LatFix3 As Single 'Dixie Dim LongFix4 As Single 'Dufferin Dim LatFix4 As Single 'Dufferin Dim Dist1 As Double Dim Dist2 As Double Dim Dist3 As Double Dim Dist4 As Double Dim stInputFile As String Dim GPSspeed As Single 'GPS device capture speed Dim BusCurrTime As Single Dim BusNumber As Single Dim Day_Bus As String Dim Hour_Bus As Single Dim Minute_Bus As Single Dim Second_Bus As Single Dim DayBus As String Dim Weekday_Bus As Single Dim Rainfall As Single 'Rainfall Dim Snowfall As Single 'Snowfall Dim SnowGround As Single 'Snow on Ground Dim TotalPrep As Single 'Total prepicitation Dim AvgVis As Single 'Predicted Daily visibility Dim HrVis As Single 'Hourly visibility Dim WeatherCondition As Single 'Weather condition Dim TypeofIncident As Single 'Incident Type Dim AffectedLane As Single 'Number of Affected Lane Dim IncStTime As Single 'Incident Start Time Dim IncEndTime As Single 'always zero but if queuing still exists then the incident time Dim IncLoc As Single 'Incident Location Dim stInputWeather As String Dim stInputIncident As String Dim stInputGPS As String Dim stInputLoop As String Dim stHistorical As String

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Dim LocationNum As Single Dim stOutputMath As String Dim Historical As Single 'generalized day of the week and hour ' Loop data Dim WestMall_1 As Single Dim WestMall_2 As Single Dim WestMall_3 As Single Dim Interchange_1 As Single Dim Interchange_2 As Single Dim Interchange_3 As Single Dim Ellis_1 As Single Dim Ellis_2 As Single Dim Ellis_3 As Single Dim Colborne_1 As Single Dim Colborne_2 As Single Dim Colborne_3 As Single Dim Parkside_1 As Single Dim Parkside_2 As Single Dim Parkside_3 As Single Dim Dowling_1 As Single Dim Dowling_2 As Single Dim Dowling_3 As Single Dim Jameson_1 As Single Dim Jameson_2 As Single Dim Jameson_3 As Single Dim Dunn_1 As Single Dim Dunn_2 As Single Dim Dunn_3 As Single Dim Dufferin_1 As Single Dim Dufferin_2 As Single Dim Dufferin_3 As Single Dim Strachan_1 As Single Dim Strachan_2 As Single Dim Strachan_3 As Single Dim Spadina_1 As Single Dim Spadina_2 As Single Dim Spadina_3 As Single Dim pi As Double Dim Dist1Cos As Single Dim Dist2Cos As Single Dim Dist3Cos As Single Dim Dist4Cos As Single Dim Radius As Single Dim TrialHour As Single Dim L1D1T5 As Single 'Historical Data Dim L1D1T9 As Single Dim L1D1T10 As Single

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Dim L1D1T11 As Single Dim L1D2T6 As Single Dim L1D2T7 As Single Dim L1D2T8 As Single Dim L1D2T9 As Single Dim L1D2T10 As Single Dim L1D2T11 As Single Dim L2D1T5 As Single Dim L2D1T9 As Single Dim L2D1T10 As Single Dim L2D1T11 As Single Dim L2D2T6 As Single Dim L2D2T7 As Single Dim L2D2T8 As Single Dim L2D2T9 As Single Dim L2D2T10 As Single Dim L2D2T11 As Single Dim L3D1T5 As Single Dim L3D1T9 As Single Dim L3D1T10 As Single Dim L3D1T11 As Single Dim L4D1T6 As Single Dim L4D1T9 As Single Dim L4D1T10 As Single Dim L4D1T11 As Single Dim L4D2T6 As Single Dim L4D2T7 As Single Dim L4D2T8 As Single Dim L4D2T9 As Single Dim L4D2T10 As Single Dim L4D2T11 As Single Dim Week As Single pi = 3.141592654 Radius = 6378.1 'Earth Radius 'Checkpoints' coordinates stInputFile = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\Coordinates.txt" Open stInputFile For Input As #1 Input #1, LongFix1 Input #1, LatFix1 Input #1, LongFix2 Input #1, LatFix2 Input #1, LongFix3 Input #1, LatFix3 Input #1, LongFix4

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Input #1, LatFix4 Close #1 'Provided by the GPS Device stInputGPS = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\GPS.txt" Open stInputGPS For Input As #4 Input #4, BusNumber Input #4, LongCurr Input #4, LatCurr Input #4, GPSspeed Input #4, DayBus 'Input #4, BusCurrTime Close #4 Hour_Bus = Hour(DayBus) Minute_Bus = Minute(DayBus) Second_Bus = Second(DayBus) Weekday_Bus = Weekday(DayBus) - 1 If Weekday_Bus = 0 Then Week = 2 ElseIf Weekday_Bus = 6 Then Week = 2 Else Week = 1 End If BusDate.Caption = Format(DayBus, "mm dd yyyy") HourBus.Caption = Hour_Bus MinuteBus.Caption = Minute_Bus SecondBus.Caption = Second_Bus BusNum.Caption = BusNumber 'Calculate Dist1Cos = (Cos(LongCurr * pi / 180) * Cos(LatCurr * pi / 180) * Cos(LongFix1 * pi / 180) * Cos(LatFix1 * pi / 180) + Cos(LongCurr * pi / 180) * Sin(LatCurr * pi / 180) * Cos(LongFix1 * pi / 180) * Sin(LatFix1 * pi / 180) + Sin(LongCurr * pi / 180) * Sin(LongFix1 * pi / 180)) If Dist1Cos <> 1 Then Dist1 = (Atn(-Dist1Cos / Sqr(-Dist1Cos * Dist1Cos + 1)) + 2 * Atn(1)) * Radius Else Dist1 = 0 End If

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Dist2Cos = (Cos(LongCurr * pi / 180) * Cos(LatCurr * pi / 180) * Cos(LongFix2 * pi / 180) * Cos(LatFix2 * pi / 180) + Cos(LongCurr * pi / 180) * Sin(LatCurr * pi / 180) * Cos(LongFix2 * pi / 180) * Sin(LatFix2 * pi / 180) + Sin(LongCurr * pi / 180) * Sin(LongFix2 * pi / 180)) If Dist2Cos <> 1 Then Dist2 = (Atn(-Dist2Cos / Sqr(-Dist2Cos * Dist2Cos + 1)) + 2 * Atn(1)) * Radius Else Dist2 = 0 End If Dist3Cos = Cos(LongCurr * pi / 180) * Cos(LatCurr * pi / 180) * Cos(LongFix3 * pi / 180) * Cos(LatFix3 * pi / 180) + Cos(LongCurr * pi / 180) * Sin(LatCurr * pi / 180) * Cos(LongFix3 * pi / 180) * Sin(LatFix3 * pi / 180) + Sin(LongCurr * pi / 180) * Sin(LongFix3 * pi / 180) If Dist3Cos <> 1 Then Dist3 = (Atn(-Dist3Cos / Sqr(-Dist3Cos * Dist3Cos + 1)) + 2 * Atn(1)) * Radius Else Dist3 = 0 End If Dist4Cos = Cos(LongCurr * pi / 180) * Cos(LatCurr * pi / 180) * Cos(LongFix4 * pi / 180) * Cos(LatFix4 * pi / 180) + Cos(LongCurr * pi / 180) * Sin(LatCurr * pi / 180) * Cos(LongFix4 * pi / 180) * Sin(LatFix4 * pi / 180) + Sin(LongCurr * pi / 180) * Sin(LongFix4 * pi / 180) If Dist4Cos <> 1 Then Dist4 = (Atn(-Dist4Cos / Sqr(-Dist4Cos * Dist4Cos + 1)) + 2 * Atn(1)) * Radius Else Dist4 = 0 End If If Dist1 < 0.2 Then LocationNum = 1 LabelLocation.Caption = "Square One Bus Terminal" LocNum.Caption = LocationNum ElseIf Dist2 < 0.2 Then LocationNum = 2 LabelLocation.Caption = "Cooksville GO Station" LocNum.Caption = LocationNum ElseIf Dist3 < 0.2 Then LocationNum = 3 LabelLocation.Caption = "Dixie GO Station" LocNum.Caption = LocationNum ElseIf Dist4 < 0.2 Then LocationNum = 4 LabelLocation.Caption = "Dufferin and Gardiner Interchange" LocNum.Caption = LocationNum Else Call MsgBox("No Bus Updating will be made at this current location", vbOKOnly + vbInformation, "Error") End If

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'Provided by ICAT stInputIncident = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\Incident.txt" Open stInputIncident For Input As #3 Input #3, TypeofIncident Input #3, AffectLane Input #3, IncStTime Input #3, IncEndTime Input #3, IncLoc Close #3 'Provided by the Weather Canada stInputWeather = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\Weather.txt" Open stInputWeather For Input As #2 Input #2, Rainfall Input #2, Snowfall Input #2, SnowGround Input #2, TotalPrep Input #2, AvgVis Input #2, HrVis Input #2, WeatherCondition Close #2 'Provided by ICAT and MTO stInputLoop = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\Loop.txt" Open stInputLoop For Input As #5 Input #5, WestMall_1 Input #5, WestMall_2 Input #5, WestMall_3 Input #5, Interchange_1 Input #5, Interchange_2 Input #5, Interchange_3 Input #5, Ellis_1 Input #5, Ellis_2 Input #5, Ellis_3 Input #5, Colborne_1 Input #5, Colborne_2 Input #5, Colborne_3 Input #5, Parkside_1 Input #5, Parkside_2 Input #5, Parkside_3 Input #5, Dowling_1 Input #5, Dowling_2 Input #5, Dowling_3

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Input #5, Jameson_1 Input #5, Jameson_2 Input #5, Jameson_3 Input #5, Dunn_1 Input #5, Dunn_2 Input #5, Dunn_3 Input #5, Dufferin_1 Input #5, Dufferin_2 Input #5, Dufferin_3 Input #5, Strachan_1 Input #5, Strachan_2 Input #5, Strachan_3 Input #5, Spadina_1 Input #5, Spadina_2 Input #5, Spadina_3 Close #5 'Historical Data Input stHistorical = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\Historical.txt" Open stHistorical For Input As #7 Input #7, L1D1T5 Input #7, L1D1T9 Input #7, L1D1T10 Input #7, L1D1T11 Input #7, L1D2T6 Input #7, L1D2T7 Input #7, L1D2T8 Input #7, L1D2T9 Input #7, L1D2T10 Input #7, L1D2T11 Input #7, L2D1T5 Input #7, L2D1T9 Input #7, L2D1T10 Input #7, L2D1T11 Input #7, L2D2T6 Input #7, L2D2T7 Input #7, L2D2T8 Input #7, L2D2T9 Input #7, L2D2T10 Input #7, L2D2T11 Input #7, L3D1T5 Input #7, L3D1T9 Input #7, L3D1T10 Input #7, L3D1T11 Input #7, L4D1T6 Input #7, L4D1T9

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Input #7, L4D1T10 Input #7, L4D1T11 Input #7, L4D2T6 Input #7, L4D2T7 Input #7, L4D2T8 Input #7, L4D2T9 Input #7, L4D2T10 Input #7, L4D2T11 Close #7 'Square One If LocationNum = 1 Then If Week = 1 Then If Hour_Bus = 5 Then Historical_Result.Caption = L1D1T5 HistoricalTime = L1D1T5 ElseIf Hour_Bus = 9 Then Historical_Result.Caption = L1D1T9 HistoricalTime = L1D1T9 ElseIf Hour_Bus = 10 Then Historical_Result.Caption = L1D1T10 HistoricalTime = L1D1T10 ElseIf Hour_Bus = 11 Then Historical_Result.Caption = L1D1T11 HistoricalTime = L1D1T11 End If End If End If If LocationNum = 1 Then If Week = 2 Then If Hour_Bus = 6 Then Historical_Result.Caption = L1D2T6 HistoricalTime = L1D2T6 ElseIf Hour_Bus = 7 Then Historical_Result.Caption = L1D2T7 HistoricalTime = L1D2T7 ElseIf Hour_Bus = 8 Then Historical_Result.Caption = L1D2T8 HistoricalTime = L1D2T8 ElseIf Hour_Bus = 9 Then Historical_Result.Caption = L1D2T9 HistoricalTime = L1D2T9 ElseIf Hour_Bus = 10 Then Historical_Result.Caption = L1D2T10 HistoricalTime = L1D2T10 ElseIf Hour_Bus = 11 Then Historical_Result.Caption = L1D2T11

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HistoricalTime = L1D2T11 End If End If End If 'Cooksville If LocationNum = 2 Then If Week = 1 Then If Hour_Bus = 5 Then Historical_Result.Caption = L2D1T5 HistoricalTime = L2D1T5 ElseIf Hour_Bus = 9 Then Historical_Result.Caption = L2D1T9 HistoricalTime = L2D1T9 ElseIf Hour_Bus = 10 Then Historical_Result.Caption = L2D1T10 HistoricalTime = L2D1T10 ElseIf Hour_Bus = 11 Then Historical_Result.Caption = L2D1T11 HistoricalTime = L2D1T11 End If End If End If If LocationNum = 2 Then If Week = 2 Then If Hour_Bus = 6 Then Historical_Result.Caption = L2D2T6 HistoricalTime = L2D2T6 ElseIf Hour_Bus = 7 Then Historical_Result.Caption = L2D2T7 HistoricalTime = L2D2T7 ElseIf Hour_Bus = 8 Then Historical_Result.Caption = L2D2T8 HistoricalTime = L2D2T8 ElseIf Hour_Bus = 9 Then Historical_Result.Caption = L2D2T9 HistoricalTime = L2D2T9 ElseIf Hour_Bus = 10 Then Historical_Result.Caption = L2D2T10 HistoricalTime = L2D2T10 ElseIf Hour_Bus = 11 Then Historical_Result.Caption = L2D2T11 HistoricalTime = L2D2T11 End If End If End If

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'Dixie without weekend service If LocationNum = 3 Then If Week = 1 Then If Hour_Bus = 5 Then Historical_Result.Caption = L3D1T5 HistoricalTime = L3D1T5 ElseIf Hour_Bus = 9 Then Historical_Result.Caption = L3D1T9 HistoricalTime = L3D1T9 ElseIf Hour_Bus = 10 Then Historical_Result.Caption = L3D1T10 HistoricalTime = L3D1T10 ElseIf Hour_Bus = 11 Then Historical_Result.Caption = L3D1T11 HistoricalTime = L3D1T11 End If End If End If 'Dufferin If LocationNum = 4 Then If Week = 1 Then If Hour_Bus = 6 Then Historical_Result.Caption = L6D1T6 HistoricalTime = L6D1T6 ElseIf Hour_Bus = 9 Then Historical_Result.Caption = L6D1T9 HistoricalTime = L6D1T9 ElseIf Hour_Bus = 10 Then Historical_Result.Caption = L6D1T10 HistoricalTime = L6D1T10 ElseIf Hour_Bus = 11 Then Historical_Result.Caption = L6D1T11 HistoricalTime = L6D1T11 End If End If End If If LocationNum = 4 Then If Week = 2 Then If Hour_Bus = 6 Then Historical_Result.Caption = L6D2T6 HistoricalTime = L6D2T6 ElseIf Hour_Bus = 7 Then Historical_Result.Caption = L6D2T7 HistoricalTime = L6D2T7 ElseIf Hour_Bus = 8 Then Historical_Result.Caption = L6D2T8

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HistoricalTime = L6D2T8 ElseIf Hour_Bus = 9 Then Historical_Result.Caption = L6D2T9 HistoricalTime = L6D2T9 ElseIf Hour_Bus = 10 Then Historical_Result.Caption = L6D2T10 HistoricalTime = L6D2T10 ElseIf Hour_Bus = 11 Then Historical_Result.Caption = L6D2T11 HistoricalTime = L6D2T11 End If End If End If LabelRain.Caption = Format(Rainfall, "###0.00") LabelSnow.Caption = Format(Snowfall, "###0.00") LabelSnowGround.Caption = Format(SnowGround, "###0.00") LabelPrep.Caption = Format(TotalPrep, "###0.00") LabelAvgVis.Caption = Format(AvgVis, "###0.00") LabelHrVis.Caption = Format(HrVis, "###0.00") LabelBad.Caption = WeatherCondition LabelInc.Caption = TypeofIncident LabelLanes.Caption = AffectedLane LabelIncStart.Caption = IncStTime LabelIncEnd.Caption = IncEndTime LabelIncLoc.Caption = IncLoc WestMall_Volume.Caption = Format(WestMall_1, "###0") WestMall_Occ.Caption = Format(WestMall_2, "###0") WestMall_Speed.Caption = Format(WestMall_3, "###0") Hwy_Volume.Caption = Format(Interchange_1, "###0") Hwy_Occ.Caption = Format(Interchange_2, "###0") Hwy_Speed.Caption = Format(Interchange_3, "###0") Ellis_Volume.Caption = Format(Ellis_1, "###0") Ellis_Occ.Caption = Format(Ellis_2, "###0") Ellis_Speed.Caption = Format(Ellis_3, "###0") Colborne_Volume.Caption = Format(Colborne_1, "###0") Colborne_Occ.Caption = Format(Colborne_2, "###0") Colborne_Speed.Caption = Format(Colborne_3, "###0") Parkside_Volume.Caption = Format(Parkside_1, "###0") Parkside_Occ.Caption = Format(Parkside_2, "###0") Parkside_Speed.Caption = Format(Parkside_3, "###0") Dowling_Volume.Caption = Format(Dowling_1, "###0") Dowling_Occ.Caption = Format(Dowling_2, "###0") Dowling_Speed.Caption = Format(Dowling_3, "###0") Jameson_Volume.Caption = Format(Jameson_1, "###0") Jameson_Occ.Caption = Format(Jameson_2, "###0") Jameson_Speed.Caption = Format(Jameson_3, "###0")

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Dunn_Volume.Caption = Format(Dunn_1, "###0") Dunn_Occ.Caption = Format(Dunn_2, "###0") Dunn_Speed.Caption = Format(Dunn_3, "###0") Dufferin_Volume.Caption = Format(Dufferin_1, "###0") Dufferin_Occ.Caption = Format(Dufferin_2, "###0") Dufferin_Speed.Caption = Format(Dufferin_3, "###0") Strachan_Volume.Caption = Format(Strachan_1, "###0") Strachan_Occ.Caption = Format(Strachan_2, "###0") Strachan_Speed.Caption = Format(Strachan_3, "###0") Spadina_Volume.Caption = Format(Spadina_1, "###0") Spadina_Occ.Caption = Format(Spadina_2, "###0") Spadina_Speed.Caption = Format(Spadina_3, "###0") stOutputMath = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\MatLab.txt" Open stOutputMath For Output As #6 Print #6, LocationNum Print #6, TypeofIncident Print #6, AffectedLane Print #6, IncStTime Print #6, IncEndTime Print #6, IncLoc Print #6, Rainfall Print #6, Snowfall Print #6, SnowGround Print #6, TotalPrep Print #6, AvgVis Print #6, HrVis Print #6, WeatherCondition Print #6, GPSspeed Print #6, WestMall_1 Print #6, WestMall_2 Print #6, WestMall_3 Print #6, Interchange_1 Print #6, Interchange_2 Print #6, Interchange_3 Print #6, Ellis_1 Print #6, Ellis_2 Print #6, Ellis_3 Print #6, Colborne_1 Print #6, Colborne_2 Print #6, Colborne_3 Print #6, Parkside_1 Print #6, Parkside_2 Print #6, Parkside_3 Print #6, Dowling_1 Print #6, Dowling_2

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Print #6, Dowling_3 Print #6, Jameson_1 Print #6, Jameson_2 Print #6, Jameson_3 Print #6, Dunn_1 Print #6, Dunn_2 Print #6, Dunn_3 Print #6, Dufferin_1 Print #6, Dufferin_2 Print #6, Dufferin_3 Print #6, Strachan_1 Print #6, Strachan_2 Print #6, Strachan_3 Print #6, Spadina_1 Print #6, Spadina_2 Print #6, Spadina_3 Print #6, HistoricalTime Close #6 End Sub --------------------------------------------------------------------------------------------------------------------- Private Sub MatLab_Click() Dim Est As Single Dim stResult As String Dim stSchedule As String Dim Est1 As Single Dim Wkday_Sq As Single Dim Loc_Sq As Single Dim Hour_Sq As Single Dim TT_Sq As Single Dim Wkday_Co As Single Dim Loc_Co As Single Dim Hour_Co As Single Dim TT_Co As Single Dim Wkday_Dix As Single Dim Loc_Dix As Single Dim Hour_Dix As Single Dim TT_Dix As Single Dim Operation As Single Dim Sch_hr As Single Dim Sch_min As Single Dim Bus_hr As Single Dim Bus_min As Single Dim Num As Single 'Estimation from MATLAB

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stResult = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\Estimation_Result.txt" Open stResult For Input As #8 Input #8, Est Close #8 'Input Schedule Time stSchedule = "F:\Andrew's Files\My Documents\Andrew\2008 Research\Input\Updates_January" + "\Schedule.txt" Open stSchedule For Input As #9 Input #9, Wkday_Sq Input #9, Loc_Sq Input #9, Hour_Sq Input #9, TT_Sq Input #9, Wkday_Co Input #9, Loc_Co Input #9, Hour_Co Input #9, TT_Co Input #9, Wkday_Dix Input #9, Loc_Dix Input #9, Hour_Dix Input #9, TT_Dix Close #9 Num = LocNum.Caption If Loc_Sq = Num Then 'Operational Strategy_3 (Learned from previous experiences) If Est < TT_Sq Then Est2 = TT_Sq / 60 Estimation_2.Caption = Format(Est2, "###0.0") Else Est2 = TT_Sq / 60 Estimation_2.Caption = Format(Est2, "###0.0") End If ElseIf Loc_Co = Num Then 'Operational Strategy_1(Learned from previous experiences) If Est < TT_Co Then Est2 = TT_Co / 60 Estimation_2.Caption = Format(Est2, "###0.0") Else Est2 = Est / 60 Estimation_2.Caption = Format(Est2, "###0.0") End If ElseIf Loc_Dix = Num Then 'Operational Strategy_1(Learned from previous experiences) If Est < TT_Dix Then Est2 = TT_Dix / 60 Estimation_2.Caption = Format(Est2, "###0.0")

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Else Est2 = Est / 60 Estimation_2.Caption = Format(Est2, "###0.0") End If End If End Sub --------------------------------------------------------------------------------------------------------------------- Private Sub CommandButton3_Click() Unload Me End Sub --------------------------------------------------------------------------------------------------------------------- % MATLAB for estimating travel time from Square One Bus Terminal to Union GO Bus Terminal with the aid of the calibrated ANN load SquareOne.mat; load MatLab.txt; Tests = MatLab; Final = sim (net_1240, Tests) save Estimation_Result Final -ASCII --------------------------------------------------------------------------------------------------------------------- % MATLAB for estimating travel time from Cooksville GO Station to Union GO Bus Terminal with the aid of the calibrated ANN load Cooksville_EB.mat; load MatLab.txt; Tests = MatLab; Final = sim (net_180, Tests) save Estimation_Result Final -ASCII --------------------------------------------------------------------------------------------------------------------- % MATLAB for estimating travel time from Dixie GO Station to Union GO Bus Terminal with the aid of the calibrated ANN load Dixie_EB.mat; load MatLab.txt; Tests = MatLab; Final = sim (net_996, Tests) save Estimation_Result Final -ASCII