Travel Time Prediction Model for Regional Bus Transit

TRAVEL TIME PREDICTION MODEL FOR REGIONAL BUS TRANSIT

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

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.

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 iv

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 v

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 vi

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

vii

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

Table 5-4: ANN Structure Summary of Direction-Based Models (Gardiner Expressway 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

Table 5-9: Direction- and Location-Based ANN Alternatives Performance Assessment (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

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

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

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

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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.

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.

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

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.

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.

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

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.

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

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

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

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

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

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

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.

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) • GO Transit, operated by Greater Toronto Transit Bus Schedule Authority Global Positioning System (GPS) Data • GO Transit, operated by Greater Toronto Transit of Bus Locations Authority • Ministry of Transportation of Ontario Freeway Loop Detector Data including • City of Toronto Speed, Occupancy and Volume • University of Toronto’s ITS Centre and Testbed • City of Toronto Incident Reports • 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.

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

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/ Number of Direction Lakeshore Detectors Locations (Eastbound/Westbound) Boulevard Available QEW Eastbound 2 • The West Mall • Highway 427 QEW Westbound 2 • The West Mall • Highway 427

Freeways/ Number of Direction Lakeshore Detectors Locations (Eastbound/Westbound) Boulevard Available Gardiner Eastbound 9 • Ellis Avenue Expressway • Colborne Lodge Road • Parkside Drive • Dowling Avenue • Jameson Avenue • Dunn Avenue • Dufferin Street • Strachan Avenue • Spadina Avenue Gardiner Westbound 6 • Strachan Avenue Expressway • Dufferin Street • Dowling Avenue • Parkside Drive • Colborne Lodge Road • Ellis Avenue Lakeshore Eastbound 4 • Windermere Avenue Boulevard • Parkside Drive • BC Drive • Newfoundland Drive Lakeshore Westbound 7 • Rees Street Boulevard • 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.

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:

• 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

• Moderate Snow

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

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

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 Number of Checkpoints, including Route Segment Direction 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

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.

(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:

D = cos−1[]cos()a1 cos ()b1 cos (a2 )cos(b2)+ cos(a1)sin(b1)cos(a2)cos(b2)()+ sin a1 sin(a2) /360

× 2π × r

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

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.

#1 #2 #3 #4

X km Y km Z km

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:

X DT2 = (DT4 − DT1) × + DT1 X + Y + Z

X +Y DT3 = (DT4 − DT1)× + DT1 X +Y + Z 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.

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

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 Square One Bus Terminal 30.42

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

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.

Table 4-10: List of Bus Travel Time-Distance Figures Gardiner Gardiner Lakeshore Lakeshore Factors Expressway Expressway Boulevard Boulevard Eastbound Westbound Eastbound Westbound AM Peak Figure A-1 Figure A-9 Figure A-17 Figure A-25 Time Off Peak Figure A-2 Figure A-10 Figure A-18 Figure A-26 Period PM Peak Figure A-3 Figure A-11 Figure A-19 Figure A-27 Late Evening Figure A-4 Figure A-12 Figure A-20 Figure A-28 Day of Weekday Figure A-5 Figure A-13 Figure A-21 Figure A-29 the Week Weekend Figure A-6 Figure A-14 Figure A-22 Figure A-30 Weather Good Figure A-7 Figure A-15 Figure A-23 Figure A-31 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.

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.

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 Public Agency(ies)/ Data Availability Time Data Academic Institution(s) Frame • Greater Toronto Transit All survey days between Bus Schedule Authority (GO Transit) January and April 2008 Global Positioning System • Greater Toronto Transit All survey days between Bus Data Authority (GO Transit) January and April 2008 5:30 a.m. – 12:00 noon. • Ministry of Transportation of Specifically 37 full days Loop Detector Data Ontario between January and April 2008* • City of Toronto 37 full days between January Loop Detector Data • University of Toronto’s ITS and April 2008* Centre and Testbed

Public Agency(ies)/ Data Availability Time Data Academic Institution(s) Frame • City of Toronto 37 full days between January Incident Reports • University of Toronto’s ITS and April 2008* Centre and Testbed Historical Daily Weather All survey days between • Environment Canada Conditions 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 Incomplete Loop Route Complete Loop Data Set Data Set Model Historical Bus Testing Origin Destination Development Journey Time Sample Size Sample Size Sample Sizes Square One Bus Union GO Bus 39 38 124 Terminal Terminal Cooksville GO Union GO Bus 42 42 121 Station Terminal Dixie GO Union GO Bus 42 20 71 Station Terminal Union GO Bus Dufferin Street 49 50 95 Terminal

Table 4-13: Gardiner Expressway Westbound Route Sample Summary Incomplete Route Complete Loop Data Set Loop Data Set Model Historical Bus Testing Origin Destination Development Journey Time Sample Size Sample Size Sample Sizes Union GO Bus Square One 44 46 107 Terminal Bus Terminal Union GO Bus Cooksville GO 44 46 107 Terminal Station

Incomplete Route Complete Loop Data Set Loop Data Set Model Historical Bus Testing Origin Destination Development Journey Time Sample Size Sample Size Sample Sizes Union GO Bus Dixie GO 34 16 65 Terminal Station Highway 427/ Square One 51 52 81 QEW Bus Terminal Highway 427/ Cooksville GO 51 52 81 QEW Station Highway 427/ Dixie GO 41 29 50 QEW Station

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.

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

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.

• 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.

• 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.

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

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

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

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)

X j = ∑ wij I i i 1 Y j = −( X −t ) 1+ e j j

th th where Xj is the weighted sum of inputs to the j hidden-neuron, Yj is the output at the j hidden- th th th neuron, wij is the weight of the i input to the j hidden-neuron, Ii is the i 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)

X k = ∑ w jk Y j j

1 Yk = 1+ e −( X k −tk )

th th where Xk is the weighted sum of inputs to the k output-neuron, Yk is the result of the k output- th th neuron, wjk is the weight of the j hidden-neuron result to the k output-neuron, Yj is the output th th at the j hidden-neuron, and tk is the bias adjustment for the k 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

∂E = Yk − Ok ∂Yk ∂E ∂E = Yk (1− Yk ) ∂X k ∂Yk ∂E ∂E = Y ∂w ∂X j jk k

th th where Xk is the weighted sum of inputs to the k output-neuron, Yk is the result of the k output- th th neuron, wjk is the weight of the j hidden-neuron result to the k output-neuron, Ok is the actual th observed result from the training sample, and Yj is the result of the j hidden-neuron (which also serves as an input to different output-neurons).

Hidden Layer

∂E ∂E = ∑ w jk ∂Y j k ∂X k ∂E ∂E = Y j (1− Y j ) ∂X j ∂Y j ∂E ∂E = I ∂w ∂X i ij j

th where Xj is the weighted sum of inputs, I1, I2, , Ii, to the j hidden-neuron, and wij is the weight th th of the i input to the j hidden-neuron. Yj, wjk, and Xk are defined as above.

Next, the weight on each input element is revised with the following equation:

∂E w'= w − c ∂w

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 Q MSE = ∑[]Y(k) − O(k) N k =1

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:

−1 w' = w − [J T J + μI] J T e

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:

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:

∂Ok Sik = ∂I i J ∂Y ' i Sik = Ok ∑ wik j=1 ∂I i J ' ' Sik = Ok ∑ w jkY j wij j=1

’ th ’ where Ok is the derivative of the transfer function used in the k output-neuron, Yj is the th th derivative of the transfer function used in the j hidden-neuron, wjk is the weight of the j th th th hidden-neuron result to the k output-neuron, and wij is the weight of the i input to the j hidden-neuron.

To simplify the above equation, the sensitivity value can be expressed as:

' ' S =OwJY wI

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 Sik (average) = ∑ Sik / N n=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:

' ' ' S = OwJY wLZ wI

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.

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:

N 2 RMSE = ∑ ()Ypredictedi − Yactuali / N i=1

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.

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.

Table 5-1: Sensitivity Significance Summary of Input Factors Relative to the Relative to the Rank Variable Most Significant Rank Variable Most Significant Variable Variable 1 Parkside_Volume 1.00 11 Spadina_Volume 0.78 Colborne 2 0.99 12 Dufferin_Speed 0.76 Lodge_Occupancy Jameson 3 0.97 13 Parkside_Speed 0.73 Exit_Occupancy Historical Bus Travel 4 Ellis_Occupancy 0.95 14 0.73 Time 5 Total Snowfall 0.94 15 Spadina_Speed 0.70 Bus Current Speed 6 captured by GPS 0.93 16 Dixie/QEW_Volume 0.70 Devices Lanes Affected by 7 0.84 17 Jameson Exit_Volume 0.69 Incidents 8 Strachan_Occupancy 0.80 18 Dunn_Volume 0.69 Colborne 9 0.79 19 Incident Start Time 0.69 Lodge_Speed 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

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.

Table 5-2: ANN Structure Summary of Direction-Based Models (Gardiner Expressway 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 8 10 1 18 Layer) Number of Neurons (2nd Hidden 1 1 5 9 Layer) Transfer Function (1st Hidden Tan-sigmoid Tan-sigmoid Log-sigmoid Log-sigmoid Layer) Transfer Function (2nd Hidden Linear Log-sigmoid Tan-sigmoid Tan-sigmoid Layer) Transfer Function (Output Layer) Tan-sigmoid Linear Linear Linear Training Rate 0.005 0.005 0.005 0.005

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 Union GO Bus 562 532 595 443 Terminal Terminal Cooksville GO Union GO Bus 230 266 266 268 Station Terminal Union GO Bus Dixie GO Station 162 194 211 216 Terminal 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.

Table 5-4: ANN Structure Summary of Direction-Based Models (Gardiner Expressway 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

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 Square Union GO Cooksville Union GO Dixie Union GO ANN Structure One Bus Bus GO Bus GO Bus Terminal Terminal Station Terminal Station Terminal ANN Name ANN-SE ANN-CE ANN-DE Number of 48 48 48 Inputs Number of 2 2 2 Hidden Layers Number of Neurons (1st 20 20 16 Hidden Layer)

Origin Destination Origin Destination Origin Destination Square Union GO Cooksville Union GO Dixie Union GO ANN Structure One Bus Bus GO Bus GO Bus Terminal Terminal Station Terminal Station Terminal Number of Neurons (2nd 10 1 8 Hidden Layer) Transfer Function (1st Log-sigmoid Tan-sigmoid Tan-sigmoid Hidden Layer) Transfer Function (2nd Tan-sigmoid Tan-sigmoid Log-sigmoid Hidden Layer) Transfer Function Linear Tan-sigmoid Linear (Output Layer) Training Rate 0.005 0.005 0.005

Table 5-7: Location-Based ANN Structure Summary (Gardiner Expressway Westbound Route) Origin Destination Origin Destination Origin Destination Union Square One Union Union ANN Structure Cooksville Dixie GO GO Bus Bus GO Bus GO Bus GO Station Station Terminal Terminal Terminal Terminal ANN Name ANN-SW ANN-CW ANN-DW Number of 48 48 48 Inputs Number of 2 2 2 Hidden Layers Number of Neurons (1st 20 10 8 Hidden Layer) Number of Neurons (2nd 1 3 1 Hidden Layer) Transfer Function (1st Log-sigmoid Tan-sigmoid Linear Hidden Layer) Transfer Function (2nd Tan-sigmoid Tan-sigmoid Tan-sigmoid Hidden Layer) Transfer Function Linear Tan-sigmoid Tan-sigmoid (Output Layer) Training Rate 0.005 0.005 0.005

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.

Table 5-8: Direction- and Location-Based ANN Alternatives Performance Assessment (Gardiner Expressway Eastbound Route) RMSE (seconds) Origin Destination Direction-Based Location-Based Square One Bus Union GO Bus 562 519 Terminal Terminal Union GO Bus Cooksville GO Station 230 240 Terminal Union GO Bus Dixie GO Station 162 149 Terminal Average 318 303

Table 5-9: Direction- and Location-Based ANN Alternatives Performance Assessment (Gardiner Expressway Westbound Route)

RMSE (seconds) Origin Destination Direction-Based Location-Based Union GO Bus Square One Bus 179 157 Terminal Terminal Union GO Bus Cooksville GO Station 168 175 Terminal Union GO Bus Dixie GO Station 187 168 Terminal 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.

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)

• 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 Expressway Eastbound Route) RMSE (seconds) Origin Destination HAE1 HAE2 HAE3 HAE4 Square One Bus Union GO Bus 591 579 623 1040 Terminal Terminal Cooksville GO Union GO Bus 286 276 285 531 Station Terminal Union GO Bus Dixie GO Station 219 258 218 540 Terminal Average 366 371 375 704

Table 6-2: Historical Average Model Alternative Performance Assessment (Gardiner Expressway Westbound Route) RMSE (seconds) Origin Destination HAW1 HAW2 HAW3 HAW4* Union GO Bus Square One Bus 190 169 171 N/A Terminal Terminal Union GO Bus Cooksville GO 181 176 201 N/A Terminal Station Union GO Bus Dixie GO Station 190 223 201 N/A Terminal 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

Y = f (xi ,βi ) +ε

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

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:

(m'−M ') 2 R 2 = ∑ ∑ (m − M ) 2

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:

• 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)

Y = 1481.42 + 0.96 × (Hist ) − 0.20 × (Ellis _Volume ) − 6.29 × (Spadina _ Speed )

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

Location-Based Model – Square One Bus Terminal to Union GO Bus Terminal (RE-LSE)

Y = 1744.48 + 0.35× (Hist _ Day) +144.90 × (Type _ Inc) − 7.56 × (Parkside _ Speed) + 0.08× (Jameson _Volume)

Table 6-4: Explanatory Variables used for RE-LSE Variables Description(s) Y Bus journey time in seconds 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)

Y = 1159.57 +1.00 × (Hist _ Day) − 0.25 × (Ellis _Volume)

Table 6-5: Explanatory Variables used for RE-LCE Variables Description(s) Y Bus journey time in seconds 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)

Y =1607.46 + 0.323×(Hist) + 55.10×(Snow_ Ground) − 3.51×(Spadina _ Speed)

− 5.41×(Ellis _ Speed)

Table 6-6: Explanatory Variables used for RE-LDE Variables Description(s) Y Bus journey time in seconds 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

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):

Y =1179.61+ 0.60 × (Hist) + 465.29 × (Loc1) + 269.23× (Loc2) − 8.47 × (Dowling _ Speed)

Table 6-7: Explanatory Variables used for RE-DW Variables Description(s) Y Bus journey time in seconds Hist Variable of historical data summarized by day of the week and bus operating hour 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)

Y = 1267.14 + 0.69 × (Hist ) − 0.69 × (Dowling _ Speed )

Table 6-8: Explanatory Variables used for RE-LSW Variables Description(s) Y Bus journey time in seconds Hist Variable of historical data summarized by day of the week and bus operating hour 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)

Y = 1586 .36 + 0.552 × (Hist ) − 8.99 × (Dowling _ Speed )

Table 6-9: Explanatory Variables used for RE-LCW Variables Description(s) Y Bus journey time in seconds Hist Variable of historical data summarized by day of the week and bus operating hour

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)

Y = 1594.43 + 0.98 × (Hist ) − 0.12 × (Strachan _Volume ) −11.75 × (Colborne _ Speed )

Table 6-10: Explanatory Variables used for RE-LDW Variables Description(s) Y Bus journey time in seconds Hist Variable of historical data summarized by day of the week and bus operating hour 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 Location-Based Model Model Square One Bus Union GO Bus 516 571 Terminal Terminal Cooksville GO Union GO Bus 284 244 Station Terminal Union GO Bus Dixie GO Station 253 185 Terminal Average 351 333

Table 6-12: Regression Models Performance Assessment (Gardiner Expressway Westbound Route) RMSE (seconds) Origin Destination Direction-Based Location-Based Model Model Union GO Bus Square One Bus 159 175 Terminal Terminal

RMSE (seconds) Origin Destination Direction-Based Location-Based Model Model Union GO Bus Cooksville GO 182 177 Terminal Station Union GO Bus Dixie GO Station 293 246 Terminal 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.

Table 6-13: Summary of Configurations of Each Model Type (Gardiner Expressway Eastbound Route) Alternative Modelling Approaches Origin Destination Historical Regression ANN Average Square One Bus Union GO Bus HAE2 RE-LSE ANN-SE Terminal Terminal Cooksville GO Union GO Bus HAE2 RE-LCE ANN-CE Station Terminal Union GO Bus Dixie GO Station HAE3 RE-LDE ANN-DE Terminal

Table 6-14: Summary of Configurations of Each Model Type (Gardiner Expressway Westbound Route) Alternative Modelling Approaches Origin Destination Historical Regression ANN Average Union GO Bus Square One Bus HAW2 RE-LSW ANN-SW Terminal Terminal Union GO Bus Cooksville GO HAW2 RE-LCW ANN-CW Terminal Station Union GO Bus Dixie GO Station HAW3 RE-LDW ANN-DW Terminal

Table 6-15: Alternative Modelling Approaches Performance Assessment (Gardiner Expressway Eastbound Route) RMSE (seconds) Origin Destination Historical Regression ANN Average Square One Bus Union GO Bus 579 571 519 Terminal Terminal Cooksville GO Union GO Bus 276 244 240 Station Terminal Union GO Bus Dixie GO Station 218 185 149 Terminal Average 358 333 303

Table 6-16: Alternative Modelling Approaches Performance Assessment (Gardiner Expressway Westbound Route) RMSE (seconds) Origin Destination Historical Regression ANN Average Union GO Bus Square One Bus 169 175 157 Terminal Terminal Union GO Bus Cooksville GO 176 177 175 Terminal Station Union GO Bus Dixie GO Station 201 246 168 Terminal 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.

Table 6-17: ANN Structure Summary at Dufferin Street Checkpoint Origin Destination ANN Structure Union GO Bus Dufferin Street 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 Destination ANN Square One Highway Highway Cooksville Highway Dixie GO Structure Bus 427/QEW 427/QEW GO Station 427/QEW Station Terminal ANN Name ANN-SQW ANN-CQW ANN-DQW Number of 48 48 48 Inputs Number of Hidden 2 2 2 Layers Number of Neurons 18 2 5 (1st Hidden Layer) Number of Neurons (2nd 3 1 2 Hidden Layer) Transfer Function Tan-sigmoid Log-sigmoid Tan-sigmoid (1st Hidden Layer) Transfer Function (2nd Log-sigmoid Tan-sigmoid Tan-sigmoid Hidden Layer)

Origin Destination Origin Destination Origin Destination ANN Square One Highway Highway Cooksville Highway Dixie GO Structure Bus 427/QEW 427/QEW GO Station 427/QEW Station Terminal Transfer Function Linear Linear Tan-sigmoid (Output Layer) Training 0.005 0.005 0.005 Rate

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 Expressway Eastbound Route)

Origin Destination RMSE (seconds) Dufferin Street Union GO Bus Terminal 82

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

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.

600

500 (s)

Error 400 Square 300 Mean 200 Root 100

0 Square One Cooksville Dixie Dufferin Major Checkpoint Location

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

200 180 (s) 160

Error 140

120

Square 100

80 Mean 60 40 Root 20 0 Union QEW/427 Major Checkpoint Location

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

200 (s)

180 160 Error 140 120

Square 100

Mean 60

40 Root 20 0 Union QEW/427 Major Checkpoint Location

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

200 (s) 180 160 Error 140 120

Square 100

Mean 60

Root 20 0 Union QEW/427 Major Checkpoint Location

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

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/ Dixie Cooksville Square Dixie Cooksville Square Destination GO GO One Bus GO GO One Bus Station Station Terminal Station Station Terminal Union GO Bus 75.0% 52.3% 43.2% 25.0% 47.7% 56.8% Terminal

Overestimation (%) Underestimation (%) Origin/ Dixie Cooksville Square Dixie Cooksville Square Destination GO GO One Bus GO GO One Bus Station Station Terminal Station Station Terminal Highway 427/ 59.0% 49.0% 60.8% 41.0% 51.0% 39.2% QEW

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

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.

Figure 7-2: Bus Operational Strategy Flow Chart

Table 7-3: Bus Stakeholders’ Wait Time with Different Bus Operational Strategies Broadcasting Critical Cases Options Wait Time Equations, Wait Information Stakeholders Scheduled Bus operator, in- #1 N/A Wait = Sch − Act Time bus travellers Scheduled Bus operator, in- #2 Wait = Sch − Act N/A Time bus travellers Passengers Scheduled #3 N/A waiting at bus Wait = Act − Sch Time stops Bus operator, in- #4 Option_1 Predicted Time Wait = Est − Act bus travellers Bus operator, in- Bus operator, in-vehicle travellers: bus travellers, t = Sch − Act #4 Option_2 Predicted Time passengers waiting at bus Passengers waiting at bus stops: stops Wait = NextBusArr − Est Scheduled Bus operator, in- #4 Option_3 Wait = Sch − Act Time bus travellers Bus operator, in- #5 Option_1 Predicted Time Wait = Est − Act bus travellers Passengers #5 Option_2 Predicted Time waiting at bus Wait = NextBusArr − Est stops

Broadcasting Critical Cases Options Wait Time Equations, Wait Information Stakeholders Passengers Scheduled #5 Option_3 waiting at bus Wait = Act − Sch Time stops Passengers #6 Option_1 Predicted Time waiting at bus Wait = Act − Est stops Passengers #6 Option_2 Predicted Time waiting at bus Wait = Act − Est stops Passengers Scheduled #6 Option_3 waiting at bus Wait = Act − Sch Time stops 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) Origin Destination Option_1 Option_2 Option_3 B_DT* P_BS* B_DT* P_BS* B_DT* P_BS* Square Union GO 103 1789 120 One Bus Bus 0 (0) 0 (0) 1 (1) (184) (1814) (180) Terminal Terminal Cooks- Union GO 172 1400 248 ville GO Bus 99 (309) 0 (0) 60 (180) (188) (1951) (361) Station Terminal Union GO Dixie GO 164 1823 240 Bus 83 (N/A) 0 (N/A) 60 (N/A) Station (N/A) (N/A) (N/A) Terminal 101 1595 125 Average 86 (117) 0 (0) 90 (140) (192) (1863) (201) *Remark: B_DT represents “Bus operator and in-bus travellers” and P_BS represents “Passengers waiting at bus stops”.

Table 7-5: Wait Time Summary for Gardiner Expressway Westbound Route Average Wait Time (Maximum Wait Time) (seconds) Origin Destination Option_1 Option_2 Option_3 B_DT* P_BS* B_DT* P_BS* B_DT* P_BS* Union Square One 157 1061 100 GO Bus Bus 77 (-) 0 (0) 0 (0) (200) (1566) (121) Terminal Terminal Union Cooksville 152 138 735 359 GO Bus 0 (0) 90 (120) GO Station (320) (441) (2013) (826) Terminal Union Dixie GO 198 1256 249 GO Bus 36 (97) 0 (0) 0 (0) Station (640) (1875) (900) Terminal 115 138 1018 120 146 Average 0 (0) (205) (386) (1818) (275) (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

Cost P = (P × 8.75 / 3600 + 41.67 / 3600) × Wait

where P is the number of in-vehicle passengers (ranging from 0 to 30) and Wait is a variable defined in Table 7-3.

Costs for passengers standing at the bus stop, CostT

Cost T = T ×8.75 / 3600 ×Wait

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

CostTot = Cost P + CostT

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 Figure 7-3b: Cost Comparison for the Origin and Destination Pair, “Square One Bus and Destination Pair, “Cooksville GO Station- Terminal-to-Union GO Bus Terminal” to-Union GO Bus Terminal”

Figure 7-3c: Cost Comparison for the Origin Figure 7-3d: Cost Comparison for the Origin and Destination Pair, “Dixie GO Station-to- and Destination Pair, “Union GO Bus Union GO Bus Terminal” Terminal-to-Square One Bus Terminal”

Figure 7-3e: Cost Comparison for the Origin Figure 7-3f: Cost Comparison for the Origin and Destination Pair, “Union GO Bus and Destination Pair, “Union GO Bus Terminal-to-Cooksville GO Station” 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

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) Square One Cooksville GO Dixie GO Union GO Bus Origin/ Destination Bus Terminal Station Station Terminal Square One Bus 10.53 Terminal Cooksville GO 25.17 Station Dixie GO Station 6.76 Union GO Bus 2.95 4.56 83.65 Terminal

Table 7-7: Ratio of Time Cost Monetary Value Comparison Summary (Option_3 vs. Option_1) Square One Cooksville GO Dixie GO Union GO Bus Origin/ Destination Bus Terminal Station Station Terminal Square One Bus 0.60 Terminal Cooksville GO 1.52 Station Dixie GO Station 1.58 Union GO Bus 0.52 2.89 26.93 Terminal 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

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

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.

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.

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

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.

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Appendix A: Historical Buses’ Travel Time Performances

150

120

Mean (min) 90 Median Time

Max 60 Travel 95th Percentile

30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-1: Time Space Diagram – AM Peak Period (Gardiner Expressway Eastbound Route)

150

120

(min) Mean 90 Time

Median

60 Travel Max

95th Percentile 30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-2: Time Space Diagram – Off-Peak Period (Gardiner Expressway Eastbound Route)

150

120

Mean (min) 90 Median Time

Max

Travel 60 95th Percentile

30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-3: Time Space Diagram – PM Peak Period (Gardiner Expressway Eastbound Route)

150

120

Mean (min) 90 Median Time

60 Max Travel 95th Percentile 30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-4: Time Space Diagram – Late Evening Period (Gardiner Expressway Eastbound Route)

100

150

120

Mean (min)

90 Median Time

Max

Travel 60 95th Percentile

Schedule 30

0 0 5 10 15 20 25 30 35 Distance from Square One GO Bus Terminal (km)

Figure A-5: Time Space Diagram – Weekday (Gardiner Expressway Eastbound Route)

150

120

Mean 90 (min)

Median Time

Max

Travel 60 95th Percentile

Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-6: Time Space Diagram – Weekend (Gardiner Expressway Eastbound Route)

101

150

120 (min) 90 Mean

Time Median

60 Max Travel 95th Percentile Schedule 30

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-7: Time Space Diagram – Good Weather Conditions (Gardiner Expressway Eastbound Route)

150

120

Mean (min)

90 Median Time

Max

Travel 60 95th Percentile

30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-8: Time Space Diagram – Bad Weather Conditions (Gardiner Expressway Eastbound Route)

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150 Mean (min) 120 Median Time

90 Max Travel 95th Percentile 60 Schedule 30

0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-9: Time Space Diagram – AM Peak Period (Gardiner Expressway Westbound Route)

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120 Median Time

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Schedule 30

0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-10: Time-space Diagram – Off-Peak Period (Gardiner Expressway Westbound Route)

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90 Max Travel 95th Percentile 60 Schedule

0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-11: Time-space Diagram – PM Peak Period (Gardiner Expressway Westbound Route)

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120 Median Time

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0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-12: Time-Space Diagram – Late Evening Period (Gardiner Expressway Westbound Route)

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90 Max Travel 95th Percentile 60 Schedule 30

0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-13: Time-Space Diagram – Weekday (Gardiner Expressway Westbound Route)

210

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0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-14: Time-Space Diagram – Weekend (Gardiner Expressway Westbound Route)

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0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-15: Time Space Diagram – Good Weather Conditions (Gardiner Expressway Westbound Route)

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60 95th Percentile

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0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-16: Time Space Diagram – Bad Weather Conditions (Gardiner Expressway Westbound Route)

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0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-17: Time Space Diagram – AM Peak Period (Lakeshore Boulevard Eastbound Route)

150

120 Mean (min) 90 Median Time

60 Max Travel 95th Percentile 30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-18: Time Space Diagram – Off-Peak Period (Lakeshore Boulevard Eastbound Route)

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Figure A-19: Time Space Diagram – PM Peak Period (Lakeshore Boulevard Eastbound Route)

150

120 (min) 90 Mean

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Max 60 Travel 95th Percentile Schedule 30

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-20: Time Space Diagram – Late Evening Peak Period (Lakeshore Boulevard Eastbound Route)

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0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-21: Time Space Diagram – Weekday (Lakeshore Boulevard Eastbound Route)

150

120 Mean (min) 90 Median Time

60 Max Travel 95th Percentile 30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-22: Time Space Diagram – Weekend (Lakeshore Boulevard Eastbound Route)

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Figure A-23: Time Space Diagram – Good Weather Conditions (Lakeshore Boulevard Eastbound Route)

150

120

Mean (min) 90 Median Time

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30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Square One Bus Terminal (km)

Figure A-24: Time Space Diagram – Bad Weather Conditions (Lakeshore Boulevard Eastbound Route)

110

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0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-25: Time Space Diagram – AM Peak Period (Lakeshore Boulevard Westbound Route)

150

120 Mean (min) 90 Median Time

60 Max Travel 95th Percentile 30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-26: Time Space Diagram – Off-Peak Period (Lakeshore Boulevard Westbound Route)

111

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60 Max Travel 95th Percentile Schedule 30

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Figure A-27: Time Space Diagram – PM Peak Period (Lakeshore Boulevard Westbound Route)

150

120

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30 Schedule

0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-28: Time Space Diagram – Late Evening Period (Lakeshore Boulevard Westbound Route)

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60 Max Travel 95th Percentile 30 Schedule 0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-29: Time Space Diagram – Weekday (Lakeshore Boulevard Westbound Route)

150

120 (min) 90 Mean

Time Median

60 Max Travel 95th Percentile Schedule 30

0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-30: Time Space Diagram – Weekend (Lakeshore Boulevard Westbound Route)

113

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Max 60 Travel 95th Percentile Schedule 30

0 0 5 10 15 20 25 30 35 Distance from Union GO Bus Terminal (km)

Figure A-31: Time Space Diagram – Good Weather Condition (Lakeshore Boulevard Westbound Route)

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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);

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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);

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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 Union GO Bus Weekday 2461 Terminal Terminal Square One Bus Union GO Bus Weekend 1681 Terminal Terminal Cooksville GO Union GO Bus Weekday 2101 Station Terminal Cooksville GO Union GO Bus Weekend 1440 Station Terminal Union GO Bus Dixie GO Station Weekday 1320 Terminal Union GO Bus Dufferin Street Weekday 439 Terminal Union GO Bus Dufferin Street Weekend 347 Terminal

Table B-2: HAE2 – Gardiner Expressway Eastbound Route Day of the Operating Bus Journey Origin Destination Week Hour Time (s) Square One Bus Union GO Bus Weekday 5 am 2461 Terminal Terminal Square One Bus Union GO Bus Weekday 9 am 2760 Terminal Terminal Square One Bus Union GO Bus Weekday 10 am 2474 Terminal Terminal Square One Bus Union GO Bus Weekday 11 am 2521 Terminal Terminal Square One Bus Union GO Bus Weekend 6 am 1621 Terminal Terminal Square One Bus Union GO Bus Weekend 7 am 1681 Terminal Terminal Square One Bus Union GO Bus Weekend 8 am 1680 Terminal Terminal Square One Bus Union GO Bus Weekend 9 am 1710 Terminal Terminal Square One Bus Union GO Bus Weekend 10 am 1681 Terminal Terminal Square One Bus Union GO Bus Weekend 11 am 1920 Terminal Terminal Cooksville GO Union GO Bus Weekday 5 am 1860 Station Terminal

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Day of the Operating Bus Journey Origin Destination Week Hour Time (s) Cooksville GO Union GO Bus Weekday 9 am 2401 Station Terminal Cooksville GO Union GO Bus Weekday 10 am 2161 Station Terminal Cooksville GO Union GO Bus Weekday 11 am 2221 Station Terminal Cooksville GO Union GO Bus Weekend 7 am 1440 Station Terminal Cooksville GO Union GO Bus Weekend 8 am 1380 Station Terminal Cooksville GO Union GO Bus Weekend 9 am 1320 Station Terminal Cooksville GO Union GO Bus Weekend 10 am 1410 Station Terminal Cooksville GO Union GO Bus Weekend 11 am 1620 Station Terminal Union GO Bus Dixie GO Station Weekday 5 am 1080 Terminal Union GO Bus Dixie GO Station Weekday 9 am 1561 Terminal Union GO Bus Dixie GO Station Weekday 10 am 1261 Terminal Union GO Bus Dixie GO Station Weekday 11 am 1320 Terminal Union GO Bus Dufferin Street Weekday 6 am 345 Terminal Union GO Bus Dufferin Street Weekday 9 am 510 Terminal Union GO Bus Dufferin Street Weekday 10 am 480 Terminal Union GO Bus Dufferin Street Weekday 11 am 433 Terminal Union GO Bus Dufferin Street Weekend 6 am 331 Terminal Union GO Bus Dufferin Street Weekend 7 am 353 Terminal Union GO Bus Dufferin Street Weekend 8 am 340 Terminal Union GO Bus Dufferin Street Weekend 9 am 350 Terminal Union GO Bus Dufferin Street Weekend 10 am 360 Terminal Union GO Bus Dufferin Street Weekend 11 am 330 Terminal

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Table B-3: HAE3 – Gardiner Expressway Eastbound Route Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Square One Bus Union GO Bus Weekday 5 am Good 2100 Terminal Terminal Square One Bus Union GO Bus Weekday 5 am Bad 2131 Terminal Terminal Square One Bus Union GO Bus Weekday 9 am Good 2641 Terminal Terminal Square One Bus Union GO Bus Weekday 9 am Bad 2851 Terminal Terminal Square One Bus Union GO Bus Weekday 10 am Good 2473 Terminal Terminal Square One Bus Union GO Bus Weekday 10am Bad 2613 Terminal Terminal Square One Bus Union GO Bus Weekday 11 am Good 2521 Terminal Terminal Square One Bus Union GO Bus Weekend 6 am Good 1621 Terminal Terminal Square One Bus Union GO Bus Weekend 7 am Good 1680 Terminal Terminal Square One Bus Union GO Bus Weekend 7 am Bad 2041 Terminal Terminal Square One Bus Union GO Bus Weekend 8 am Good 1680 Terminal Terminal Square One Bus Union GO Bus Weekend 9 am Good 1710 Terminal Terminal Square One Bus Union GO Bus Weekend 10 am Good 1681 Terminal Terminal Square One Bus Union GO Bus Weekend 11 am Good 1800 Terminal Terminal Cooksville GO Union GO Bus Weekday 5 am Good 1860 Station Terminal Cooksville GO Union GO Bus Weekday 5 am Bad 1651 Station Terminal Cooksville GO Union GO Bus Weekday 9 am Good 2375 Station Terminal Cooksville GO Union GO Bus Weekday 9 am Bad 2521 Station Terminal Cooksville GO Union GO Bus Weekday 10 am Good 2161 Station Terminal Cooksville GO Union GO Bus Weekday 10am Bad 2223 Station Terminal Cooksville GO Union GO Bus Weekday 11 am Good 2221 Station Terminal

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Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Cooksville GO Union GO Bus Weekend 6 am Good 1440 Station Terminal Cooksville GO Union GO Bus Weekend 7 am Good 1380 Station Terminal Cooksville GO Union GO Bus Weekend 7 am Bad 1560 Station Terminal Cooksville GO Union GO Bus Weekend 8 am Good 1320 Station Terminal Cooksville GO Union GO Bus Weekend 9 am Good 1410 Station Terminal Cooksville GO Union GO Bus Weekend 10 am Good 1440 Station Terminal Cooksville GO Union GO Bus Weekend 11 am Good 1620 Station Terminal Dixie GO Union GO Bus Weekday 5 am Good 1080 station Terminal Dixie GO Union GO Bus Weekday 9 am Good 1500 station Terminal Dixie GO Union GO Bus Weekday 9 am Bad 1681 station Terminal Dixie GO Union GO Bus Weekday 10 am Good 1261 station Terminal Dixie GO Union GO Bus Weekday 10am Bad 1383 station Terminal Dixie GO Union GO Bus Weekday 11 am Good 1320 station Terminal Union GO Bus Dufferin Street Weekday 6am Good 345 Terminal Union GO Bus Dufferin Street Weekday 9 am Good 510 Terminal Union GO Bus Dufferin Street Weekday 10 am Good 445 Terminal Union GO Bus Dufferin Street Weekday 11 am Good 427 Terminal Union GO Bus Dufferin Street Weekend 6 am Good 331 Terminal Union GO Bus Dufferin Street Weekend 7 am Good 360 Terminal Union GO Bus Dufferin Street Weekend 8 am Good 320 Terminal Union GO Bus Dufferin Street Weekend 9 am Good 350 Terminal Union GO Bus Dufferin Street Weekend 10 am Good 360 Terminal

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Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Union GO Bus Dufferin Street Weekend 11 am Good 330 Terminal Union GO Bus Dufferin Street Weekday 6 am Bad 345 Terminal Union GO Bus Dufferin Street Weekday 9 am Bad 510 Terminal Union GO Bus Dufferin Street Weekday 10 am Bad 620 Terminal Union GO Bus Dufferin Street Weekday 11 am Bad 531 Terminal Union GO Bus Dufferin Street Weekend 6 am Bad 331 Terminal Union GO Bus Dufferin Street Weekend 7 am Bad 345 Terminal Union GO Bus Dufferin Street Weekend 8 am Bad 460 Terminal Union GO Bus Dufferin Street Weekend 9 am Bad 460 Terminal Union GO Bus Dufferin Street Weekend 10 am Bad 420 Terminal Union GO Bus Dufferin Street Weekend 11 am Bad 330 Terminal

Table B-4: HAE4 – Gardiner Expressway Eastbound Route Day of Operating Weather Bus Journey Origin Destination Incidents the Week Hour Condition Time (s) Square One Union GO Bus Bus Weekday 5 am Good N/A 2100 Terminal Terminal Square One Union GO Bus Bus Weekday 5 am Bad N/A 2131 Terminal Terminal Square One Union GO Bus Bus Weekday 9 am Good N/A 2701 Terminal Terminal Square One Union GO Bus Bus Weekday 9 am Good Roadwork 2589 Terminal Terminal Square One Union GO Bus Bus Weekday 9 am Bad N/A 2851 Terminal Terminal Square One Union GO Bus Bus Weekday 10 am Good N/A 2461 Terminal Terminal

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Day of Operating Weather Bus Journey Origin Destination Incidents the Week Hour Condition Time (s) Square One Union GO Bus Bus Weekday 10 am Bad N/A 2584 Terminal Terminal Square One Union GO Bus Bus Weekday 10 am Good Roadwork 2640 Terminal Terminal Square One Union GO Bus Bus Weekday 10 am Good Unknown 2701 Terminal Terminal Square One Union GO Bus Bus Weekday 11 am Good N/A 2521 Terminal Terminal Square One Union GO Bus Bus Weekday 11 am Good Roadwork 2401 Terminal Terminal Square One Union GO Bus Bus Weekday 11 am Good Unknown 2760 Terminal Terminal Square One Union GO Bus Bus Weekend 6 am Good N/A 1621 Terminal Terminal Square One Union GO Bus Bus Weekend 7 am Good N/A 1680 Terminal Terminal Square One Union GO Bus Bus Weekend 7 am Bad N/A 2041 Terminal Terminal Square One Union GO Bus Bus Weekend 8 am Good N/A 1680 Terminal Terminal Square One Union GO Bus Bus Weekend 9 am Good N/A 1710 Terminal Terminal Square One Union GO Bus Bus Weekend 10 am Good N/A 1681 Terminal Terminal Square One Union GO Bus Bus Weekend 11 am Good N/A 1920 Terminal Terminal Union GO Cooksville Bus Weekday 5 am Good N/A 1860 GO Station Terminal Union GO Cooksville Bus Weekday 5 am Bad N/A 1651 GO Station Terminal

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Day of Operating Weather Bus Journey Origin Destination Incidents the Week Hour Condition Time (s) Union GO Cooksville Bus Weekday 9 am Good N/A 2400 GO Station Terminal Union GO Cooksville Bus Weekday 9 am Good Roadwork 2349 GO Station Terminal Union GO Cooksville Bus Weekday 9 am Bad N/A 2521 GO Station Terminal Union GO Cooksville Bus Weekday 10 am Good N/A 2101 GO Station Terminal Union GO Cooksville Bus Weekday 10 am Bad N/A 2344 GO Station Terminal Union GO Cooksville Bus Weekday 10 am Good Roadwork 2340 GO Station Terminal Union GO Cooksville Bus Weekday 10 am Good Unknown 2551 GO Station Terminal Union GO Cooksville Bus Weekday 11 am Good N/A 2221 GO Station Terminal Union GO Cooksville Bus Weekday 11 am Good Roadwork 2101 GO Station Terminal Union GO Cooksville Bus Weekday 11 am Good Unknown 2460 GO Station Terminal Union GO Cooksville Bus Weekend 6 am Good N/A 1440 GO Station Terminal Union GO Cooksville Bus Weekend 7 am Good N/A 1380 GO Station Terminal Union GO Cooksville Bus Weekend 7 am Bad N/A 1560 GO Station Terminal Union GO Cooksville Bus Weekend 8 am Good N/A 1320 GO Station Terminal Union GO Cooksville Bus Weekend 9 am Good N/A 1410 GO Station Terminal

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Day of Operating Weather Bus Journey Origin Destination Incidents the Week Hour Condition Time (s) Union GO Cooksville Bus Weekend 10 am Good N/A 1440 GO Station Terminal Union GO Cooksville Bus Weekend 11 am Good N/A 1620 GO Station Terminal Union GO Dixie GO Bus Weekday 5 am Good N/A 1080 Station Terminal Union GO Dixie GO Bus Weekday 9 am Good N/A 1531 Station Terminal Union GO Dixie GO Bus Weekday 9 am Good Roadwork 1389 Station Terminal Union GO Dixie GO Bus Weekday 9 am Bad N/A 1681 Station Terminal Union GO Dixie GO Bus Weekday 10 am Good N/A 1260 Station Terminal Union GO Dixie GO Bus Weekday 10 am Bad N/A 1383 Station Terminal Union GO Dixie GO Bus Weekday 10 am Good Roadwork 1560 Station Terminal Union GO Dixie GO Bus Weekday 10 am Good Unknown 1620 Station Terminal Union GO Dixie GO Bus Weekday 11 am Good N/A 1320 Station Terminal Union GO Dixie GO Bus Weekday 11 am Good Roadwork 1140 Station Terminal Union GO Dixie GO Bus Weekday 11 am Good Unknown 1380 Station Terminal Union GO Dufferin Bus Weekday 6am Good N/A 345 Street Terminal Union GO Dufferin Bus Weekday 9 am Good N/A 510 Street Terminal

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Day of Operating Weather Bus Journey Origin Destination Incidents the Week Hour Condition Time (s) Union GO Dufferin Bus Weekday 10 am Good N/A 445 Street Terminal Union GO Dufferin Bus Weekday 11 am Good N/A 427 Street Terminal Union GO Dufferin Bus Weekend 6 am Good N/A 331 Street Terminal Union GO Dufferin Bus Weekend 7 am Good N/A 360 Street Terminal Union GO Dufferin Bus Weekend 8 am Good N/A 320 Street Terminal Union GO Dufferin Bus Weekend 9 am Good N/A 350 Street Terminal Union GO Dufferin Bus Weekend 10 am Good N/A 360 Street Terminal Union GO Dufferin Bus Weekend 11 am Good N/A 330 Street Terminal Union GO Dufferin Bus Weekday 6 am Bad N/A 345 Street Terminal Union GO Dufferin Bus Weekday 9 am Bad N/A 510 Street Terminal Union GO Dufferin Bus Weekday 10 am Bad N/A 620 Street Terminal Union GO Dufferin Bus Weekday 11 am Bad N/A 531 Street Terminal Union GO Dufferin Bus Weekend 6 am Bad N/A 331 Street Terminal Union GO Dufferin Bus Weekend 7 am Bad N/A 345 Street Terminal Union GO Dufferin Bus Weekend 8 am Bad N/A 460 Street Terminal

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Day of Operating Weather Bus Journey Origin Destination Incidents the Week Hour Condition Time (s) Union GO Dufferin Bus Weekend 9 am Bad N/A 460 Street Terminal Union GO Dufferin Bus Weekend 10 am Bad N/A 420 Street Terminal Union GO Dufferin Bus Weekend 11 am Bad N/A 330 Street Terminal

Table B-5: HAW1 – Gardiner Expressway Westbound Route Origin Destination Day of the Week Bus Journey Time (s) Union GO Bus Square One Bus Weekday 2340 Terminal Terminal Union GO Bus Square One Bus Weekend 1740 Terminal Terminal Union GO Bus Cooksville GO Weekday 1981 Terminal Station Union GO Bus Cooksville GO Weekend 1381 Terminal Station Union GO Bus Dixie GO Terminal Dixie GO Weekday 1081 Station Station Square One Bus Highway 427/ QEW Weekday 1523 Terminal Square One Bus Highway 427/ QEW Weekend 907 Terminal Cooksville GO Highway 427/ QEW Weekday 1141 Station Cooksville GO Highway 427/ QEW Weekend 546 Station Dixie GO Highway 427/ QEW Weekday 271 Station

Table B-6: HAW2 – Gardiner Expressway Westbound Route Day of the Operating Bus Journey Origin Destination Week Hour Time (s) Union GO Bus Square One Bus Weekday 5 am 3495 Terminal Terminal Union GO Bus Square One Bus Weekday 6 am 3255 Terminal Terminal Union GO Bus Square One Bus Weekday 7 am 2760 Terminal Terminal

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Day of the Operating Bus Journey Origin Destination Week Hour Time (s) Union GO Bus Square One Bus Weekday 8 am 2819 Terminal Terminal Union GO Bus Square One Bus Weekday 9 am 2340 Terminal Terminal Union GO Bus Square One Bus Weekday 10 am 2221 Terminal Terminal Union GO Bus Square One Bus Weekday 11 am 2310 Terminal Terminal Union GO Bus Square One Bus Weekend 7 am 1591 Terminal Terminal Union GO Bus Square One Bus Weekend 8 am 1741 Terminal Terminal Union GO Bus Square One Bus Weekend 9 am 1740 Terminal Terminal Union GO Bus Square One Bus Weekend 10 am 1801 Terminal Terminal Union GO Bus Square One Bus Weekend 11 am 1891 Terminal Terminal Union GO Bus Cooksville GO Weekday 5 am 3255 Terminal Station Union GO Bus Cooksville GO Weekday 6 am 1741 Terminal Station Union GO Bus Cooksville GO Weekday 7 am 2340 Terminal Station Union GO Bus Cooksville GO Weekday 8 am 2340 Terminal Station Union GO Bus Cooksville GO Weekday 9 am 1966 Terminal Station Union GO Bus Cooksville GO Weekday 10 am 1800 Terminal Station Union GO Bus Cooksville GO Weekday 11 am 1921 Terminal Station Union GO Bus Cooksville GO Weekend 7 am 1171 Terminal Station Union GO Bus Cooksville GO Weekend 8 am 1380 Terminal Station Union GO Bus Cooksville GO Weekend 9 am 1380 Terminal Station Union GO Bus Cooksville GO Weekend 10 am 1440 Terminal Station Union GO Bus Cooksville GO Weekend 11 am 1411 Terminal Station Union GO Bus Dixie GO Station Weekday 5 am 2475 Terminal

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Day of the Operating Bus Journey Origin Destination Week Hour Time (s) Union GO Bus Dixie GO Station Weekday 6 am 960 Terminal Union GO Bus Dixie GO Station Weekday 7 am 1260 Terminal Union GO Bus Dixie GO Station Weekday 8 am 1500 Terminal Union GO Bus Dixie GO Station Weekday 9 am 101 Terminal Union GO Bus Dixie GO Station Weekday 10 am 960 Terminal Union GO Bus Dixie GO Station Weekday 11 am 1051 Terminal Highway 427/ Square One Bus Weekday 6 am 1334 QEW Terminal Highway 427/ Square One Bus Weekday 7 am 1599 QEW Terminal Highway 427/ Square One Bus Weekday 8 am 1694 QEW Terminal Highway 427/ Square One Bus Weekday 9 am 1526 QEW Terminal Highway 427/ Square One Bus Weekday 10 am 1440 QEW Terminal Highway 427/ Square One Bus Weekday 11 am 1506 QEW Terminal Highway 427/ Square One Bus Weekend 7 am 962 QEW Terminal Highway 427/ Square One Bus Weekend 8 am 8712 QEW Terminal Highway 427/ Square One Bus Weekend 9 am 881 QEW Terminal Highway 427/ Square One Bus Weekend 10 am 974 QEW Terminal Highway 427/ Square One Bus Weekend 11 am 937 QEW Terminal Highway 427/ Cooksville GO Weekday 6 am 1034 QEW Station Highway 427/ Cooksville GO Weekday 7 am 1179 QEW Station Highway 427/ Cooksville GO Weekday 8 am 1239 QEW Station Highway 427/ Cooksville GO Weekday 9 am 1066 QEW Station Highway 427/ Cooksville GO Weekday 10 am 960 QEW Station

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Day of the Operating Bus Journey Origin Destination Week Hour Time (s) Highway 427/ Cooksville GO Weekday 11 am 1149 QEW Station Highway 427/ Cooksville GO Weekend 7 am 720 QEW Station Highway 427/ Cooksville GO Weekend 8 am 478 QEW Station Highway 427/ Cooksville GO Weekend 9 am 547 QEW Station Highway 427/ Cooksville GO Weekend 10 am 621 QEW Station Highway 427/ Cooksville GO Weekend 11 am 534 QEW Station Highway 427/ Cooksville GO Weekday 6 am 253 QEW Station Highway 427/ Cooksville GO Weekday 7 am 278 QEW Station Highway 427/ Cooksville GO Weekday 8 am 305 QEW Station Highway 427/ Cooksville GO Weekday 9 am 241 QEW Station Highway 427/ Cooksville GO Weekday 10 am 300 QEW Station Highway 427/ Cooksville GO Weekday 11 am 249 QEW Station

Table B-7: HAW3 – Gardiner Expressway Westbound Route Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Union GO Bus Square One Weekday 5 am Good 3495 Terminal Bus Terminal Union GO Bus Square One Weekday 6 am Good 2041 Terminal Bus Terminal Union GO Bus Square One Weekday 7am Good 2701 Terminal Bus Terminal Union GO Bus Square One Weekday 7am Bad 2761 Terminal Bus Terminal Union GO Bus Square One Weekday 8am Good 2821 Terminal Bus Terminal Union GO Bus Square One Weekday 8 am Bad 2581 Terminal Bus Terminal Union GO Bus Square One Weekday 9am Good 2311 Terminal Bus Terminal Union GO Bus Square One Weekday 9am Bad 2340 Terminal Bus Terminal

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Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Union GO Bus Square One Weekday 10 am Good 2221 Terminal Bus Terminal Union GO Bus Square One Weekday 10 am Bad 2131 Terminal Bus Terminal Union GO Bus Square One Weekday 11 am Good 2281 Terminal Bus Terminal Union GO Bus Square One Weekday 11 am Bad 2700 Terminal Bus Terminal Union GO Bus Square One Weekend 7 am Good 1471 Terminal Bus Terminal Union GO Bus Square One Weekend 7 am Bad 1710 Terminal Bus Terminal Union GO Bus Square One Weekend 8 am Good 1710 Terminal Bus Terminal Union GO Bus Square One Weekend 8 am Bad 1891 Terminal Bus Terminal Union GO Bus Square One Weekend 9 am Good 1680 Terminal Bus Terminal Union GO Bus Square One Weekend 9 am Bad 1921 Terminal Bus Terminal Union GO Bus Square One Weekend 10 am Good 1770 Terminal Bus Terminal Union GO Bus Square One Weekend 10 am Bad 1861 Terminal Bus Terminal Union GO Bus Square One Weekend 11 am Good 1891 Terminal Bus Terminal Union GO Bus Square One Weekend 11 am Bad 1891 Terminal Bus Terminal Union GO Bus Cooksville Weekday 5 am Good 3255 Terminal GO Station Union GO Bus Cooksville Weekday 6 am Good 1741 Terminal GO Station Union GO Bus Cooksville Weekday 7am Good 2251 Terminal GO Station Union GO Bus Cooksville Weekday 7am Bad 2341 Terminal GO Station Union GO Bus Cooksville Weekday 8am Good 2340 Terminal GO Station Union GO Bus Cooksville Weekday 8 am Bad 2190 Terminal GO Station Union GO Bus Cooksville Weekday 9am Good 1944 Terminal GO Station Union GO Bus Cooksville Weekday 9am Bad 1980 Terminal GO Station

130

Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Union GO Bus Cooksville Weekday 10 am Good 1800 Terminal GO Station Union GO Bus Cooksville Weekday 10 am Bad 1741 Terminal GO Station Union GO Bus Cooksville Weekday 11 am Good 1920 Terminal GO Station Union GO Bus Cooksville Weekday 11 am Bad 2220 Terminal GO Station Union GO Bus Cooksville Weekend 7 am Good 1171 Terminal GO Station Union GO Bus Cooksville Weekend 7 am Bad 1260 Terminal GO Station Union GO Bus Cooksville Weekend 8 am Good 1350 Terminal GO Station Union GO Bus Cooksville Weekend 8 am Bad 1561 Terminal GO Station Union GO Bus Cooksville Weekend 9 am Good 1380 Terminal GO Station Union GO Bus Cooksville Weekend 9 am Bad 1501 Terminal GO Station Union GO Bus Cooksville Weekend 10 am Good 1411 Terminal GO Station Union GO Bus Cooksville Weekend 10 am Bad 1440 Terminal GO Station Union GO Bus Cooksville Weekend 11 am Good 1411 Terminal GO Station Union GO Bus Cooksville Weekend 11 am Bad 1530 Terminal GO Station Union GO Bus Dixie GO Weekday 5 am Good 2475 Terminal Station Union GO Bus Dixie GO Weekday 6 am Good 960 Terminal Station Union GO Bus Dixie GO Weekday 7am Good 1261 Terminal Station Union GO Bus Dixie GO Weekday 7am Bad 1200 Terminal Station Union GO Bus Dixie GO Weekday 8am Good 1500 Terminal Station Union GO Bus Dixie GO Weekday 8 am Bad 1410 Terminal Station Union GO Bus Dixie GO Weekday 9am Good 1081 Terminal Station Union GO Bus Dixie GO Weekday 9am Bad 1200 Terminal Station

131

Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Union GO Bus Dixie GO Weekday 10 am Good 960 Terminal Station Union GO Bus Dixie GO Weekday 10 am Bad 991 Terminal Station Union GO Bus Dixie GO Weekday 11 am Good 1021 Terminal Station Union GO Bus Dixie GO Weekday 11 am Bad 1260 Terminal Station Highway 427/ Square One Weekday 6 am Good 1334 QEW Bus Terminal Highway 427/ Square One Weekday 7 am Good 1599 QEW Bus Terminal Highway 427/ Square One Weekday 8 am Good 1711 QEW Bus Terminal Highway 427/ Square One Weekday 9 am Good 1494 QEW Bus Terminal Highway 427/ Square One Weekday 10 am Good 1440 QEW Bus Terminal Highway 427/ Square One Weekday 11 am Good 1506 QEW Bus Terminal Highway 427/ Square One Weekend 7 am Good 962 QEW Bus Terminal Highway 427/ Square One Weekend 8 am Good 795 QEW Bus Terminal Highway 427/ Square One Weekend 9 am Good 854 QEW Bus Terminal Highway 427/ Square One Weekend 10 am Good 941 QEW Bus Terminal Highway 427/ Square One Weekend 11 am Good 937 QEW Bus Terminal Highway 427/ Square One Weekday 6 am Bad 1334 QEW Bus Terminal Highway 427/ Square One Weekday 7 am Bad 1599 QEW Bus Terminal Highway 427/ Square One Weekday 8 am Bad 1577 QEW Bus Terminal Highway 427/ Square One Weekday 9 am Bad 1526 QEW Bus Terminal Highway 427/ Square One Weekday 10 am Bad 1479 QEW Bus Terminal Highway 427/ Square One Weekday 11 am Bad 1515 QEW Bus Terminal Highway 427/ Square One Weekend 7 am Bad 962 QEW Bus Terminal

132

Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Highway 427/ Square One Weekend 8 am Bad 995 QEW Bus Terminal Highway 427/ Square One Weekend 9 am Bad 1141 QEW Bus Terminal Highway 427/ Square One Weekend 10 am Bad 1007 QEW Bus Terminal Highway 427/ Square One Weekend 11 am Bad 937 QEW Bus Terminal Highway 427/ Square One Weekday 6 am Good 1334 QEW Bus Terminal Highway 427/ Square One Weekday 7 am Good 1599 QEW Bus Terminal Highway 427/ Square One Weekday 8 am Good 1711 QEW Bus Terminal Highway 427/ Square One Weekday 9 am Good 1494 QEW Bus Terminal Highway 427/ Square One Weekday 10 am Good 1440 QEW Bus Terminal Highway 427/ Square One Weekday 11 am Good 1506 QEW Bus Terminal Highway 427/ Square One Weekend 7 am Good 962 QEW Bus Terminal Highway 427/ Square One Weekend 8 am Good 795 QEW Bus Terminal Highway 427/ Square One Weekend 9 am Good 854 QEW Bus Terminal Highway 427/ Square One Weekend 10 am Good 941 QEW Bus Terminal Highway 427/ Square One Weekend 11 am Good 937 QEW Bus Terminal Highway 427/ Square One Weekday 6 am Bad 1334 QEW Bus Terminal Highway 427/ Square One Weekday 7 am Bad 1599 QEW Bus Terminal Highway 427/ Square One Weekday 8 am Bad 1577 QEW Bus Terminal Highway 427/ Square One Weekday 9 am Bad 1526 QEW Bus Terminal Highway 427/ Square One Weekday 10 am Bad 1479 QEW Bus Terminal Highway 427/ Square One Weekday 11 am Bad 1515 QEW Bus Terminal Highway 427/ Square One Weekend 7 am Bad 962 QEW Bus Terminal

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Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Highway 427/ Square One Weekend 8 am Bad 995 QEW Bus Terminal Highway 427/ Square One Weekend 9 am Bad 1141 QEW Bus Terminal Highway 427/ Square One Weekend 10 am Bad 1007 QEW Bus Terminal Highway 427/ Square One Weekend 11 am Bad 937 QEW Bus Terminal Highway 427/ Cooksville Weekday 6 am Good 1034 QEW GO Station Highway 427/ Cooksville Weekday 7 am Good 1179 QEW GO Station Highway 427/ Cooksville Weekday 8 am Good 1260 QEW GO Station Highway 427/ Cooksville Weekday 9 am Good 1059 QEW GO Station Highway 427/ Cooksville Weekday 10 am Good 1080 QEW GO Station Highway 427/ Cooksville Weekday 11 am Good 1149 QEW GO Station Highway 427/ Cooksville Weekend 7 am Good 720 QEW GO Station Highway 427/ Cooksville Weekend 8 am Good 495 QEW GO Station Highway 427/ Cooksville Weekend 9 am Good 546 QEW GO Station Highway 427/ Cooksville Weekend 10 am Good 660 QEW GO Station Highway 427/ Cooksville Weekend 11 am Good 534 QEW GO Station Highway 427/ Cooksville Weekday 6 am Bad 1034 QEW GO Station Highway 427/ Cooksville Weekday 7 am Bad 1170 QEW GO Station Highway 427/ Cooksville Weekday 8 am Bad 1217 QEW GO Station Highway 427/ Cooksville Weekday 9 am Bad 1166 QEW GO Station Highway 427/ Cooksville Weekday 10 am Bad 909 QEW GO Station Highway 427/ Cooksville Weekday 11 am Bad 1125 QEW GO Station Highway 427/ Cooksville Weekend 7 am Bad 720 QEW GO Station

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Day of the Operating Weather Bus Journey Origin Destination Week Hour Condition Time (s) Highway 427/ Cooksville Weekend 8 am Bad 395 QEW GO Station Highway 427/ Cooksville Weekend 9 am Bad 781 QEW GO Station Highway 427/ Cooksville Weekend 10 am Bad 527 QEW GO Station Highway 427/ Cooksville Weekend 11 am Bad 534 QEW GO Station Highway 427/ Dixie GO Weekday 6 am Good 253 QEW Station Highway 427/ Dixie GO Weekday 7 am Good 278 QEW Station Highway 427/ Dixie GO Weekday 8 am Good 300 QEW Station Highway 427/ Dixie GO Weekday 9 am Good 220 QEW Station Highway 427/ Dixie GO Weekday 10 am Good 299 QEW Station Highway 427/ Dixie GO Weekday 11 am Good 249 QEW Station Highway 427/ Dixie GO Weekend 6 am Bad 253 QEW Station Highway 427/ Dixie GO Weekend 7 am Bad 278 QEW Station Highway 427/ Dixie GO Weekend 8 am Bad 317 QEW Station Highway 427/ Dixie GO Weekend 9 am Bad 386 QEW Station Highway 427/ Dixie GO Weekend 10 am Bad 309 QEW Station Highway 427/ Dixie GO Weekend 11 am Bad 225 QEW Station 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

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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

155 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")

156

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