Ana Sasic. Copyright by Ana Sasic 2012

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1 Modelling Departure Time and Mode Choice for Commuting in the Greater Toronto and Hamilton Area (GTHA): Evaluation of Dynamic Travel Demand Management Policies by Ana Sasic A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Department of Civil Engineering University of Toronto Copyright by Ana Sasic 2012

2 Modelling Departure Time and Mode Choice for Commuting in the Greater Toronto and Hamilton Area (GTHA): Evaluation of Dynamic Travel Demand Management Policies Abstract Ana Sasic M.A.Sc Department of Civil Engineering University of Toronto 2012 This thesis develops econometric models of departure time and travel mode choice to evaluate dynamic transportation policies. Dynamic policies affect travel attributes differently throughout the day. Both departure time and mode choice are modelled with Random Utility Maximizing (RUM) Generalized Extreme Value (GEV) discrete choice models that capture systematic and random heterogeneity. Departure time is represented by a heteroskedastic generalized extreme value model (Het-GEV) with overlapping choice sets. Studying the Greater Toronto and Hamilton Area (GTHA), models are estimated using Revealed Preference (RP) household travel data from the 2006 Transportation Tomorrow Survey (TTS). Empirical models are used to evaluate dynamic transit and road pricing policies. Results indicate that the models are capable of capturing mode and time switching behaviour in response to peak pricing policies. To alleviate demand while maintaining transit mode share, a road charge and a moderate, flat, transit fare increase throughout the morning peak are recommended. ii

3 Acknowledgments Thanks go to Khandker Nurul Habib, among other things, for providing the original model formulation and estimation code. Also, thanks to Maya Nastic and specific individuals in the UofT transportation group for offering their expertise, technical assistance, and advice. iii

4 Table of Contents Acknowledgments... iii Table of Contents... iv List of Tables... vii List of Figures... ix List of Appendices... xvi Chapter 1 Introduction Objective Context Modelling Dynamic Transportation Policies Evaluating Dynamic Transportation Policies Overview...5 Chapter 2 Literature Review Mode Choice Models Mode Choice Literature Review Summary Departure Time Models Travel Time Reliability Effect of Traveller Information Combined Mode and Departure Time Choice Models Transportation Demand Management Policy Literature Literature Review Summary...21 Chapter 3 Data Description Data Trends Variables Kernel Densities of Temporal Demand Distribution...39 iv

5 Chapter 4 Departure Time Model Departure Time Choice Model Formulation Theoretical Formulation Empirical Models of Departure Time Choice Departure Time Choice Model for Non-Motorized Travel Departure Time Choice Model for Public Transit Departure Time Choice Model for Auto Comparing Parameters Estimates across Models...75 Chapter 5 Validation of Departure Time Choice Model Non-Motorized Departure Time Choice Model Validation Public Transit Departure Time Choice Model Validation Auto Departure Time Choice Model Validation Comparison with Previous Studies...88 Chapter 6 Mode Choice Model Empirical Models Mode Choice Model - Seven Mode Version Mode Choice Model - Three mode version Mode Choice Comparison with Previous Studies Chapter 7 Validation of Mode and Departure Time Choice Models Chapter 8 Policy Analysis Policy Analysis Overview Departure Time Policy Analysis Transit Fare Departure Time Choice Transit In-Vehicle Travel Time Departure Time Choice Transit Wait Time Departure Time Choice Auto Cost Departure Time Choice v

6 Auto In-Vehicle Travel Time Departure Time Choice Comparison of Departure Time Parameter Estimates and Elasticities Mode Policy Analysis Method - Mode Split Change in Response to Policies Mode Choice Elasticity Mode Choice Policies Mode and Departure Time Choice Policy Analysis Combined Mode and Departure Time Policy Analysis Results Policy Recommendations Policy Results Comparison: Chapter 9 Conclusion Future Work References Appendices Appendix A: Transit Wait Times 25 TTC Surface Routes Appendix B: Variables Appendix C: Final Departure Time Model Estimation Code Appendix D: Departure Time Multinomial Logit Model Results Appendix E: Mode Choice Model Estimation Code 7 modes Appendix F: Results for the Mode Choice Model 7 modes Appendix G: Mode Choice Model Estimation Code 3 modes vi

7 List of Tables Table 3.1 Trips by Mode Table 3.2 Number of Trips made by Mode and Occupation Table 3.3 Kernel Density Bandwidths Table 4.1 Non-Motorized Departure Time Model Results Table 4.2 Public Transit Departure Time Model Results Table 4.3 Auto Departure Time Model Results Table 5.1 Non-Motorized Departure Time Model Validation Table 5.2 Public Transit Departure Time Model Validation Table 5.3 Auto Departure Time Model Validation Table 6.1 Mode Utility Functions - Seven Mode Version Table 6.2 Mode Utility Functions - Three Mode Version Table 7.1 Observed Choice Distribution across Time Intervals and Modes Table 7.2 Predicted Choice Distribution across Time Intervals and Modes Table 8.1 Aggregate Reactions to Transit Price Policies Table 8.2 Average Reaction to Transit Fare Policies Table 8.3 Summary of Parameter Estimates Table 8.4 Summary of Elasticities Table 8.5 Direct Elasticity of Mode Choice with respect to Transit Fare Table 8.6 Direct Elasticity of Mode Choice with respect to Auto Cost vii

8 Table 8.7 Mode Choice Changes subject to Policies Table 8.8 Mode Choice Change subject to Auto and Transit Cost Policies Table 8.9 Policy = Fare increase = 2x between 8 and Table 8.10 Policy = Fare increase = 1.31x between 6:30 and 9:30 -London Table 8.11 Policy = Fare increase = 0x between 7 and Table 8.12 Policy = Fare increase = 0x between 8 and Table 8.13 Policy = Fare increase = 1.22x from open to 9:30 and 1.34x between 7:30 and 9 - Washington Table 8.14 Policy = Fare increase = 1.25x from 7 to 7:30, 1.5x 7:30 to 8, 1.75x 8 to Table 8.15 Policy = Fare increase = 1.4x from 6:30 to 7, 2.5x 7 to 8:30, 1.2x 8:30 to Table 8.16 Policy = Auto charge =$10 between 8:30 and Table 8.17 Policy = Auto charge =$10 between 8 and Table 8.18 Policy = Auto charge =$10 between 7:30 and 9: Table 8.19 Policy = ACOST charge $10 and Fare increase = 1.31x both from 6:30 to 9: Table 8.20 Policy = ACOST charge $5 and Fare increase = 1.31x both from 6:30 to 9: Table 8.21 Policy = ACOST charge $1.02 and Fare increase = 1.31x both from 6:30 to 9: Table 8.22 Effect of Policies on Mode Split: Comparison Table 8.23 Effect of Road Pricing Policies on Mode Split Table 8.24 Summary of Policy Effects: Mode Split and Departure Time Distribution viii

9 List of Figures Figure 3.1 GO Transit Trips by Hour Figure 3.2 Subway Trips by Hour Figure 3.3 Trips by Mode: Auto vs. Non-Auto Figure 3.4 Trips by Mode Figure 3.5 Trips by Trip Origin Region Figure 3.6 Trips by Trip Destination Region Figure 3.7 Trips by Parking Cost Figure 3.8 Trips by Auto Cost Figure 3.9 Trips by Total Transit Fare Figure 3.10 Trips by Total Transit In-vehicle Travel Time Figure 3.11 Trips by Total Transit Wait Time Figure 3.12 Trips by Age Figure 3.13 Trips by Age Category Figure 3.14 Trips by Mobility Tool Ownership Figure 3.15 Trips by Employment Status Figure 3.16 Trips by Occupation Type Figure 3.17 Trips by Travellers with Free Parking at Work Figure 3.18 Trips by Employment Region Figure 3.19 Trips by School Region ix

10 Figure 3.20 Subway Headway Scaling Factors Figure 3.21 Trips by Mode and Occupation Figure 3.22 Trips by Occupation and Mode Figure 3.23 Kernel Density Plot 2006 Auto Driver, General Office/Clerical Figure 3.24 Kernel Density Plot 2006 Auto Driver, Manufacturing/Construction Figure 3.25 Kernel Density Plot 2006 Auto Driver, Professional Figure 3.26 Kernel Density Plot 2006 Auto Driver, Retail Sales Figure 3.27 Kernel Density Plot 2006 Auto Driver, Unemployed Figure 3.28 Kernel Density Plot 2006 Auto Passenger, General Office/Clerical Figure 3.29 Kernel Density Plot 2006 Auto Passenger, Manufacturing/Construction Figure 3.30 Kernel Density Plot 2006 Auto Passenger, Professional Figure 3.31 Kernel Density Plot 2006 Auto Passenger, Retail Sales Figure 3.32 Kernel Density Plot 2006 Auto Passenger, Unemployed Figure 3.33 Kernel Density Plot 2006 Non-Motorized, General Office/Clerical Figure 3.34 Kernel Density Plot 2006 Non-Motorized, Manufacturing/Construction Figure 3.35 Kernel Density Plot 2006 Non-Motorized, Professional Figure 3.36 Kernel Density Plot 2006 Non-Motorized, Retail Sales Figure 3.37 Kernel Density Plot 2006 Non-Motorized, Unemployed Figure 3.38 Kernel Density Plot 2006 Transit, General Office/Clerical Figure 3.39 Kernel Density Plot 2006 Transit, Manufacturing/Construction x

11 Figure 3.40 Kernel Density Plot 2006 Transit, Professional Figure 3.41 Kernel Density Plot 2006 Transit, Retail Sales Figure 3.42 Kernel Density Plot 2006 Transit, Unemployed Figure 4.1 Departure Time Choice Framework Figure 4.2 Table 4 Non-Motorized Departure Time Parameter Estimate: Constant Figure 4.3 Non-Motorized Departure Time Parameter Estimate: Work Duration and Trip Distance Figure 4.4 Non-Motorized Departure Time Parameter Estimate: Occupation Type Figure 4.5 Non-Motorized Departure Time Parameter Estimate: Age, Gender, Full-Time Status Figure 4.6 Public Transit Departure Time Parameter Estimate: Constant Figure 4.7 Public Transit Departure Time Parameter Estimate: In-vehicle Travel Time and Wait Time Figure 4.8 Public Transit Departure Time Parameter Estimate: Work Duration Figure 4.9 Public Transit Departure Time Parameter Estimate: Downtown Destination Figure 4.10 Public Transit Departure Time Parameter Estimate: Occupation Type Figure 4.11 Public Transit Departure Time Parameter Estimate: Other Figure 4.12 Auto Departure Time Parameter Estimate: Constant Figure 4.13 Auto Departure Time Parameter Estimate: Cost and In-vehicle Travel Time Figure 4.14 Auto Departure Time Parameter Estimate: Work Duration Figure 4.15 Auto Departure Time Parameter Estimate: Downtown Destination Figure 4.16 Auto Departure Time Parameter Estimate: Occupation Type xi

12 Figure 4.17 All Modes Departure Time Parameter Estimate: Constant Figure 4.18 All Modes Departure Time Parameter Estimate: Work Duration Figure 4.19 All Modes Departure Time Parameter Estimate: Downtown Destination Figure 4.20 All Modes Departure Time Parameter Estimate: Office/Clerical Figure 4.21 All Modes Departure Time Parameter Estimate: Professional Figure 4.22 All Modes Departure Time Parameter Estimate: Manufacturing/Construction Figure 5.1 Non-Motorized Departure Time Model Validation Figure 5.2 Non-Motorized Departure Time Model Validation: Parameter Comparison to MNL 81 Figure 5.3 Non-Motorized Departure Time Model Validation: Comparison to MNL Figure 5.4 Public Transit Departure Time Model Validation Figure 5.5 Public Transit Departure Time Model Validation: Parameter Comparison to MNL.. 84 Figure 5.6 Public Transit Departure Time Model Validation: Comparison to MNL Figure 5.7 Auto Departure Time Model Validation Figure 5.8 Auto Departure Time Model Validation: Parameter Comparison to MNL Figure 5.9 Auto Departure Time Model Validation: Comparison to MNL Figure 6.1 Mode Choice Model Framework: Seven Modes Figure 6.2 Seven Mode Choice Model Parameter Estimate: Cost Figure 6.3 Seven Mode Choice Model Parameter Estimate: Effect of Trip Distance on Non- Motorized Utility Figure 6.4 Seven Mode Choice Model Parameter Estimate: Transit Level of Service Attributes 96 Figure 6.5 Seven Mode Choice Model Parameter Estimate: Auto Ownership xii

13 Figure 6.6 Seven Mode Choice Model Parameter Estimate: Effect of Auto Ownership of Transit Utility Figure 6.7 Seven Mode Choice Model Parameter Estimate: Age Figure 6.8 Seven Mode Choice Model Validation: Mode Split Figure 6.9 Seven Mode Choice Model Validation Figure 6.10 Three Mode Choice Model Parameter Estimate: Constant Figure 6.11 Three Mode Choice Model Parameter Estimate: Cost Figure 6.12 Three Mode Choice Model Parameter Estimate: Effect of Trip Distance on Non- Motorized Utility Figure 6.13 Three Mode Choice Model Parameter Estimate: Transit Level of Service Attributes Figure 6.14 Three Mode Choice Model Parameter Estimate: Auto Ownership Figure 6.15 Three Mode Choice Model Parameter Estimate: Age Figure 6.16Three Mode Choice Model Parameter Estimate: Gender Figure 6.17 Three Mode Choice Model Validation: Mode Split Figure 6.18 Three Mode Choice Model Validation Figure 7.1 Observed vs. Predicted Mode and Departure Time Choice Distribution Figure 7.2 Observed vs. Predicted Departure Time Distribution Figure 7.3 Observed vs. Predicted Mode Split Figure 7.4 Mode and Departure Time Choice Validation Summary: By Time Figure 7.5 Mode and Departure Time Choice Validation Summary: By Mode Figure 8.1 Direct Elasticity of Departure Time Choice with respect to Transit Fare xiii

14 Figure 8.2 Washington vs. London: Policies Figure 8.3 Washington vs. London: Impacts Figure 8.4 Gradual vs. Demand-Relative: Policies Figure 8.5 Gradual vs. Demand-Relative: Impacts Figure 8.6 Partially Free Policies Figure 8.7 Partially Free Policies: Impacts Figure 8.8 Average Behaviour Change Relative to Fare Ratio Change Figure 8.9 Departure Time Choice Behaviour Change subject to Price Change Figure 8.10 Direct Elasticity of Departure Time Choice with respect to Transit In-vehicle Travel Time Figure 8.11 Change in Time distribution subject to Doubled Transit In-vehicle Travel Time Figure 8.12 Direct Elasticity of Departure Time Choice with respect to Transit Wait Time Figure 8.13 Change in Transit Time Distribution subject to Doubled Wait Time Figure 8.14 Direct Elasticity of Departure Time Choice with respect to Auto Cost Figure 8.15 Change in Time Distribution subject to Doubled Auto Cost Figure 8.16 Change in Time Distribution subject to $10 Auto Charge Figure 8.17 Direct Elasticity of Departure Time Choice with respect to Auto In-vehicle Travel Time Figure 8.18 Change in Time Distribution subject to Doubled Auto In-vehicle Travel Time Figure 8.19 Transit In-vehicle Travel Time: Parameter Estimates and Elasticities Figure 8.20 Transit Wait Time: Parameter Estimates and Elasticities xiv

15 Figure 8.21 Auto Cost: Parameter Estimates and Elasticities Figure 8.22 Auto In-vehicle Travel Time: Parameter Estimates and Elasticities Figure 8.23 Effect of Fare Increase/Decrease on Transit Mode Share Figure 8.24 Mode Share Subject to Auto Charge Figure 8.25 Mode Split Changes subject to Policies Figure 8.26 Mode Split Change subject to Road Pricing Policies Figure 8.27 Effect of Transit Fare Policies on Departure Time Figure 8.28 Effect of Road Pricing Policies on Departure Time xv

16 List of Appendices Appendix A: Transit Wait Times 25 TTC Surface Routes Appendix B: Variables Appendix C: Final Departure Time Model Estimation Code Appendix D: Departure Time Multinomial Logit Model Results Appendix E: Mode Choice Model Estimation Code 7 modes Appendix F: Results for the Mode Choice Model 7 modes Appendix G: Mode Choice Model Estimation Code 3 modes xvi

17 1 Chapter 1 Introduction 1.1 Objective The goals of this thesis are to develop policy-responsive econometric choice models of mode choice and trip departure time and to apply them to evaluate the effects of dynamic transportation policies. Transportation policies such as dynamic public transit pricing and road pricing are intended to influence the distribution of travel demand throughout the day by providing disincentives to travel during certain periods usually the peak hours. To design such policies, it is important to understand the nature of travel demand with respect to time of day and mode choice. Individuals make the choice to conduct a trip at a certain time of day using a certain mode based on many factors. It is the goal of this research to study such decision making processes in order to predict the potential effects of dynamic/time-based transportation policies on travel demand in the Greater Toronto and Hamilton (GTHA). The models are representations of the relationship between mode and departure time choice and the characteristics of the trip (origin/destination, purpose, travel time/cost, etc.) and the individual (age, auto ownership, home location, etc.). 1.2 Context There has been an increase in awareness and support for innovative transportation pricing strategies such as automated road pricing and integrated transit fare systems. With the acceptance of new technologies such as transit fare smart cards, GPS monitoring, and cell-phone based vehicle tracking, dynamic transportation pricing strategies are becoming more practical to implement. It may be possible to employ dynamic transportation pricing as a tool to manage urban travel demand, especially during peak hours. Some cities already have public transit systems with variable costs, often administered using smart card technology for example: London (Transport for London, 2011), Seattle (King County, 2011), and Washington D.C. (WMATA, 2011). Moreover, dynamic transportation policies are not a recent concept; it is said that vehicular traffic in the Roman Empire was restricted from entering the central city during daytime peak hours (Lay, 1993).

18 2 The Greater Toronto (and Hamilton) Area (GTHA) has recently introduced an integrated fare smart card (the Presto card) into its regional rail GO Transit system, suburban bus systems, and into some subway stations of the Toronto Transit Commission system (TTC) (PRESTO, 2011). While installation of the hardware is ongoing, users are charged on the basis of existing single ride fares. The Toronto Transit Commission uses a flat fare pricing strategy regardless of time of day or distance travelled (TTC, 2000), although this strategy has been questioned recently (Higgins, 2010). There will be an opportunity to define a new pricing framework when the smart card technology is fully implemented. In general, peak transit pricing may contribute to encouraging off-peak ridership; continuous transit use throughout the day is in line with the goals of urban regions striving for transit-oriented development (Walker, 2010). Imposing higher fares during the peak periods would charge those users who contribute to crowding while possibly preventing those who can travel before or after the height of the peak period from contributing to the congestion. Variable transit pricing may thus lead to a wider peak period, avoiding incidents where demand exceeds capacity and allowing the transit system to run at more efficient passenger volumes throughout the day. However, there exists a danger that higher peak period pricing may deter transit users and induce them to drive instead. Using variable road pricing in combination with variable transit fares could be a powerful tool in managing and shaping travel demand. The potential effects of various pricing strategies require investigation. Evaluating such policies requires good analytical tools and appropriate data. In terms of analytical tools, it is important to have models that can capture the behavioural tradeoffs involved in commuters mode choice and departure time decisions; these two key decisions determine the distribution of demand on road and transit networks. Policies such as variable transit fares and road prices can affect mode choice and departure time decisions among work trips. Modelling techniques that enable the testing of a wide variety of hypothetical policy initiatives are required. This research aims to develop models of departure time and mode choice in order to evaluate the effectiveness of various pricing strategies in managing peak period travel demand, considering the GTHA as a case study.

19 3 1.3 Modelling Dynamic Transportation Policies In a time when high travel demand is causing pressure on the transportation system, strategies that make better use of the supply available need to be developed. If policies targeted at shifting some demand out of the peak period are to be implemented in the GTHA, policy makers must understand the way that people may react. Then, pricing strategies that are expected to reshape transit demand over time in desirable ways can be recommended. First, useful models developed with a basis of informative data are required. The models of departure time and mode choice in this study are estimated using data from the Transportation Tomorrow Survey (TTS), a Revealed Preference (RP) household travel diary collected in the GTHA. In the survey, commuting modes are classified into private car, public transit, regional commuter rail, and non-motorized transportation categories. The public transportation system in the GTHA consists of the Toronto Transit Commission (TTC) which provides subway, streetcar, and bus service within the City of Toronto, the regional commuter rail system GO transit, and multiple suburban transit systems providing bus service around their regions and toward the subway. The modelling structure presents a hierarchical framework where the departure time choice is made at the lower level (using separate datasets for each travel mode), and the mode choice is made at the upper level. The departure time choice is represented by a Heteroskedastic Generalized Extreme Value (Het-GEV) model that can accommodate the ordered and correlated nature of adjacent time intervals. The mode choice component is represented by a tree logit model where the seven mode choices of auto driver, auto passenger, subway auto access, GO transit with auto access, GO with transit or walk access, local transit with walk access, and nonmotorized travel are organized into the categories of auto, GO transit, other transit, and nonmotorized transportation modes. Combined, the mode choice and departure time choice models provide a modelling system that can be used to evaluate dynamic pricing strategies for roads or transit. The development of the mode and departure time choice models is motivated by the knowledge that the two choices of time and mode influence each other (i.e. public transit service is infrequent at night and therefore an undesirable choice). Increasing peak period congestion in the GTHA indicates that the future of transportation planning must include an awareness of temporal

20 4 demand distributions. In traditional travel demand models that only consider peak period travel, departure time choice is overlooked. Recent modelling practices have moved toward a continuous, 24-hour perspective of travel demand. To capture the continuous dimension of travel demand, departure time choice needs to be explicitly modelled. This research models departure time choice over a 24-hour period with a focus on commuting trips because they are the subject of many transportation policies since they represent the most frequent and dominant trip type. 1.4 Evaluating Dynamic Transportation Policies Using the departure time and mode choice models, a variety of transportation policies can be evaluated. The models can be used to predict the effects of dynamic transportation policies on travel behaviour patterns. Specifically, the policy of imposing variable public transit pricing throughout the day has been presented as a case study. The potential effects of imposing a higher transit fare during the peak hours as compared to off-peak hours are investigated. The hypothesis is that the utility of a particular trip occurring during peak hours would be reduced by imposing this policy. Subsequently, the departure time choice as well as mode choice decisions would be affected. One potential outcome may be a higher incidence of public transit trips occurring outside of the peak period. If the utility of conducting a particular trip during the peak hour were reduced while the utility of conducting the same trip off-peak stayed the same, the individual would be inclined to reschedule the trip into the off-peak period. Another potential outcome is a shift away from the affected public transit modes for trips during the peak period. If the utility of conducting a certain trip by public transit were reduced as a result of the price increase such that it were to become less desirable to take transit than to drive (given that the trip is occurring during the peak period), individuals may decide against using public transit resulting in a decline in transit ridership. The degree to which these effects manifest themselves is of interest in the policy design process. If the model predicts that a large number of trips would reschedule their departure time out of the peak while relatively few transit trips would switch to other modes if such a dynamic pricing strategy were implemented, it could be concluded that implementing the pricing policy would yield desirable effects. It could be argued that the opposite outcome is undesirable; a situation where many transit users choose instead to drive while few choose to reschedule their transit trip as a result of a peak-period transit pricing policy may have negative impacts on the transportation system and the city.

21 5 1.5 Overview The thesis presents a review of existing relevant literature and an analysis of the data available to define the need for this work in policy-responsive mode and departure time choice modelling and to position the study in its context. Subsequently, the final departure time choice model formulation is presented; the structure was chosen to represent the reality of decision making behaviour. The results and validation of the empirical models demonstrate the suitability of the chosen model structure for representing temporal patterns in the data. The mode choice model is then presented, and is combined with the departure time model to find the predicted choice probabilities for both decisions. The predicted distribution of work trips between travel modes and over time is compared to the observed distribution. Finally, both models are applied to test hypothetical dynamic transportation demand management policies. General policy design recommendations are derived from predicted reactions to the policies tested. The study concludes by summarizing findings from the choice modelling and policy analysis and by identifying potential future projects that may make use of this work.

22 6 Chapter 2 Literature Review This chapter presents a comprehensive literature review of previous works that relate to one or more aspects of this study. Since this thesis presents policy-responsive models of mode and departure time choice, it is necessary to place it in the context of existing mode and departure time choice models, as well as other studies on travellers reactions to demand management policies. This literature review examines existing studies in order to show that these topics are being studied by the wider community, that there is a need to further improve travel demand modelling practices, and that this study can make a useful contribution to this discipline. The related areas of study examined here are: mode choice modelling and departure time modelling (formulations and applications), users valuation of time, the potential effect of user information on commuting choices, examples of other studies that have examined both mode and departure time choices, and examinations of transportation demand management policies. Existing modelling practices motivate the choice of model framework used in this study. Studies of the effect of information and travel time reliability on choice behaviour relate to this study because both examine travellers propensity to change their behaviour in response to the system state. The findings of other studies on the subject of travel demand policies can be compared to the policy analysis portion of this thesis Mode Choice Models In transportation modelling, the discrete choice between travel modes is represented by the concept of maximizing random utility. Attributes of each travel mode (i.e. travel time, cost) influence its desirability for travellers. Mode choice models predict the proportion of travellers or trips that will select each mode given the attribute values and their relative importance. Several modelling frameworks have been used to represent mode choice in previous studies. The most basic is the multinomial logit model, computationally practical and representative of observed choice behaviour. The multinomial logit represents the probability of selecting a mode as the ratio of the exponent of its utility to the sum of the exponents of each mode s utility. A related modelling structure is the nested logit model, where alternative modes are arranged in a hierarchical structure corresponding to the sets and subsets of travel modes (i.e. subway and bus belong to the set of public transit modes). Some studies made use of a mixed logit mode choice

23 7 model which combines inputs from revealed and stated preference information. Another option is the probit model which includes a stochastic component in the utility function, adding realism but making the model computationally demanding; the probit model is thus rarely employed in practice. Still other modelling approaches have been used to represent mode choice some such studies are reviewed here. Furthermore, some studies address mode choice in terms of a tour (the set of trips that an individual makes in a day) rather than a single trip. The reality that many trips are part of tours imposes certain constraints on mode choice: a vehicle taken from home must be returned, the availability of vehicles is limited by the sequence of trips. Finally, some studies discussed here explore a specific issue or attribute of travel mode choice for example, the relationship between mode choice and auto ownership. The multinomial logit model (MNL) represents the choice between discrete alternatives in a clear structure (McFadden, 1973). A potential weakness of this model structure is the assumption of Independence of Irrelevant Alternatives (IIA property); enforcing that the utilities of alternatives are independent of each other (Ben-Akiva & Lerman, 1985). This manifests itself as insensitivity to the correlation between related alternatives. As a result, many studies choose to use a variation on the multinomial logit model to relax this rigidity. Bhatta and Larsen (2011) is a recent example of a mode choice study using the multinomial logit model. The study quantifies errors in parameter estimates due to the weaknesses of the MNL formulation. Martinez et al. (2009) presents the constrained multinomial logit, a variation on the MNL structure where the feasible choice set is defined. Some studies use the multinomial logit model in addition to other formulations for the purposes of comparison: Zhou and Lu (2011) applies a multinomial logit model and a probabilistic neural network to predict urban mode choice and Arunotayanun and Polak (2009) studied freight mode choice using multinomial logit, nested logit, and cross-nested logit models. They find that the more sophisticated formulations represent choice behaviour better than the multinomial logit model. The nested or tree logit model presents alternatives in a hierarchical tree structure corresponding to their relationships (bus and train are subsets of transit modes). A decision maker would directly compare closely related modes within the transit nest. In comparison, the multinomial logit would present all options to the decision maker at the start, without grouping them into subsets. While the nested logit relaxes the zero covariance assumption from the multinomial logit, the covariance structure is limited by the nesting structure; alternatives in the same nest all

24 8 have equal covariance while being fully unrelated to alternatives in other nests. This requires that the sets of alternatives which demonstrate the IIA property must be decided upon in advance, leading to the need to test many different formulations. Moreover, some sets of alternatives cannot be accurately partitioned into distinct subsets. The nested logit also has a closed form, making it practical to use (Ben-Akiva & Lerman, 1985). Abdel-Aty and Abdelwahab (2002) is an example of a nested logit structure with three hierarchical levels: the mode choice was represented as a choice between highway and transit, with a secondary choice between driver/passenger modes or transit sub-modes respectively, and transit users also chose whether they access the transit by car or on foot. This structure is consistent with the data used in this study trips are categorized by primary mode and access/egress modes. A study examining access mode choice behaviour for high-speed rail access using a nested logit model found that access mode choice is motivated by cost considerations (Wen et al. 2012). Arunotayanun and Polak (2009) show that the nested logit model and cross-nested logit model (presented by Vovsha, 1997) perform better than the multinomial logit. Hess et al. (2011) use the cross-nested logit, a formulation of the nested logit where alternatives can belong to multiple nests, to examine mode choice for trips accessing an airport in addition to airport choice and airline choice. The nested structure is suitable for representing the joint decision of these three related choices. In another application of the nested logit model to examine multiple related choices, Dissanayake and Morikawa (2009) studied household vehicle ownership, mode choice and trip sharing decisions in the Bangkok Metropolitan Region. Another variation on the multinomial logit model is the mixed logit, providing greater flexibility in accommodating correlations among various alternatives in a discrete choice model. Train (2003) explains various formulations of the mixed logit model. (Cherchi and Cirillo, 2008) used household travel survey data to estimate a mixed logit model, accounting for variation between individual preferences. This study involved a component of household interaction by analyzing the correlation in responses across members of a family. Also, the study found that an individual s subjective weighting of the importance of travel time and cost is stable over time allowing for habit formation, but that these weights vary significantly between individuals. Long et al. (2010) used a hierarchical random-coefficient mixed logit model to examine commuters mode choice in the Chicago area. It was found that choice behaviour differs between individuals

25 9 living in different parts of the city and exhibiting differing socio-economic attributes. Yang and Sung (2009) use a mixed logit model to investigate mode choice behaviour subject to the introduction of a new high-speed rail mode option in the study area of Taiwan. They find that travel cost is the dominant explanatory variable in terms of mode choice. Using stated preference data, Dissanayke and Morikawa (2009) were able to examine choice preference for a rapid transit mode that was not yet implemented at the time of the survey. Shen (2009) used stated preference data to estimate a mixed logit model in order to represent transport mode choice data in Japan. Another mode choice model, the probit model is theoretically sound but is seldom used due to its high computational demands. The model includes a stochastic term in the utility function which provides greater realism by accounting for individual variation where the multinomial logit assumes a deterministic utility formula for all trips. This error term is also the cause of an impractical model structure that has no closed form solution. The choice probabilities are represented by multidimensional integrals of the normal probability density function. Since there is no analytical closed form solution, choice probabilities can only be computed numerically (by simulation) and if there are more than approximately four choice alternatives, the computational demand becomes very high (Horowitz, 1991). Ghareib (1996) applied both logit and probit models in a mode choice study and compared the results. The study shows that the versatility of the probit model does not guarantee a superior outcome. Particularly in a binary mode choice situation, the results of this comparison suggest that the probit model does not provide a better result than the logit and that its added complexity is not justified by performance benefits. The probit model has been used to represent mode choice between a small number of travel modes (three to five) in the central business district of Washington, D.C. (Hausman and Wise, 1978). Another demonstrated application of the probit model in the transportation research field is the forecasting of freight transportation demand (Garrido and Mahmassani, 2000). Still other modelling frameworks have been used to represent transportation mode choice. Bhat (1995) applied the heteroskedastic extreme value model. Choice alternatives under the heteroskedastic model are represented as independent but not identically distributed allowing the level of service attributes to exhibit differing degrees of variability for each choice alternative. This model was found to provide greater accuracy than the multinomial logit model in an intercity rail case study. Specifically, the heteroskedastic model predicted less drastic and

26 10 more realistic reactions to a rail service improvement compared to the logit model. Similar to the work presented here, the intercity rail study is concerned with predicting ridership reactions to changes in public transit levels of service. A heteroskedastic mode choice model was also applied by Golias (2002) to evaluate the impacts of the introduction of a new subway system in Athens on mode choice. Using revealed preference survey data, the model accounted for random variation between individual decision makers and found that increasing auto travel times and costs would cause increased demand for the subway but not for the bus. The paired combinatorial logit (PCL) model also avoids the IIA property of the multinomial logit model and the nest-specific covariance restriction of the nested logit. The PCL model represents the relation between alternatives by a different covariance for each pair of choices. This is a useful feature, allowing the relationship between each pair of alternatives to represent the competition exhibited between them in real travel decisions. In its simplest form, the PCL collapses to a multinomial logit model with high computational efficiency. (Koppelman and Wen, 2000) However, when the flexibility of the PCL model is used by specifying a different covariance for each pair, there is a trade-off in terms of computational efficiency. As another representation of mode choice, a study by Dial (1979) defined the choice of travel mode as a special case of route choice. The model included mode specific attributes such as level of service into the utility functions of alternate routes. This approach is compelling, but is not applicable to this study because external route assignment software is used to assign trips to routes after the mode has been selected. Some mode choice models are based on the concept that trips are not isolated, rather they belong to tours, chains of trips taken by an individual throughout the day. Understanding that trips occur in tours imposes certain constraints on mode choice (i.e. a vehicle taken from home in the morning should be returned) (Miller et al., 2005). In the framework used, individuals choose the best combination of modes for a tour, given the activities and locations they plan to visit. Each trip is assigned a mode subject to tour-based constraints such as auto availability, determined by intra-household allocation. The utility of a potential combination of modes is represented as the sum of the utilities of each trip within the tour. Tour-based mode choice studies include Cirillo and Axhausen (2006), a study of travel patterns. The study compared the travel pattern of workers and non-workers throughout the day. The findings quantify aspects of tour scheduling

27 11 and mode choice (i.e. workers leave the house more in the evening than non-workers, only around one percent of people pursue more than three tours a day). Also, Muralidhar et al. (2005) demonstrated an application of a tour-based mixed logit model assuming one primary mode per tour. Household auto ownership is known to be a significant explanatory variable of mode choice. Many of the factors that influence the mode choice of individual trips (home location, habits, and work location) are also predictors of auto ownership behaviour. Therefore, some studies have modelled mode choice and auto ownership jointly as endogenous variables. Train (1980) estimated the marginal probabilities of certain mode choices and auto ownership levels and the conditional probabilities of modes chosen given cars owned (and vice versa) as logit models, then combined them to find the joint probabilities of all combinations of auto ownership and mode choice. Lerman (1976) included household location decisions as part of a joint model also using a multinomial logit model to represent the effect of transportation, geography and socioeconomic attributes on utility. Finally, some mode choice studies have chosen to focus on a specific issue or explanatory variable. A study by Cervero (2002) examined the effect of mixed use, high density land use on mode choice finding that there is a significant correlation. Train and McFadden (1977) examined the impact of personal income on subjective weights of the importance of time and cost attributes. One study specifically analyzed the effect of free parking at the workplace on mode choice (Hess, 2001). It shows that the mode share shifts significantly toward transit and away from driving when workplace parking costs six dollars compared to when it is free. Ewing et al. (2004) examined the mode choice decision for school trips from kindergarten through high school, finding that school size and land use do not effect mode choice while walking distance is a significant factor Mode Choice Literature Review Summary A heteroskedastic tree mode choice framework was chosen for this study because existing mode choice modelling practices have indicated that such a framework is appropriate to represent mode choice behaviour. The analysis of existing mode choice modelling practices indicates that nested formulations represent the grouped nature of travel modes (typically into auto, transit, and non-motorized categories) and thus represent choice behaviour better than multinomial logit

28 12 models. Therefore, this study uses a tree logit formulation which recognizes that travel modes can be grouped into logical clusters. Mixed logit models can provide the added benefit of accommodating stated preference data where it exists; however, stated preference data is not available for this study. Furthermore, it has been observed that choice behaviour can vary widely between individuals; specifically, travel mode choices are closely linked to other lifestyle characteristics. Lerman (1976), Train and McFadden (1977), and Cervero (2002) have examined the relationship between travel mode choice and specific lifestyle factors including income, auto ownership and land use. Like Golias, (2002) and Bhat (1995), this study considers a heteroskedastic approach to explain the differences between individual decision makers behaviour. Lifestyle considerations such as household income may explain the differing variance between individuals choice behaviour. This analysis of existing mode choice modelling practices has motivated the decision to represent travel mode choice with a heteroskedastic tree logit model Departure Time Models Departure time models represent an individual s choice of a point or interval in time at which to begin a trip. These models can be represented as random utility choice models. Types of models used to represent the departure time choice include the multinomial logit model, the nested logit model, the cross-nested logit model, the mixed logit model, and the Ordered Generalized Extreme Value (OGEV) model. Two issues in departure time modelling are accurately representing the continuous and gradually changing nature of time and capturing the common effect of choice captivity, often due to rigid work schedules. As an example of a multinomial logit model (Equation 2.1), Hendrickson and Plank (1984) estimated discrete departure time interval choice as well as mode choice and found departure time choice to be more elastic than mode choice subject to external influences. Basic multinomial logit models are not ideally suited to representing departure time choice because they do not capture the similarities between adjacent time interval choices. MNL P ij = e Vij / J k=1 e Vik (2.1) Nested logit models to some degree relax the independence assumption due to their hierarchical structure (Bhat and Steed, 2002). The cross-nested logit structure introduced by (Vovsha, 1997)

29 13 allows for further correlation between alternatives by placing alternatives in multiple nests, removing the assumption of fully independent subsets of alternatives. As a variation on the cross-nested model structure, (Lemp et al., 2010) uses a continuous cross-nested logit model (CCNL). The advantages of this structure are the capacity for correlation between alternatives inherent to the cross-nested model and the realism of a continuous time variable. To generalize the cross-nested model for a continuous variable, the CCNL model groups ordered discretized intervals of a continuous variable into nests. The cross-nested structure relates to the conceptual choice framework used in this work. Using a mixed logit model, Kristoffersson (2007) combines stated preference (SP) and revealed preference (RP) data collected from drivers in Stockholm to estimate a departure time and mode choice model, connected to a dynamic traffic assignment model. The weakness of mixed logit models is their computational complexity. Kristoffersson chose to use a mixed logit instead of an OGEV model because they used stated preference responses from respondents, and OGEV models do not capture the correlation of SP personal factors affecting departure time choice. Borjesson (2007) also used a combination of RP and SP data in a mixed logit model to represent departure time choice, accounting for the response variation between stated and revealed responses. A number of departure time models use other types of model formulation. Bhat and Steed (2002) used a continuous hazard model to represent departure time choice for urban shopping trips throughout the day. Abu-Eisheh and Mannering (1989) used a combination of discrete and continuous time variables in an econometric modelling structure to study commuter departure time choice. Bin Ran et al. (1996) modelled user optimal departure time and route choices at each point in time subject to a dynamic representation of travel times. In another study involving route choice, Arnott et al. (1990) considers the effects of varying pricing regimes on morning commuters departure time and route decisions and finds that these choices depend on travel time, and desired and achieved arrival time. Arnott found that most of the reduction in congestion that may be realized by road tolling would be attributed to commuters change in departure time decisions. Finally, two studies, Gadda et al. (2009) and Lemp et al. (1998) apply Bayesian techniques to estimate model parameters and predict departure time choices on a continuous time dimension.

30 14 The weakness of a purely continuous time variable is its inability to capture the correlation of adjacent time intervals, making it unsuitable to a study of policies that may shift and spread peak period demand. Moreover, individuals choose approximate departure times within discrete intervals, so that a fully continuous time variable is neither necessary nor useful. A continuous cross-nested model formulation can overcome the limitations of a purely continuous time variable, although it induces a high computational burden. The ordered generalized extreme value (OGEV) captures the correlation of adjacent time interval alternatives which allows it to be used for policy analysis (Equation 2.2). Another benefit is that a closed form exists, allowing computational simplicity without the need for simulation. (Kristoffersson, 2007) OGEV models, unlike logit models, accept that the choice between adjacent and similar time intervals differs from the choice between distant time intervals (choosing to leave for work around 7:00 versus 7:30 is a very different choice from the choice between leaving at 7:00 or 9:00). P OGEV ij = (e Vij/p )/( J+1 r=1 (e Vir-1/p + e Vir/p ) p ) x [(e Vij-1/p + e Vij/p ) p-1 + (e Vij/p + e Vij+1/p ) p-1 ] (2.2) The OGEV model matches the sequential nature of time where the correlation between ordered points is proportional to their proximity. Small (1982) provided an early definition of the theory of the ordered generalized extreme value model and studied the effect of work arrival time flexibility, occupation, and mode choice on departure time. Using San Francisco auto commuters data, the study found that carpoolers are likely to arrive early to work, that professional workers are likely to select later arrival times, and that workers with flexible work schedules tend to travel to work later in the morning. These findings can be compared to the results of this work. A special case of the OGEV model is the dogit ordered generalized extreme value model (DOGEV). It combines an OGEV model with a dogit model, capable of capturing constraints in a choice set such as work start time captivity. Presented by Gaudry and Dagenais (1977), the dogit model can represent the choice between both independent and related alternatives (Equation 2.3). The dogit model includes a parameter that varies the influence of all attributes on each alternative choice. Fry et al. (2005) combined the dogit model with the ordered generalized extreme value model. The resulting DOGEV framework represents the choice between a set of ordered alternatives, where a preference for particular responses exists (Equation 2.4). The

31 15 combination of ordered correlation from the OGEV model and choice preference from the dogit model represents the nature of departure time choice in reality the start time of trips is chosen from preferred intervals subject to limitations. P DOGIT ij = (e Vij + θ j J k=1e Vik )/(1+ J k=1θ k ) J k=1e Vik ) (2.3) P DOGEV ij = θ j /(1+ M k=1θ k ) + [(1/(1+ M k=1θ k )) x P OGEV ij ] (2.4) Chu (2009) used the DOGEV model to represent departure time choice for morning peak work trips in the New York City metropolitan area. The study modelled the influence of socioeconomic factors, employment characteristics, trip specific attributes, land use and location of the home and workplace on the discrete choice between six work departure time intervals (half hour intervals between 6am and 9am). The results of this study indicate that workers are more likely to be constrained (by their work start time) to depart during time intervals in the middle of the peak period as compared to time intervals at the earliest and latest parts of the peak period. Specific findings of the model state that those likely to depart for work later in the peak period include people living alone, those with fewer children, higher-income workers, younger people, those with relatively shorter work days, people with professional/technical careers, part-time employees, transit users, people living relatively close to the city, and those not working downtown. In addition, expected travel times as they vary throughout the peak period were a significant motivating factor; people avoided time intervals where the longest driving time occurred and the effect was most pronounced earlier in the morning. However, trip cost was not found to motivate departure time choice, likely due to the fact that road tolls in New York are constant during the peak period. Some general concepts of departure time modelling raised by previous research include schedule delay the deviation between the desired and actual arrival time and its effect on departure time choice. Hendrickson and Kocur (1981) modelled schedule delay using user equilibrium concepts and deterministic queuing theory. Abkowitz (1981) has shown that work schedule flexibility, mode, occupation, income, age, transportation level of service, the uncertainty in work arrival time and consequences of various work arrival times influence departure time choice. Furthermore, the travel mode selected can influence departure time decisions for example transit users departure times are often subject to the level of service provided. Abkowitz (1981) states that a flexible work schedule induces people to select departure times

32 16 that will allow them to reach work on time or later, auto travellers leave in order to arrive exactly on time, transit users are unlikely to leave earlier than needed due to unfavourable off-peak service in the early morning, those in professional, technical, management, or administration position are unlikely to strive to arrive early, while lower income workers and older workers tend to choose departure times such that they arrive to work slightly early. Similar to this work, the San Francisco study by Abkowitz (1981) focuses on morning work trips, and its findings can be compared to the results of this study. Two important aspects of departure time choice are the concepts of correlation and captivity. Adjacent time intervals share similar characteristics such that an individual who is likely to choose one interval will probably also attach a high utility to choosing the adjacent intervals. The structure of the OGEV model captures this logic. Captivity regards the fact that certain departure time choices are not applicable to an individual because of activity schedule constraints. Some time intervals will not be considered valid for a certain trip if the activity start time is fixed, regardless of their perceived utility. There are multiple ways to represent captivity in departure time choice models. The DOGEV model accounts for the phenomenon of choice captivity by the inclusion of the dogit model in combination with the OGEV model of choice between ordered alternatives. However, a weakness of the OGEV and DOGEV model formulations is that they are computationally intensive when representing a large number of choice alternatives. Also, estimation of the OGEV modelling structure would require use of the constrained maximum likelihood method instead of conventional maximum likelihood estimation. To account for choice correlation and captivity, this study combines a heteroskedastic GEV departure time choice model with the GenL (choice set Generation Logit model) method of choice set generation (Swait, 2001). Using GenL, the choice probabilities are expressed as the probability of a choice set being selected multiplied by the conditional probability of selecting the choice from within the choice set. The probability that a choice set is selected depends on the expected maximum utility of the choice alternatives within the set. Several other studies of departure time choice, using a variety of model formulations, present findings that may be relevant to this work. A study conducted in the Netherlands found that departure time choice is influenced by travel time and cost and that departure time choice is likely to change in response to policies that affect travel time and cost variables (De Jong et al.,

33 ). The study used stated preference information from drivers and rail passengers to estimate an error components logit model. One study on departure time choice used the approach of prospect theory, such that travellers are rewarded when they arrive at work during their preferred time period, and experience a loss otherwise (Jou et al., 2008). It was found that people will adjust their departure time to increase the likelihood of arriving during the desired time interval. A study of commuter trips in Singapore focussed specifically on the influence of work start times and related policies such as staggered working hours on departure time choice (Chin, 1990). Using a multinomial logit model and a nested logit model, it found that work start times, travel times and costs influence departure time choice. Finally, a study with a different goal, but with a related concept is Brey and Walker (2011), a study of airline latent preference. Compared to road travel, air travel temporal demand is more constrained subject to the schedules provided and latent demand is not readily observable. Similarly to other departure time studies, Brey sought to quantify the demand distribution of airline passengers over time Travel Time Reliability Departure time choice is considered to be dependent upon expected travel times and desired arrival times. Studies on the value of reliability for travel decisions such as departure time have generally come to the conclusion that: departure time is the most sensitive choice to changes in generalized cost due to transportation policies, that punctuality is of great importance to travellers, that one s value of reliability is related to schedule considerations, and that transit users are particularly concerned with reliability due to the scheduled nature of transit routes (Bates et al., 2001). Also, it was found that trip duration and start time have a reciprocal causality relationship (Fosgerau and Karlström, 2010). One specific study of travel demand presents a discrete version of Vickrey s (1969) model of traffic congestion (Otsubo and Rapoport, 2008). Vickrey represents departure time as an endogenous decision in travel behaviour. Otsubo and Rapoport find that uncertainty regarding the volume of traffic on the roads leads individuals to select earlier departure times, subject to the fact that commuters seek to maximize their personal utility of travel. Li et al. (2010) also studied the value of travel time reliability and found that reliability is worth more to drivers than an early arrival time.

34 Effect of Traveller Information Some travel behaviour studies consider the effect of traveller information on travel choices. Traveller information can have an effect on departure time choice, and scheduled times can have an effect on route choices. Hickman (1993) considered the effect of real time passenger information on departure time choice as well as route choice using static and dynamic choice analyses with data from Massachusetts. Hickman found that policies that provide real-time passenger information cause route and departure time changes that only result in very small travel time savings for the individual transit user. A related study (Xu, 2010) considered the effect of real time information on route choice using a multinomial logit model estimated with stated preference data from China. It found that the effect of traveller information on route choice decisions varies during different times of day. The finding that traveller information influences travel behaviour is supported by Tsirimpa et al. (2007) which applies travel diary data to estimate a mixed multinomial logit model of departure time and route choice. Specifically, traveller information on route closures provided before or during the trip influences departure time choice because route closures are correlated to travel time changes. Another study (Larsen and Sunde, 2008) on the subject of real-time information found that transit users presented with schedule information at transit stops react in a heterogeneous and stochastic way in terms of adjusting their route choices Combined Mode and Departure Time Choice Models Some studies model both travel mode choice and departure time choice in combination. They involve a variety of model formulations, methods of combining the mode and departure time choice components, and applications. The methods and results of other mode and departure time choice studies can be compared with this study. A study by De Jong et al. (2003) uses a mixed logit formulation to jointly estimate mode and departure time choice using stated preference data. It differs from this study by using stated preference survey data to estimate the model. The stated preference survey asked respondents for their reaction to alternate departure times and modes based on varying attributes such as travel time, cost, and transit service frequency. The results of this study suggest that departure time choice depends on travel time and cost and that policies imposed can be effective in spreading peak period demand. Other findings state that younger, part time and less educated workers are

35 19 less likely to shift their departure time, that people prefer to extend the activity duration rather than to travel longer, and that travelling longer is more favourable than arriving too late or too early for an activity. Rather unfortunately for the transit system, the study found that subject to unfavourable travel times or costs, there will be more transit users switching to the auto mode than drivers switching to transit. Another study that combines models of trip time and mode choice is Bhat (1996), an examination of urban shopping trips. The model structure involves a nested logit model where mode choice represents the higher level with departure time choice below. Structuring the choice this way is consistent with the statement that people are more likely to change their departure time than their mode subject to unfavourable policies. The mode component is represented by a multinomial logit while the departure time choice is based on an OGEV model. This was found to perform better than a combination of multinomial logit and nested logit as a representation of mode and departure time choice. However, the study did not account for the presence of captivity to certain departure time choices. Other studies involving the choice of mode and departure time choice include a study the effect of cordon pricing on morning peak trips in Stockholm. (Kristoffersson, 2011) Using a mesoscopic simulation addressing the cost to the user of changing their departure time, the study found that cordon pricing policies affect route and mode choice, that people are reluctant to deviate from their habitual start time, and that such pricing policies reduce congestion but are not equitable to those who must drive to work and have difficulty affording the charges. Another study examined the effect of traveller information on time route and mode choice using both an ordered logit probability model and a Weibull duration model. (Mannering et al. 1994) A recent publication represented mode choice using a nested logit structure with departure time as a contributing factor. The mode choice is linked to a route assignment algorithm (Zhang et al., 2011). Also, De Jong et al. (2003) examined mode, route, day, and departure time choice for intercity travel in Denmark. Hendrickson and Plank (1984) looked at the flexibility of departure times and modes for work trips using a logit model to simultaneously estimate mode and departure time. They found that departure time decisions are much more elastic that mode decisions. A study of the choice between the free bridge and the toll tunnel in Copenhagen used a nested logit route and departure time choice model to examine route and time switching (Havnetunnelgruppen, 1999). A study of Tokyo morning commuters mode and departure time

36 20 choices found that accounting for preference heterogeneity between individuals improves model performance and that recognizing that alternate choices are correlated also improves the model (Bajwa et al., 2006). The study was based on a mixed nested logit model using stated preference survey data. A local study takes into account features of both mode and time scheduling decisions (Habib, 2012, Day et al. 2009). Using a joint discrete-continuous-continuous model to represent mode choice, work start time and work duration, the study forecasts work schedules for users of different travel modes. Similarly, Wilson (1989) presents a discrete model of joint mode and work start time relating to the issue of departure time choice. The findings suggest that individuals find it approximately equally undesirable to extend their travel time by a certain amount of time or to move their work start time away from the peak by the same amount. This has implications for departure time choice; specifically, suggesting that people have a strong aversion to rescheduling their work start time very likely due to organizational constraints Transportation Demand Management Policy Literature There has been substantial research conducted on the predicted effects of transportation demand management policies on travel demand. This summary specifically considers works that sought to predict the effect of various policies on mode and departure time decisions. A study of the effect of road tolls on the time, mode and route choices of Stockholm drivers found that departure time adjustments were overestimated by the simulation model because it used stated preference data (Kristoffersson, 2011). A comparison of graduated tolls versus flat tolls indicates that gradual step tolls provide the higher social benefit by tolling proportionally to the severity of one s contribution to congestion, but that step tolls and flat tolls yield similar effects in terms of reshaping demand. A publication by the Transportation Research Board on the subject of transit fare pricing strategies states that the effect of a fare increase for higher order transit on mode switching behaviour is lower than the effect of a bus fare increase (TRB,2004). Rapid transit fare elasticities are found to be approximately half of bus mode share elasticities with respect to fare changes. The study compares transit fare elasticities with respect to mode choice during peak and off-peak hours. The goal of peak transit pricing is said to include charging proportionally to the

37 21 load placed on the system and shifting demand out of the crowded peak periods. Prior studies on Denver, Louisville, Lowell, and Trenton all indicate a shift in demand from peak to off-peak times in response to an introduced or increased fare differential between peak and off-peak times. This study also compiled findings from studies on free transit policies. While no studies examined introducing free transit during off-peak hours only, the general finding is that free transit policies limited to a route or central area can successfully increase ridership. A compilation study states that non-work trips are more sensitive to fares than work trips, consistent with the fact that mandatory travel is inflexible (Litman, 2004). Transit fare elasticities are generally found to be times higher during off-peak times as compared to peak hours. Specifically peak transit fare elasticities are said to be between and -0.3 while off peak elasticities range from -0.3 to A related study also finds that peak transit fare elasticities can range from to and are approximately half of off-peak elasticities (-0.11 to -0.84) (Gillen, 1994). VIVA transit, a bus system operating in York Region (within the GTHA) recently examined the possibility of introducing a difference between peak and off-peak fares with the goal of shifting demand and increasing ridership (VIVA, 2011). The study considered applying a fare reduction that would take effect during off-peak hours only. It was found that such a fare reduction would incur large revenue losses. In order to balance the reduction in revenue due to fare discounts, large increases in ridership would be required. Specifically potential off-peak discounts of 25%, 33% and 50% would require a ridership increase of 33%, 49%, or 100% respectively in order to prevent a reduction in system revenue. These large ridership increases were deemed unlikely and it was decided not to introduce an off-peak fare discount strategy Literature Review Summary The literature indicates that the transportation industry recognizes the need for departure time modelling; recent work has tended toward the inclusion of departure time models in travel behaviour analyses. Mode choice modelling practices indicate an awareness of the categorized nature of travel modes indicating that the continued use of nested/tree logit models is justified. Also, it is accepted that mode choice behaviour is related to personal habits and differs between people. Thus, it is desirable to address this property directly using a heteroskedastic approach. Departure time needs to be represented with a discrete, correlated, constrained, and

38 22 computationally efficient modelling framework. Many existing model structures applied to study departure time choice exhibit some but not all of these characteristics. Finally, the literature review reveals that it is beneficial to position travel demand behaviour research in the context of policy analysis; many previous studies apply advanced modelling techniques to give insight on practical transportation issues.

39 23 Chapter 3 Data Description The data used in this study was collected by the Transportation Tomorrow Survey (TTS), a household based travel demand survey conducted in the Greater Toronto (and Hamilton) Area every five years. (DMG, 2012) The survey provides detailed information on trips made on a typical weekday by all individuals in the selected households. Five percent of households in the GTHA are contacted by telephone and all trips made by residents eleven years of age or older on a specific weekday are recorded. Trends observed in travel behaviour from the 2001 and 2006 TTS datasets indicate a need for innovative transportation demand management policy investigations. The dataset was enhanced to suit the needs of this modelling study and policy investigation. To motivate the structure and discretization of the departure time model, observed temporal demand distributions were analyzed Data Trends The datasets from 2001 and 2006 reveal informative trends. Overall, there have been changes with regards to travel demand and level of service attributes. Note that all transit trips in the 2001 dataset are subway or GO trips while the 2006 dataset includes surface transit trips. Therefore, for this analysis, surface transit trips from 2006 were excluded. There has been discussion in the transportation community on the subject of spreading peak periods. The theory is that with growing congestion, people will elect to travel just outside the peak hours thereby inducing a wider peak period. Also, higher demands on the transportation system and changing lifestyles and travel patterns have an impact on the shape of the distribution of trips throughout the day. The datasets show that in 2006, the afternoon peak period among GO transit trips was more intense than in 2001 but was not noticeably longer while the morning peak was unchanged (Figure 3.1). This is likely due to inflexible work start times which influence morning departure time choices for many commuters. During the midday period, the 2006 data shows more travel than 2001 as well as an earlier start to the afternoon peak period. In 2006, the earlier part of the afternoon peak period shows more travel than in 2001 but travel later in the evening appears reduced. These patterns can be attributed to population growth and lifestyle

40 24 changes such as flexible work schedules that may encourage non-work travel during the work day. Among subway trips, some peak spreading effects are also visible (Figure 3.2). The absolute number of subway trips reported is higher in 2006 than in 2001 but the peak hour demand appears to have reduced and shifted into off-peak hours. The difference between travel patterns observed among GO transit and subway trips can be explained by schedule flexibility. Subway users can adjust their departure time by small increments to avoid peak demand while GO transit users are limited by fixed, infrequent service. Figure 3.1 GO Transit Trips by Hour

41 25 Figure 3.2 Subway Trips by Hour In addition to changes in departure time distributions, the data also reveals trends regarding mode choice. The number of auto trips shows a decreasing trend, while the number of trips using non-auto modes is remaining constant (Figure 3.3). This is an encouraging finding with regards to improving the ridership and efficiency of the transit system in this region. Figure 3.3 Trips by Mode: Auto vs. Non-Auto

42 26 Specifically, there has been a measurable increase in subway and GO transit usage (Figure 3.4) (Table 3.1). The number of auto driver and auto passenger trips decreased between 2001 and 2006 while the number of subway and GO trips increased (Note: Figure 3.4 and Table 3.1 include 2006 surface transit trips). Here, travel modes are defined in terms of seven categories: auto driver (AD), auto passenger (AP), transit walk access (TWA), subway auto access (SAA), GO auto access (GAA), GO transit access (GTA), and non-motorized travel (NMT). The transit walk access mode consists of all transit trips that do not fall into the categories of subway auto access, GO auto access and GO transit access. This includes surface transit trips, subway walk access, subway transit access trips, and GO walk access trips because the attributes of these trip categories are deemed to be similar to each other but distinct from the SAA, GAA and GTA categories. Bicycle and walking trips comprise the non-motorized category while motorcycle, school bus, and taxi trips were excluded from further analysis. Figure 3.4 Trips by Mode

43 27 Table 3.1 Trips by Mode AD AP TWA SAA GAA GTA NMT taxi Schoolbus Other In 2006, fewer trips originated and ended in the City of Toronto and the downtown area while there was a slight increase in travel to and from some suburban regions (Figure 3.5 and 3.6). This trend is correlated to increased suburbanization, caused by ongoing construction of low-density residential units on the edges of the urban region. Specifically, York and Halton regions are shown to have experienced a relative increase in travel demand. Figure 3.5 Trips by Trip Origin Region Figure 3.6 Trips by Trip Destination Region

44 28 The data also provides insight into trends among level of service attributes. Auto and parking costs as well as transit fares show an increase between 2001 and 2006 (Figure 3.7, 3.8 and 3.9). Unfortunately, in-vehicle travel times and wait times for public transit also show an increasing trend (Figure 3.10 and 3.11). While this is discouraging for the prospects of good public transit in this city, worsening transit service does not appear to have had a negative effect on transit mode share, at least between 2001 and Figure 3.7 Trips by Parking Cost Figure 3.8 Trips by Auto Cost

45 29 Figure 3.9 Trips by Total Transit Fare Figure 3.10 Trips by Total Transit In-vehicle Travel Time

46 30 Figure 3.11 Trips by Total Transit Wait Time Finally, demographic information as it relates to travel can be found in the datasets. Plots of trips by age and age group show an increase in travel by teens and those over forty (Figure 3.12 and 3.13). This is consistent with an aging population. There was a decrease in travel by holders of driver s licences and an increase in travel by transit pass owners (Figure 3.14). This is consistent with the observed trend of increasing transit usage in the region. Fewer trips in 2006 were attributed to full-time workers than in 2001 while more were attributed to unemployed travellers (Figure 3.15). There has been an increase in travel by sales and office workers but a reduction in professional and manufacturing worker travel (Figure 3.16). Also, there was a reduction in travel by people who have free parking at work, perhaps indicative of a reduction in the availability of free parking (Figure 3.17). Travel patterns by employment region and school region are consistent with observed suburbanization trends (Figure 3.18 and 3.19).

47 31 Figure 3.12 Trips by Age Figure 3.13 Trips by Age Category

48 32 Figure 3.14 Trips by Mobility Tool Ownership Figure 3.15 Trips by Employment Status

49 33 Figure 3.16 Trips by Occupation Type Figure 3.17 Trips by Travellers with Free Parking at Work

50 34 Figure 3.18 Trips by Employment Region Figure 3.19 Trips by School Region Patterns visible in the data indicate overall trends toward suburbanization, peak spreading, worsening levels of service as well as a promising shift toward higher transit use. There is evidence to suggest a pattern of peak spreading and increasing demand on the transportation system throughout the day. These findings indicate the need for studies to be done on the subject of temporal transportation demand management strategies. Studying the interaction of departure time and mode choice can help to improve the utilization of the transit

51 35 system. The data shows that demand during the peak periods is becoming more intense for some modes, and that travel during off-peak times such as the middle of the day is increasing (perhaps due to increased leisure travel). Managing the temporal demand distribution of the transportation system can make better use of existing capacity and allow for higher ridership. The public transit experience appears to be worsening due to higher fares, waits and travel times; imposing a policy that may induce some demand to move out of the peak periods is a way to relieve some of the pressure on the system. A fair pricing policy that encourages more efficient use of the transit system could reduce crowding and may allow for faster operation Variables With the motivation for the model defined, it was necessary to prepare useful datasets to estimate the model. To prepare the survey data for analysis and modelling, all trips reported in TTS needed to be linked to the corresponding level of service attributes, not reported by survey respondents. Also, supplementary attributes were linked to the trips and the data was interpreted into usable variables. Route assignment software was used to find the travel times and costs likely experienced by survey trips, thus avoiding reporting biases that would have been incurred if individuals were directly asked about observed levels of service. For each hour of the day, the number of auto trips made between each origin-destination pair were used as input for the auto assignment function of the route assignment software, EMME (INRO, 2011). This process yielded expected auto travel time and cost information for each origin-destination pair during each hour of the day. Similarly, the transit trips made by respondents of the TTS survey were used as input for a transit assignment procedure that provided in-vehicle travel time, fare, walk time, and wait time for transit trips between each origin-destination pair. Unfortunately, the transit assignment only yields results for the peak hour because transit agencies provided detailed characteristics for only the peak hour as inputs into the route assignment. To expand the peak hour transit level of service attributes for all twenty-four hours of the day, the following principles are defined: wait times vary proportionally to the variation in headways over time, subway travel times do not vary throughout the day due to the designated right-ofway, surface transit zone-to-zone travel times vary similarly to auto travel times, and walk times and fares are known to be constant through the day. Specifically, off-peak subway headways are

52 36 reported to be 4-5 minutes in Toronto, compared to 2-3 minutes at peak times. Off-peak wait times for surface transit are found by applying a different scaling factor to the peak hour wait times for each hour of the day. The scaling factor for each hour is found by taking the average deviation between current and peak headways over twenty-five TTC bus and streetcar routes (Appendix A). For intra-zonal travel, auto travel times and costs are based on the size of the zone. Due to the relatively small distances of intra-zonal trips, it was assumed that auto travel time and cost do not vary throughout the day. Parking costs by destination zone were also assumed to be a flat rate regardless of time of day or duration of stay. The level of service attributes for each hour (auto travel time, cost and parking cost, and transit fare, wait time, walk time, travel time, and access time/cost) were linked to trips made in the corresponding hour. Level of service information was computed rather than collected to avoid respondent error or omission. Attributes that depend only on trip start time, origin and destination zone (auto travel time, auto cost, and parking cost) were applied to all trips. Intrazonal driving times and costs were included based on average distances within zones. Parking costs for each trip depend only on the destination zone, while driving times and costs were linked to the observed trips based on time, origin and destination. For trips conducted by transit, the auto trip attributes represent the travel time and cost that the trip would have hypothetically experienced if it had been conducted by an auto mode from the same origin and destination within the same hour of the day. Next, transit-specific attributes were linked to the corresponding transit trips. For GO transit trips, the estimated fare, travel time, and wait time were assigned using schedule data based on access and egress zones. For subway trips, the travel time, walk time and fare were taken from the peak period transit assignment data. Subway headways are defined such that off-peak trips experience wait times that are approximately twice as long as waits during peak hours (Figure 3.20). Subway trip data was linked based on trip access and egress zones.

53 37 Figure 3.20 Subway Headway Scaling Factors For surface transit trips, wait times and travel times vary throughout the day depending on auto traffic. Walk times and fares are constant through the day and were applied to surface trips based on access and egress zones. Surface transit travel times vary by the hour and were calculated by applying hourly factors to the peak hour transit assignment results. These travel time scaling factors were obtained by finding the deviation between peak hour auto travel time and the auto travel times experienced in each other hour as found in the auto assignment process. The difference in driving time between an off-peak and peak hour trip depends on the trip s origin and destination zones. Thus the estimated surface transit travel time for each hour and each O-D pair was found by multiplying the peak hour transit travel time by the auto travel time deviation factor for the corresponding hour, origin, and destination. Twenty-four hour transit wait times for surface routes were found by multiplying the peak hour wait time by a scaling factor computed using headway variation patterns in the schedules of TTC surface routes (Appendix A). Travel times and wait times were assigned to surface trips based on their start time and access/egress zones. After the main level of service attributes experienced by each transit trip were assigned, trips were sorted by their access and egress modes in order to apply the relevant access/egress level of service attributes. For transit trips that were accessed or followed by an auto trip, the relevant parking, auto travel time, and auto cost attributes were assigned based on the hour and the origin

54 38 and access zones or the egress and destination zones respectively. For transit trips served by other transit trips or by walking, the relevant walk time and (if applicable) transit fare, in-vehicle travel time, and wait time were assigned using the expanded 24-hour transit assignment data and connected to the trips by matching zones and start times. Transit trips serving other transit trips were assumed to be surface transit and the appropriate 24-hour surface transit level of service values were used. Finally, the level of service attributes of the access/egress trips were added to service attributes experienced during the main transit trip to provide seven transit attributes for each trip: total fare, total wait, total in-vehicle travel time, total walk time, total auto access parking cost, total auto access drive time, and total auto access cost. In order to find the trip attributes that would have been experienced by non-transit trips if they had chosen to use transit instead, the maximum of each attribute within each O-D pair and start time was assigned to trips conducted in the matching location and time. This matching could only be conducted for non-transit trips whose O-D pair had been served by an existing transit trip. In this way, all trips collected in the TTS survey were linked with the observed auto or transit attributes as well as the hypothetical auto and transit attributes that the trip might have experienced if it had been conducted with a different mode. After joining the level of service attributes to the trip, household, and personal variables as provided in the TTS data, other attributes were added and the data was prepared for model estimation. Information about home zone population density and median income was attached to each trip based on the individual s home location. Trip duration and work duration were calculated using the TTS data. Other supplementary calculations were made: the logarithm of an individual s age, the total auto cost, and the transit fare per kilometre. Finally, the data was prepared for modelling by converting all attributes to a numerical value, adding binary category variables where necessary, and labelling the travel mode as: auto driver (AD), auto passenger (AP), transit walk access (TWA), subway auto access (SAA), GO auto access (GAA), GO transit access (GTA), or non-motorized travel (NMT). See Appendix B for a full list of variables used in the modelling process.

55 Kernel Densities of Temporal Demand Distribution For the purposes of temporal distribution analysis, the dataset was divided into four travel mode categories: Auto Driver, Auto Passenger, Non-Motorized Travel, and Transit and five job types: general office/clerical, manufacturing/construction/trades, professional/management/technical, retail sales/service and unemployed. The distribution of trips across these categories is shown in Table 3.2 and Figures 3.21 and For all employed groups, auto modes are the dominant travel choice. Transit is a viable second choice for individuals working in general office, professional, or retail sales positions; manufacturing/construction workers make relatively few transit trips. Data from the 2006 TTS survey is used for this analysis and for subsequent model estimation. Table 3.2 Number of Trips made by Mode and Occupation #Trips AD AP NMT TRANS General office/clerical Manufacturing/construction/trades Professional/Management/Technical Retail Sales and Service Unemployed

56 40 Figure 3.21 Trips by Mode and Occupation Figure 3.22 Trips by Occupation and Mode Kernel density plots were used to investigate the appropriate aggregation level for the departure time choice decision. R statistical software was used to create kernel density plots in order to visualize the departure time choice distribution within each mode and to find the degree of granularity required to represent the departure time choices (R Project, 2011). Kernel density plots present a smooth distribution resembling a histogram; accordingly the interval width that is recommended to best represent the variability of the distribution is computed. Trends indicate that the work trips of general office workers and professionals tend to be contained within the

57 41 conventional morning peak period while manufacturing/construction workers and retail workers are more likely to travel to work outside of the morning peak. The trips of unemployed travellers, often students, are typically conducted using the auto passenger, non-motorized, or transit travel modes and are clustered narrowly around school start times in the morning. The plots below show the distribution of travel demand through time for each mode and occupation type; the x-axis represents time in minutes after 4 a.m., the start of the day as defined in TTS. Figure 3.23 Kernel Density Plot 2006 Auto Driver, General Office/Clerical Figure 3.24 Kernel Density Plot 2006 Auto Driver, Manufacturing/Construction

58 42 Figure 3.25 Kernel Density Plot 2006 Auto Driver, Professional Figure 3.26 Kernel Density Plot 2006 Auto Driver, Retail Sales

59 43 Figure 3.27 Kernel Density Plot 2006 Auto Driver, Unemployed For trips made by the Auto Driver mode, the distribution in time throughout the day varies between members of different occupation types. General office and professional workers departure times for work trips occur predominantly during the morning peak period (Figure 3.23 and 3.25). Sales workers who drive to work also depart largely within the morning peak but they are also somewhat likely to start work in the afternoon (Figure 3.26). Manufacturing work is often schedules in shifts that begin at various times in the day (Figure 3.24). This work schedule pattern is represented in the departure time distribution by a large morning peak in addition to two smaller peaks later in the day, corresponding with shift work start times. In the dataset, unemployed individuals making work or school trips are likely to be students or drivers facilitating a passenger trip. Trips made by unemployed drivers are not constrained by work schedules and are distributed more widely throughout the day than trips by workers (Figure 3.27). The reccomended bandwidths/interval widths for discretizing auto driver work trips are smaller than 15 minutes due to the large number of auto driver trips. The bandwidths for office and professional worker datasets are the smallest (less than 10 minutes) due to the narrow morning peak observed in the departure time distribution for those workers.

60 44 Figure 3.28 Kernel Density Plot 2006 Auto Passenger, General Office/Clerical Figure 3.29 Kernel Density Plot 2006 Auto Passenger, Manufacturing/Construction

61 45 Figure 3.30 Kernel Density Plot 2006 Auto Passenger, Professional Figure 3.31 Kernel Density Plot 2006 Auto Passenger, Retail Sales

62 46 Figure 3.32 Kernel Density Plot 2006 Auto Passenger, Unemployed Trips made by the Auto Passenger mode demonstrate similar patterns to trips in the Auto Driver dataset. Professional and office workers have the narrowest departure time distributions, focussed closely on the morning peak (Figure 3.28 and 3.30). As a result, bandwidths of the departure time distribution for these worker groups are the narrowest, in order to capture variations within the narrow morning peak period. Sales and manufacturing jobs follow work schedules that are likely to demand start time outside of the morning peak and the departure time distribution plots represent this pattern (Figure 3.29 and 3.31). Contrary to the auto driver dataset, work or school trips made by unemployed individuals using the auto passenger mode are largely concentrated in the morning peak (Figure 3.32). This is because unemployed passengers making work/school trips are likely to be students who are often driven to school by a relative. The kernel density plot for unemployed passengers uses a very narrow bandwidth (under 5 minutes) to capture variation within the narrow peak representing school start times.

63 47 Figure 3.33 Kernel Density Plot 2006 Non-Motorized, General Office/Clerical Figure 3.34 Kernel Density Plot 2006 Non-Motorized, Manufacturing/Construction

64 48 Figure 3.35 Kernel Density Plot 2006 Non-Motorized, Professional Figure 3.36 Kernel Density Plot 2006 Non-Motorized, Retail Sales

65 49 Figure 3.37 Kernel Density Plot 2006 Non-Motorized, Unemployed Despite the relatively small number of non-motorized work/school trips, the departure time distributions of each occupation type follow the patterns seen among trips using other modes. Office and professional workers making non-motorized work trips depart within the morning peak as do their colleagues using other travel modes (Figure 3.33 and 3.35). Interestingly, with only 379 non-motorized trips reported by manufacturing workers, the departure time distribution is seen to follow the pattern of shift schedules with three observable peak periods (Figure 3.34). Again, most sales workers depart in the morning with some sales work trips occuring later in the day (Figure 3.36). Among unemployed individuals (likely students), non-motorized travel is the dominant choice for work/school trips; departure times are distributed very narrowly at the morning school start time because they are likely to be short trips (Figure 3.37).

66 50 Figure 3.38 Kernel Density Plot 2006 Transit, General Office/Clerical Figure 3.39 Kernel Density Plot 2006 Transit, Manufacturing/Construction

67 51 Figure 3.40 Kernel Density Plot 2006 Transit, Professional Figure 3.41 Kernel Density Plot 2006 Transit, Retail Sales

68 52 Figure 3.42 Kernel Density Plot 2006 Transit, Unemployed For transit, the departure time distributions of office, professional, manufacturing, and sales workers repeat the patterns visible among users of other modes (Figure ). For unemployed individuals making work/school trips, public transit is the third mode of choice after non-motorized travel and auto passenger. These trips occur largely during the morning peak but also extend into afternoon, possibly because unemployed transit users are less likely to be school-age children and may be making occasional work trips or attending classes (Figure 3.42). Table 3.3 Kernel Density Bandwidths Recommended Time Interval (min) AD AP NMT TRANS General office/clerical Manufacturing/construction/trades Professional/Management/Technical Retail Sales and Service Unemployed The kernel density plots inform the decision regarding the size of discrete time interval to use as a representation of the departure time choice decision (Table 3.3). To discretize the departure time distributions, the kernel density plots use narrow bandwidths (often minutes). Fifteen minute intervals are commonly used for simulation but may be too computational demanding. Half-hour or one hour time intervals were considered as options for the model instead. The halfhour or one hour intervals may be able to represent the variability in the departure time choice distribution without the need for finer granularity.

69 53 Chapter 4 Departure Time Model The departure time model used in this study applies the Heteroskedastic Generalized Extreme Value (Het-GEV) modelling framework in combination with a Generalized Logit (GenL) captivity component. The Het-GEV model represents the correlation between adjacent choice alternatives while the GenL form represents the captivity of decision makers to specific choices due to schedule constraints Departure Time Choice Model Formulation The choice framework is represented by Figure 4.1. Trips to work contribute most heavily to the disproportionate burden on the transportation system over time. The goal of policies that impose higher peak travel costs is often to shift some peak hour work trips out of the most heavily congested time intervals. As a result, the model is estimated using all trips from home to work or school made by employed individuals, distributed throughout the day in accordance with various work schedules. The time intervals in the choice set span the full 24 hours of the day with shorter intervals used during the morning peak period when the majority of home-based work trips occur, and with wider time intervals through the afternoon and night when there are comparatively few home-based work trips. The choice framework represents a decision process where an individual may select a time interval directly, or by comparing it to adjacent time intervals. This is representative of decision making behaviour in reality where an individual may choose their departure time out of all the possible times of day or they may narrow down the selection to a certain range and select a departure time within that portion of the day.

70 54 Figure 4.1: Departure Time Choice Framework The model captures elements of generic, systematic, and scale heterogeneity. The generic utility of all time intervals is explained by a weighted sum of relevant variables. The systematic utility of each different time interval is also a weighted sum of explanatory variables, though the weight/parameter values and even the set of significant variables may differ between time intervals. Scale heterogeneity refers to the component of variation between choice alternatives which is explained by differences between individual decision makers. In this case, it is expected that an individual s work duration is likely to affect their subjective evaluation of different potential departure time intervals for their work trip. Accordingly, a scale parameter associated with work duration is included in the model formulation. The value of the scale parameter varies between different time intervals and it may not be significant to some intervals, indicating that the influence of work duration exerts a different influence on the subjective utility of different departure times and that it may not be relevant to the utility of certain intervals Theoretical Formulation The departure time model is based on principles of Random Utility Maximization (RUM) where the utility of a discrete choice alternative is represented by the weighted sum of variables relevant to the choice as well a random component. U = V + ε (4.1)

71 55 Where U is the utility of a discrete choice, V is the systematic utility, and ε represents the random utility component. The generalized extreme value (GEV) theorem (McFadden, 1978) forms the basis of the Generalized Logit (GenL), a choice set generation model presented by Swait (2001). Alternatives are presented in a network representation where there are multiple possible choice paths leading to any alternative. In this case, a decision maker may select a time interval directly, or they may narrow down the choice to two adjacent intervals before selecting a departure time. Thus the probability of choosing an alternative is denoted by sum of the conditional probabilities of arriving at that choice by means of any of the choice paths leading to it weighted by the likelihood of that path. In this departure time model, the systematic utility, V of a certain trip considering a certain time interval (i) is a weighted sum of explanatory variables (x) where the parameters values (B) are found by estimating the model. The systematic utility of the first time interval (before 6:30) is set to 0 for all trips as a reference. V i = Bx for all trips, note B and x selections vary between time intervals (4.2) The root scale (MuR) for all trips and applying equally to each of the time intervals is defined as the exponent of a weighted sum of relevant explanatory variables. This is a measure of the generic utility of any time interval in terms of universally relevant variables. MuR = exp Bx for all trips, for all time intervals (different variables than V) (4.3) Every pair of adjacent time intervals is grouped into a cluster to represent the trade-offs that individuals make between adjacent departure time interval choices. The correlation among clusters (Mu) for each pair (j) of adjacent time interval choices is defined in terms of the root scale (MuR) and any scale parameters. It is expressed as the root scale MuR added to the exponent of the weighted work duration variable value (Swait, 2001). For time intervals where the work duration is not shown to influence choice heterogeneity, the cluster correlation Mu is equal to the root scale MuR. Mu represents generic utility combined with scale heterogeneity for each pair of intervals. Mu j = MuR + exp(b*work duration) where B is an unknown parameter value (4.4)

72 56 The utility of each of the time intervals separately is defined as a product of Mu and V in order to combine generic, systematic, scale components. Then, the inclusive value (IV) of the clusters is a representation of the combined utility of a pair of adjacent alternatives. It is defined as: IV j =ln(exp(mu j + V j )+exp(mu j + V j+1 ))/Mu j (4.5) for j ε 1 to (N-2) where N is the number of time intervals and is defined as: IV j =ln(exp(mu j + V j )+exp(mu j + V j+1 ))/Mu j-1 for j = N-1 (4.6) In this way, the two utilities are combined such that higher interval utilities lead to a higher combined cluster utility. The combined cluster utility will be more similar to the larger of the two interval utilities than the smaller. This states that a cluster containing a highly desirable interval will be at least as desirable as that individual interval. Additionally, this formulation enforces that two adjacent time intervals found to have a low correlation (small Mu) while both being desirable (high Vs) will combine to result in a very desirable cluster. In fact, with a lower correlation between intervals, there is an exponentially higher added benefit gained from combining two desirable but less correlated intervals into a cluster. Next, the utility of each cluster grouping is compared to the utility of all interval pairings and all individual time intervals. Q values for clusters 1-8 represent the probability that a certain pair of intervals (j) will be selected for a trip over all other pairs and all individual intervals (i). Qcluster j =exp(mur x IV j )/( 8 j=1 exp(murxiv j )+ 9 i=1 exp(murxv i )) (4.7) Similarly, the utility of all nine individual time intervals is compared to the utility of all intervals and all pairs of intervals. This is represented by Q values labelled 9 through 17. It represents the probability that a certain time interval (i) will be selected over all other intervals and all pairs of intervals (j). Qindividual i =exp(mur x V i )/( 8 j=1 exp(murxiv j )+ 9 i=1 exp(murxv i )) (4.8) Finally, the probability that an individual will choose to conduct any trip during each of the time intervals of the day is defined as the weighted sum of the probabilities of: choosing this time

73 57 interval among all nine intervals, choosing this time interval over the one preceding it, and choosing this time interval over the one adjacent and after it. Specifically, the probability of selecting the time interval without comparing it to adjacent intervals is represented by the appropriate Q value. The probability of selecting the time interval over an adjacent interval is found by comparing the exponents of the total utilities (systematic and generic with scale parameter) of both intervals. The conditional probability of choosing the given interval within a cluster of two intervals is then multiplied by the probability of having chosen the cluster containing that pair of intervals. P i =(exp(mu i-1 x V i )./(exp(mu i-1 x V i-1 )+ exp(mu i-1 x V i ))xqcluster i-1 )+(exp(mu i x V i )./(exp(mu i +V i )+exp(mu i + V i+1 ))xqcluster i )+Qindividual i (4.9) This model formulation captures the decision behaviour where individuals compare potential departure time intervals to adjacent and correlated intervals when scheduling their work trips. In this formulation, the utility of each time interval is affected by explanatory variables that are constant throughout the day (generic variables such age and trip destination), variables whose effects vary throughout the day (level of service attributes defining the systematic utility), and scale parameters which explain additional choice heterogeneity (in this case, work duration can explain interpersonal scheduling variations) Empirical Models of Departure Time Choice Separate departure time choice models are estimated for three travel mode categories using GAUSS software (APTECH, 2011): auto (including auto driver and auto passenger trips), public transit (including subway, GO transit and other transit trips), and non-motorized travel. Different models were estimated for each mode because the trip attributes affecting departure time choice behaviour are believed to vary between mode categories. Moreover, these three mode categories were chosen because departure time choice behaviour does not appear to differ widely across sub-modes within the categories. Specifically, only trips between home and work/school made by employed individuals were used to estimate the departure time choice models. The models were limited to home-based work trips in order to target the policy analysis goal of this work. Transportation policies are often targeted at mitigating congestion and crowding among work trips. Thus, departure time choice models that focus on commuters behaviour are an effective

74 58 tool to evaluate such policies. The departure time choice is represented by nine discrete time intervals spanning 24 hours of the day. There are smaller choice intervals during the morning peak period and larger intervals spanning the remainder of the day. Specifically, the choices for departure time are: 4:00-6:30, 6:30-7:00, 7:00-7:30, 7:30-8:00, 8:00-8:30, 8:30-9:00, 9:00-9:30, 9:30-10:00, and after 10:00. These intervals were chosen because they provide sufficient granularity during the period of interest; 30 minute intervals represent the departure time distribution. For each travel mode, the departure time choice model involves alternative specific variables, generic variables, and scale parameters relative to the work duration attribute. There are demonstrated differences in departure time distributions between different employment types. Therefore employment type categories (office/clerical, manufacturing/trades, and professional) represent alternative specific variables in all three departure time choice models. Work duration is also seen to have an important influence on work trip departure time choice behaviour so it represents an alternative specific variable for each mode s departure time choice model. Each model also includes demographic generic variables as well as level of service attributes that are specific to the travel mode used. The model estimation process involved testing a variety of model specifications to find the combination of variables that explains departure time choice behaviour (Appendix C). The variables that proved to have an influence on departure time choice were retained in the model. The final model specifications presented here show the effect of all explanatory variables on departure time choice behaviour Departure Time Choice Model for Non-Motorized Travel For non-motorized travel, the variables of work duration, trip distance, job type, age, and fulltime worker status were found to affect work trip departure time choice behaviour. In this case, trip distance in kilometres represents the relevant level of service attribute, and the relative desirability of a particular trip. The departure time choice model for non-motorized travel was estimated using 5888 trips, 6 alternative specific variables, 5 generic variables, and 2 scale parameters; the mean log-likelihood was The resulting parameter estimates reveal the following patterns (Table 4.1). (Note that parameters for the 1 st time choice alternative before 6:30 are all set at 0) (Cells highlighted green represent parameter estimates that are statistically significant subject to a 95% confidence interval)

75 59 Table 4.1 Non-Motorized Departure Time Model Results Variable Time Estimates t statistics Alternative specific constant 6:30-6: Alternative specific constant 7:00-7: Alternative specific constant 7:30-7: Alternative specific constant 8:00-8: Alternative specific constant 8:30-8: Alternative specific constant 9:00-9: Alternative specific constant 9:30-9: Alternative specific constant 10 or after Work duration 6:30-6: Work duration 7:00-7: Work duration 7:30-7: Work duration 8:00-8: Work duration 8:30-8: Work duration 9:00-9: Work duration 9:30-9: Work duration 10 or after Trip distance (km) 6:30-6: Trip distance (km) 7:00-7: Trip distance (km) 7:30-7: Trip distance (km) 8:00-8: Trip distance (km) 8:30-8: Trip distance (km) 9:00-9: Trip distance (km) 9:30-9: Trip distance (km) 10 or after Office/clerical work 6:30-6: Office/clerical work 7:00-7: Office/clerical work 7:30-7: Office/clerical work 8:00-8: Office/clerical work 8:30-8: Office/clerical work 9:00-9: Office/clerical work 9:30-9: Office/clerical work 10 or after Manufacturing work 6:30-6: Manufacturing work 7:00-7: Manufacturing work 7:30-7: Manufacturing work 8:00-8: Manufacturing work 8:30-8: Manufacturing work 9:00-9: Manufacturing work 9:30-9: Manufacturing work 10 or after

76 60 Professional work 6:30-6: Professional work 7:00-7: Professional work 7:30-7: Professional work 8:00-8: Professional work 8:30-8: Professional work 9:00-9: Professional work 9:30-9: Professional work 10 or after Male Generic Age less than 25 Generic Age Generic Age Generic Full-time worker Generic Work Duration interval 7 Scale Work Duration interval 8 Scale The parameter estimates for the constant component of the systematic utility show that nonmotorized travel to work in the morning is highest between 7:30 and 9:00 and that there is also a large number of non-motorized work trips occurring after 10:00 (Figure 4.2). Figure 4.2 Table 4 Non-Motorized Departure Time Parameter Estimate: Constant The alternative specific work duration variable shows reducing parameter estimates later in morning, meaning that those with longer work durations prefer to depart earlier for work (Figure 4.3). This is consistent with the concept that longer work days start earlier in order to allow the worker to leave at a reasonable time. The trip distance measured in kilometres has the largest

77 61 negative effect on the utility of a departure time choice near the end of the conventional morning peak (Figure 4.3). This suggests that those with longer trips to make are more likely to begin them earlier in the peak period, to allow time to get to work. Non-motorized work trips very early in the morning are not affected by trip distance. This observation is very likely due to the small number of early morning non-motorized work trips in the dataset and perhaps to the captive nature of departure time choice among those obligated to travel so early. The negative effect of distance on utility is lessened after the morning peak, reflecting the fact that work days starting later in the day do not share the urgency found among morning work trips to arrive at work around nine. Figure 4.3 Non-Motorized Departure Time Parameter Estimate: Work Duration and Trip Distance The parameter estimates for the alternative specific job type variables reveal that office and professional workers are most likely to travel to work during the middle of the morning peak period (8-9:30 among non-motorized workers), while manufacturing/trades workers demonstrate a very different pattern (Figure 4.4). They are more likely to travel to work before or after peak period, likely because shift work in those industries starts at multiple times throughout the day, compared to the common 9:00 start times for many office jobs.

78 62 Figure 4.4 Non-Motorized Departure Time Parameter Estimate: Occupation Type In the departure time choice model for non-motorized work trips, demographic characteristics were used as generic variables. It was found that gender is not significant, that older workers are averse to the use of non-motorized travel (at any time interval), and that full-time status also applies a disutility to non-motorized travel (Figure 4.5). Figure 4.5 Non-Motorized Departure Time Parameter Estimate: Age, Gender, Full-Time Status

79 63 The work duration scale parameter only enters the model with regards to time intervals later in the day. The negative value of the parameter indicates an added personal reluctance to choose later departure times among those with long work days. Work duration has relatively little effect on departure time choice behaviour early in the morning when there is less urgency to schedule the day efficiently Departure Time Choice Model for Public Transit For work trips using public transit modes, it was found that level of service attributes (in-vehicle travel time, wait time, fare, and auto access cost/time if applicable) affect departure time choice behaviour, as well as certain trip attributes (whether or not the trip origin/destination are downtown ), and personal attributes (work duration, job type, age, full-time status). For the purposes of this study, downtown Toronto is defined as the area bounded by Front Street, Bloor Street, Yonge Street, and Spadina Avenue; the geometry of the borders of selected census tracts define the area. Fares are constant throughout the day and therefore represent a generic variable, while other level of service attributes are alternative specific because they vary throughout the day as defined by the data description. The model was estimated using trips, 8 alternative specific variables, 10 generic variables, and 2 scale parameters; the mean log-likelihood was The results are shown in Table 4.2. (Note that parameters for the 1st time choice alternative before 6:30 are all set at 0) (Cells highlighted Green represent parameter estimates that are statistically significant subject to a 95% confidence interval)) Table 4.2 Public Transit Departure Time Model Results Variable Time Estimates t statistics Alternative specific constant 6:30-6: Alternative specific constant 7:00-7: Alternative specific constant 7:30-7: Alternative specific constant 8:00-8: Alternative specific constant 8:30-8: Alternative specific constant 9:00-9: Alternative specific constant 9:30-9: Alternative specific constant 10 or after In-vehicle travel time 6:30-6: In-vehicle travel time 7:00-7:

80 64 In-vehicle travel time 7:30-7: In-vehicle travel time 8:00-8: In-vehicle travel time 8:30-8: In-vehicle travel time 9:00-9: In-vehicle travel time 9:30-9: In-vehicle travel time 10 or after Wait time 6:30-6: Wait time 7:00-7: Wait time 7:30-7: Wait time 8:00-8: Wait time 8:30-8: Wait time 9:00-9: Wait time 9:30-9: Wait time 10 or after Work duration 6:30-6: Work duration 7:00-7: Work duration 8:30-7: Work duration 8:00-8: Work duration 8:30-8: Work duration 9:00-9: Work duration 9:30-9: Work duration 10 or after Downtown destination 6:30-6: Downtown destination 7:00-7: Downtown destination 7:30-7: Downtown destination 8:00-8: Downtown destination 8:30-8: Downtown destination 9:00-9: Downtown destination 9:30-9: Downtown destination 10 or after Office/clerical work 6:30-6: Office/clerical work 7:00-7: Office/clerical work 7:30-7: Office/clerical work 8:00-8: Office/clerical work 8:30-8: Office/clerical work 9:00-9: Office/clerical work 9:30-9: Office/clerical work 10 or after Manufacturing work 6:30-6: Manufacturing work 7:00-7: Manufacturing work 7:30-7: Manufacturing work 8:00-8:

81 65 Manufacturing work 8:30-8: Manufacturing work 9:00-9: Manufacturing work 9:30-9: Manufacturing work 10 or after Professional work 6:30-6: Professional work 7:00-7: Professional work 7:30-7: Professional work 8:00-8: Professional work 8:30-8: Professional work 9:00-9: Professional work 9:30-9: Professional work 10 or after In-vehicle travel time Generic Fare Generic Age less than 25 Generic Age Generic Age Generic Auto access cost Generic Auto access in-vehicle travel time Generic Downtown origin Generic Downtown destination Generic Full-time worker Generic Work duration interval 7 Scale Work duration interval 8 Scale The variation of the parameter estimates for the constant component of the systematic utility across departure time choices indicates the highest utility of taking transit to work occurs during between 7:30 and 9:30 in morning, when service is at its most frequent (Figure 4.6). Figure 4.6 Public Transit Departure Time Parameter Estimate: Constant

82 66 The behaviour of the alternative specific level of service attributes (in-vehicle travel time and wait time) also reflect the nature of transit service. Rail transit in-vehicle travel times are not vulnerable to road congestion conditions, so the effect of travel time variation on the utility of departure time choices is low. It does however indicate that those with longer commute times are more likely to depart earlier in the morning in order to arrive at work on time. Most parameter estimates for in-vehicle travel time are negative as expected, indicating a disutility, although estimates are positive earlier in the morning, showing that long trips are correlated with early start times (Figure 4.7). Transit wait times vary throughout the day, with the shortest occurring during the morning peak. The parameter estimates of transit wait time show a correlation between longer wait times and departure times outside of the peak hours. All estimates for wait time are negative, suggesting accurately that longer waits induce a negative effect on the utility of a departure time choice (Figure 4.7). This negative effect on utility is largest between 8:30 and 9:00, meaning that transit users who depart for work shortly before the common work start time of 9:00 are especially sensitive to long wait times that may prevent them from arriving on time. Figure 4.7 Public Transit Departure Time Parameter Estimate: In-vehicle Travel Time and Wait Time The effect of work duration on the utility of transit work trips is negative and is the most negative later in the morning peak period (Figure 4.8). This is consistent with the fact that those with longer work days are less likely to leave for work later in the day.

83 67 Figure 4.8 Public Transit Departure Time Parameter Estimate: Work Duration The parameter estimates for the downtown destination variable are all positive, meaning that a downtown destination encourages transit use, and has a positive effect on the utility of all departure time choices. The positive effect on departure time choice utility is highest close to 9 in the morning, because morning peak transit service is especially frequent on routes leading to the city centre. Before 10 in the morning, the majority of transit users are travelling to the city centre (Figure 4.9). The effect of a downtown destination on departure time choice utility is lower after 10, meaning that transit trips after 10 are less likely to have a downtown destination as compared to those in the morning peak.

84 68 Figure 4.9 Public Transit Departure Time Parameter Estimate: Downtown Destination Job type variables have a similar effect on transit work departure time choice as the pattern observed among non-motorized work trips. Office and professional workers are most likely to depart for work in the middle of the peak period, between 7:30 and 9:00, while manufacturing workers are more likely to travel outside of the main peak hours (Figure 4.10). Figure 4.10 Public Transit Departure Time Parameter Estimate: Occupation Type For transit work trips, the following attributes were used as generic variables: fare, age, auto access time/cost, origin and destination locations and full-time status. They are modelled as

85 69 having the same effect on utility across all departure time choice alternatives. The results show that transit users are more sensitive to fare than to in-vehicle travel time, while both variables have a negative effect on utility. Also, those between 25 and 35 years of age appear to be the most likely to use transit. Longer auto access times for transit induce a disutility, meaning that transit trips without large auto access components are preferred. The location of a trip origin within downtown Toronto is a factor that encourages transit use, but not as much as the presence of a downtown destination. This can be explained by the fact that many trips originating downtown are walking trips; while a large portion of work trips commuting into the central area are made by transit. The effect of full-time status is negative, suggesting that full-time workers have an inherent disincentive to using transit (Figure 4.11). Figure 4.11 Public Transit Departure Time Parameter Estimate: Other Finally, as with the non-motorized mode, the work duration scale parameter is only significant for time intervals later in the day. The negative value of the scale parameter indicates that later time intervals are undesirable for those individuals with long work durations Departure Time Choice Model for Auto For work trips made by auto modes, in-vehicle travel time, cost, work duration, downtown destination, and job type were found to be significant explanatory variables. All variables are alternative specific and enter into the systematic utility of departure time choice. The model was estimated using trips, and the mean log-likelihood was Certain alternative

86 70 specific variables were found to be insignificant for particular time intervals and were removed; they are the variables representing the manufacturing job type between 8 and 10 in the morning and the office/clerical job type after 10:00. These are time periods where workers of the job types in question are very unlikely to depart on work trips. The results are presented here (Table 4.3). (Note that parameters for the 1st time choice alternative before 6:30 are all set at 0) (Cells highlighted Green represent parameter estimates that are statistically significant subject to a 95% confidence interval)) Table 4.3 Auto Departure Time Model Results Variable Time Estimates t statistics Alternative specific constant 6:30-6: Alternative specific constant 7:00-7: Alternative specific constant 7:30-7: Alternative specific constant 8:00-8: Alternative specific constant 8:30-8: Alternative specific constant 9:00-9: Alternative specific constant 9:30-9: Alternative specific constant 10 or after Auto cost 6:30-6: Auto cost 7:00-7: Auto cost 7:30-7: Auto cost 8:00-8: Auto cost 8:30-8: Auto cost 9:00-9: Auto cost 9:30-9: Auto cost 10 or after In-vehicle travel time 6:30-6: In-vehicle travel time 7:00-7: In-vehicle travel time 7:30-7: In-vehicle travel time 8:00-8: In-vehicle travel time 8:30-8: In-vehicle travel time 9:00-9: In-vehicle travel time 9:30-9: In-vehicle travel time 10 or after Work duration 6:30-6: Work duration 7:00-7: Work duration 7:30-7:

87 71 Work duration 8:00-8: Work duration 8:30-8: Work duration 9:00-9: Work duration 9:30-9: Work duration 10 or after Downtown destination 6:30-6: Downtown destination 7:00-7: Downtown destination 7:30-7: Downtown destination 8:00-8: Downtown destination 8:30-8: Downtown destination 9:00-9: Downtown destination 9:30-9: Downtown destination 10 or after Office/clerical work 6:30-6: Office/clerical work 7:00-7: Office/clerical work 7:30-7: Office/clerical work 8:00-8: Office/clerical work 8:30-8: Office/clerical work 9:00-9: Office/clerical work 9:30-9: Manufacturing work 6:30-6: Manufacturing work 7:00-7: Manufacturing work 7:30-7: Manufacturing work 10 or after Professional work 6:30-6: Professional work 7:00-7: Professional work 7:30-7: Professional work 8:00-8: Professional work 8:30-8: Professional work 9:00-9: Professional work 9:30-9: Professional work 10 or after Correlation (Mu) All The results show that auto work trips are more likely to occur in the middle of the peak period as compared to off-peak times. Also, many auto work trips occur after 10 in the morning, indicating that auto is the preferred mode among those who start work later in the day (such as those in manufacturing or sales jobs) (Figure 4.12).

88 72 Figure 4.12 Auto Departure Time Parameter Estimate: Constant The effect of auto cost does not follow a clear pattern, suggesting that people are not heavily affected by costs incurred as a result of driving. This is reasonable, given that drivers consider gasoline, insurance and auto ownership as sunk costs, and that time-variable road pricing does not yet exist in the Toronto region. Travel time for auto work trips has a negative effect on the utility of departure time choices, as expected. Later in the morning, the effect of travel time is the most negative, meaning that longer work trips are more likely to begin earlier in the morning (Figure 4.13). Figure 4.13 Auto Departure Time Parameter Estimate: Cost and In-vehicle Travel Time

89 73 The effect of the work duration alternative specific variable on the utility of departure time choices is negative and decreasing over time meaning that those with longer work durations leave earlier for work (Figure 4.14). Figure 4.14 Auto Departure Time Parameter Estimate: Work Duration It seems that auto trips to downtown attempt to avoid the middle of the peak period. Positive values of the parameter estimate for the destination downtown alternative specific variable are found before 7 or after 8:30, meaning that auto trips going downtown are likely to occur either before the middle of the peak period or later in the morning peak, closer to 9:00 (Figure 4.15).

90 74 Figure 4.15 Auto Departure Time Parameter Estimate: Downtown Destination Similarly to the findings from the models using non-motorized and public transit trips, auto trip patterns indicate that the work trips of office and professional workers occur in the middle of the peak period while manufacturing workers travel to work outside of the morning peak (Figure 4.16). Figure 4.11 Auto Departure Time Parameter Estimate: Occupation Type

91 Comparing Parameters Estimates across Models When the results of the three departure time choice models for non-motorized, transit, and auto work trips are compared, more patterns emerge. For example, comparing parameter estimates of the constant component of the utility function shows that non-motorized work trip start times are closely clustered at the middle of the morning peak probably because they are often short trips and can begin close to the work start time. Next transit trips are slightly more spread over time, yet still clustered around the peak hours when service is more frequent. By comparison, the utility of making auto work trips varies less throughout the morning (Figure 4.17). Figure 4.17 All Modes Departure Time Parameter Estimate: Constant For work duration, all three models demonstrate the effect where longer work durations induce a disincentive to travel later in the morning. However, this effect is more pronounced for nonmotorized travel and transit than for auto work trips (Figure 4.18). This can be explained by the fact that transit service becomes less frequent after the peak work travel period. Thus, transit users with long work durations are more likely to depart earlier in the morning, both because they are hoping to begin and end work early and because they do not want to risk tardiness due to infrequent service.

92 76 Figure 4.18 All Modes Departure Time Parameter Estimate: Work Duration As expected, the effect of downtown destinations on the utility of a departure time choice alternative is much higher for transit trips than auto trips, due to the radial nature of the transit system (Figure 4.19). Transit trips that end downtown experience a positive utility for peak period travel while auto trips experience a disutility to peak travel toward downtown. Figure 4.19 All Modes Departure Time Parameter Estimate: Downtown Destination The effect of job type on the utility of departure time choices differs between travel modes. Office and professional job types have the largest effect on departure time choice among auto

93 77 users and the lowest effect among commuters using non-motorized modes (Figure 4.20 and 4.21). Among transit users and non-motorized travellers, there is a large disutility attached to the manufacturing job type, at any time of day. By contrast, auto users, those who are most likely to have a manufacturing job, experience only a small disutility for most of the day (Figure 4.22). Figure 4.20 All Modes Departure Time Parameter Estimate: Office/Clerical Figure 4.21 All Modes Departure Time Parameter Estimate: Professional

94 Figure 4.22 All Modes Departure Time Parameter Estimate: Manufacturing/Construction 78

95 79 Chapter 5 Validation of Departure Time Choice Model The three departure time choice models were subjected to validation tests. For each travel mode, the model was estimated again using a subset of the data. The parameter estimates of the validation test were compared to the original model estimates made using the full dataset. It is desirable for the parameter estimates of the partial dataset to be similar to those of the full dataset. Then, the parameters estimates of the partial model were used to predict the departure time choice behaviour of the remainder of the data. The predicted time distribution pattern using the heteroskedastic GEV model was similar to the observed departure time pattern for all three models. Next, multinomial logit (MNL) departure time models were estimated for each of the three travel mode datasets. A validation test was performed on the MNL models using the same datasets as the Het-GEV validation tests. Finally, the predicted departure time choice distribution using MNL was compared to the predicted distribution from the Het-GEV model and to the observed departure time choice distribution. The validation shows that the Het-GEV model formulation is a much better fit to the observed departure time choice distribution as compared to the MNL model for all three travel modes Non-Motorized Departure Time Choice Model Validation A subset of 5000 trips out of 5888 from the non-motorized travel dataset was used for validation. The parameter estimates of the model using the partial dataset were found to be very close to those from the original model. When the parameters were applied to predict the outcome of the remaining trips, it was found that the predicted time distribution pattern was a good fit to the observed pattern (Table 5.1 and Figure 5.1). Table 5.1 Non-Motorized Departure Time Model Validation Trips/Time Observed % Predicted %

96 80 Figure 5.1 Non-Motorized Departure Time Model Validation A multinomial logit model of departure time choice was estimated for non-motorized trips using the same variables and dataset as the Het-GEV model (Appendix D). The parameter estimates differ from those found using the Het-GEV model and the mean log-likelihood is (compared to for Het-GEV). As compared to the Het-GEV model, it appears that the MNL model of departure time choice for non-motorized work trips overestimates the influence of the constant component and tends to underestimate the effects of other explanatory variables (Figure 5.2). The sign of the parameter estimates is often the same between the Het-GEV and MNL models.

97 81 Figure 5.2 Non-Motorized Departure Time Model Validation: Parameter Comparison to MNL The partial dataset of non-motorized work trips was used for validation of the MNL departure time choice model (the same partial dataset as used for validation of the Het-GEV model). The parameter estimates of the partial dataset were similar to those of the full dataset. When the MNL model was used to predict departure time choice behaviour for the remainder of the dataset, the results were poor. The Het-GEV departure time choice model provides a much better fit to the observed departure time choice distribution as compared to the MNL model (Figure 5.3).

98 82 Figure 5.3 Non-Motorized Departure Time Model Validation: Comparison to MNL 5.2. Public Transit Departure Time Choice Model Validation Validation of the public transit model yields very similar results. Using out of trips, the parameter estimates of the partial dataset were found to closely resemble those of the original model. The validation of the Het-GEV model presented a good fit between the predicted and observed departure time choice distributions (Table 5.2 and Figure 5.4). (Note: the scale parameter associated with work duration in the 7 th time choice interval was set to 0 because its parameter estimate value was too highly negative to compute choice probabilities) Table 5.2 Public Transit Departure Time Model Validation Trips/Time Observed % Predicted %

99 83 Figure 5.4 Public Transit Departure Time Model Validation The multinomial logit model for transit departure time choice presents parameter estimates with different values, but usually with the same sign as those found using the Het-GEV model. The MNL model overestimates the effect of transit in-vehicle travel time and of a downtown destination (Figure 5.5). Its mean log-likelihood is as compared to using Het- GEV.

100 84 Figure 5.5 Public Transit Departure Time Model Validation: Parameter Comparison to MNL The validation of the MNL version of the transit departure time choice model yields a far inferior fit to the observed departure time choice distribution as compared to the Het-GEV model (Figure 5.6).

101 85 Figure 5.6 Public Transit Departure Time Model Validation: Comparison to MNL 5.3. Auto Departure Time Choice Model Validation Finally, the validation of the departure time choice model for auto trips also yields promising results. The model was estimated using out of trips and the departure time choice of the remaining trips was predicted. The predicted departure time choice distribution was a good fit to the observed distribution showing that the Het-GEV model correctly captures departure time choice behaviour (Table 5.3 and Figure 5.7). Table 5.3 Auto Departure Time Model Validation Trips/Time Observed % Predicted %

102 86 Figure 5.7 Auto Departure Time Model Validation In the multinomial logit model of departure time choice for auto trips, the mean log-likelihood was compared to in the Het-GEV model. All variables are found to be significant except for auto cost and downtown destination for some early and late time periods. The values of parameter estimates from the MNL model are similar to the Het-GEV parameter estimates for auto level of service attributes. However, the MNL model appears to underestimate the effect of work duration on the utility of a departure time choice (Figure 5.8).

103 87 Figure 5.8 Auto Departure Time Model Validation: Parameter Comparison to MNL As with the other two travel modes, the validation of the MNL auto departure time choice model presents a far inferior fit to the observed departure time choice distribution as compared to the results found using the Het-GEV model (Figure 5.9).

104 88 Figure 5.9 Auto Departure Time Model Validation: Comparison to MNL Overall, the Het-GEV departure time choice models provide a good fit to the observed time choice distribution, while the MNL departure time choice models consistently provide a poor fit to reality and forecast that people will depart for work earlier in the morning than they do. This may be due to the susceptibility of the MNL model to researcher-defined discretization schemes Comparison with Previous Studies A comparison of these results with previous departure time choice studies indicates similarities. Small (1982), a study of auto commuters departure time choice in San Francisco, shows that professional workers and those with flexible work schedules are likely to travel to work later in the morning. Comparing this to the departure time choices of Toronto auto commuters in 2006 shows that those with shorter work duration potentially a characteristic comparable to flexible work hours also tend to leave later in the morning. Also, the results of this study show that professional or management workers are more likely to arrive to work after 9 in the morning than

105 89 clerical staff. This is consistent with Small s finding that professional workers are likely to travel later. Next, another study of San Francisco morning commuter departure time choice states that transit users are not likely to travel early in the morning due to infrequent off-peak transit service, and that professional and administrative workers are unlikely to depart early for work (Abkowitz, 1981). The results of this work support the fact that transit is undesirable before the peak service begins; the constant parameter for transit departure time choice has a negative value before seven in the morning and the utility of taking transit is shown to be highest between eight and nine in the morning. With regards to job type, the results of this study also show that professional and administrative workers prefer to travel to work in the middle of the morning peak period as compared to very early in the morning. The results of this work have been compared to a recent study of work trip departure time in New York (Chu, 2009). Like Chu, the results of this study suggest that work schedules strongly influence work departure time choices. Specifically, Chu s finding that those with shorter work schedules depart later for work has been supported by the results of this work. Similar to Chu, these results find that drivers are more strongly motivated by travel time than by cost because neither New York nor Toronto currently use variable road pricing strategies. Chu also states that professional workers and those not working downtown travel to work later in the morning. The results of auto departure time choice in this study also states that early departure time choices are undesirable for those who work downtown, while the opposite is true of transit users. De Jong et al. (2003) found that departure time choice is affected by travel time and cost and (Chin, 1990) stated that work start times also influence departure time, which is in agreement with the results presented here. In addition, Bajwa et al. (2006) found that models that recognize that alternate choices are correlated perform better than those that do not; this has been supported by the validation tests of the Het-GEV model in comparison to the comparable MNL departure time model.

106 90 Chapter 6 Mode Choice Model The model of mode choice used for this analysis follows a tree logit formulation structure with scale heterogeneity to account for variations between individuals. The tree logit model represents the choice between modes in a hierarchical nested network, where comparable modes are grouped together. Similarly to the departure time models, this mode choice model involves systematic utility and scale parameters to define the value of choice alternatives. Also, the model groups choices into clusters and defines the probability of selecting a mode as conditional on the probability of selecting the cluster to which the mode belongs. The model formulation includes systematic utility (V), defined as the weighted sum of variables relevant to the mode choice (m). The variables (x) chosen and their parameter values (B) differ for each mode. V m = Bx (6.1) Next, clusters of modes are defined and each cluster is associated with a scale parameter. The scale parameters are defined in terms of a variable that is expected to explain the variation in decision behaviour between individuals in this case average/median household income of their home area. One of the scale parameters is set to the reference constant value while other are expressed as: Mu nest = exp (B*ln (income/10000)) where B is a parameter value to be estimated (6.2) The inclusive value of each cluster (I nest ) represents its combined utility to decision makers. For each cluster, the inclusive value is defined in terms of the utility of each mode within the cluster (V m ) and the Mu value of the cluster/nest. I nest = 1/ (Mu nest ) x ln ( m exp (Mu nest V m )) (6.3)

107 91 The inclusive values of each nest are then used to find the construct nodes (Q nest ) for all nests, a representation of the probability that an individual will choose to conduct a given trip using a mode within that cluster. Q nest = (exp (Mu nest I nest ) / ( nest=1 exp (Mu nest I nest ) (6.4) Note that the feasibility of all modes is defined for each trip. Non-motorized trips can only be conducted for distances of 10 km or less, transit trips can only be conducted between origindestination pairs where transit level-of-service attributes exist, auto driver trips can only be made by liscenced drivers, and passenger trips are feasible for all individuals. Thus nests where all component modes are infeasible are removed from the calculation for construct nodes. Finally, the probability of choosing a mode (P m ) is defined as the conditional probability of choosing the mode within its cluster given that the appropriate cluster has been chosen. As before, infeasible modes are excluded from the calculation. P m = [exp (Mu nest V m )/ ( m=1 exp (Mu nest V m )] x Q nest (6.5) The model is estimated by changing parameter values to maximize the likelihood function (the sum over all trips of predicted choice probabilities for the observed chosen mode). (Daly, 1987) 6.1. Empirical Models Mode Choice Model - Seven Mode Version The seven travel modes represented in the full choice structure are: Auto consisting of auto driver (AD) and auto passenger (AP) modes, GO Transit commuter rail consisting of the submodes where GO Transit is accessed by driving (GAA) or by surface transit and walking (GTA), all other public transit aside from GO which is also separated into trips accessed by driving (TAA) or walking (TWA), and Non-motorized travel (NMT) (Figure 6.1).

108 92 Figure 6.1 Mode Choice Model Framework: Seven Modes Data As with the departure time model, the data used to estimate the mode choice model is taken from the 2006 TTS survey. The specific dataset used for the mode choice model with seven detailed modes consists of morning peak trips conducted using a variety of modes. For many trips, this dataset provides alternate level of service attributes that the individual might have encountered had they taken a different mode (including alternate level of service attributes between different transit modes a feature that is not included in the dataset used to estimate the departure time choice model). The presence of disaggregate transit level of service attributes allows a more detailed visualization of mode split. However, this specific dataset only includes peak hour level of service attributes Model The model is based on utility maximization the utility of each travel mode for each trip is calculated based on attributes of the trip and the person. To account for the stochastic nature of mode choice decisions, the average income of the decision makers census tract of residence is introduced as a scale parameter (Appendix E). The systematic utility functions for all modes include level of service attributes, specifically a measure of travel time and total cost, as well as the demographic variables of gender and age. Measures of travel time and cost are specific to the mode: for example GO with auto access combines the auto travel time with the transit in-vehicle travel time, the cost of driving is proportional to distance and time travelled as well as parking

109 93 costs. In all cases, the total trip cost is interacted with the individual s occupation type because it is believed that income and lifestyle influence one s perceived disutility of parking costs and transit fares. Utility functions for modes conducted in whole or in part by auto modes (auto driver, auto passenger, GO with auto access, and other transit with auto access) also include a measure of the number of vehicles in the household as it applies to the nature of the specific mode. For example, the auto driver mode s utility function considers the effect of 2 or more cars in the household on one s willingness to drive because high auto ownership is a known indicator of auto mode choice. The utility of choosing the auto passenger mode distinguishes between the effect of one car or more than one car because one is likely to travel as a passenger in a household with fewer cars or drivers. The number of vehicles is also a variable for the utility functions of transit modes with auto access modes because the availability of cars in the home is expected to influence one s ability to choose these modes. The utility functions of all transit modes also include walk times and wait times. These are separate variables from in-vehicle travel time because individuals perceive the disutility of longer walk and wait times as being higher than the disutility of a long travel time. The level of service attribute relevant to the nonmotorized travel mode is distance; therefore, the non-motorized utility function distinguishes between trips shorter than 1 kilometre, between 1 and 2 kilometres and those between 2 and 3 km. A list of the variables included in the utility functions is presented (Table 6.1). Table 6.1 Mode Utility Functions Seven Mode Version Mode Auto Driver (AD) Auto Passenger (AP) Transit Walk Utility of the Mode is a Function of Variables: auto'saivtt (auto's acost+(auto's park/2))*professional (auto's acost+(auto's park/2))*generaloffice (auto's acost+(auto's park/2))*sales (auto's acost+(auto's park/2))*manufacturing 2vehicles at home morethan2vehicles auto'saivtt ((auto's acost+(auto's park/2))/2)*professional ((auto's acost+(auto's park/2))/2)*general office ((auto's acost+(auto's park/2))/2)*sales ((auto's acost+(auto's park/2))/2)*manufacturing 1vehicle morethanequalto2vehicles male under over55 TWA's tivtt TWA's fare*professional

110 94 Access (TWA) TWA's fare*general office TWA's fare*sales TWA's fare * manufacturing TWA's walk TWA's wait male under Transit Auto Access (TAA) GO Transit Access (GTA) GO Auto Access (GAA) Non- Motorized Travel (NMT) over55 (TAA's accessaivtt + TAA's TIVTT) (TAA's fare + (TAA's park/2))*professional (TAA's fare + (TAA's park/2))*generaloffice (TAA's fare + (TAA's park/2))*sales (TAA's fare + (TAA's park/2))* manufacturing TAA's walk TAA's wait nveh male under over55 (GTA's accesstivtt + GTA's maintivtt) GTA's fare*professional GTA's fare*general office GTA's fare*sales GTA's fare*manufacturing GTA's walk GTA's wait male, under over55 GAA's accessaivtt + GAA's TIVTT) (GAA's fare + (GAA's park/2))*professional (GAA's fare + (GAA's park/2))* general office (GAA's fare + (GAA's park/2))* sales (GAA's fare + (GAA's park/2))* manufacturing GAA's walk GAA's wait nveh male under over55 under1km 1-2km 2-3 km male under over55 The probability of a given trip being conducted by each of the seven modes is calculated in terms of the utility of the mode as compared to other modes in its category/nest, the utility of the

111 95 category, as well as the feasibility of the mode (i.e. for trips longer than 10 kilometres, nonmotorized travel is not considered an eligible mode) Results of Mode Choice Model Seven Mode Version The mode choice model was estimated using observed peak period trips with a variety of travel modes. The estimation yielded a mean-log likelihood of The results of the model estimation indicate that level of service attributes and demographics affect mode choice decisions. Higher trip times and costs are consistently shown to induce a disutility for any mode. Full results of the mode choice model with seven modes are presented in Appendix F. The effect on mode choice of total trip cost as it interacts with occupation type yields promising results. All parameter estimates for trip cost are negative indicating a disutility, and those in the trades and manufacturing are the most negatively affected by higher trip costs (Figure 6.2). This may be due to lower incomes among people in this sector as compared to those in other categories, as well as a tendency to drive to work in areas with free parking thus avoiding transit fares and parking costs. Those in the sales industry perceive high travel costs less negatively than manufacturing workers while than those in professional or office jobs are shown to be least affected by travel costs. In addition to being explained by income trends, professional and office workers are also most likely to incur costs due to transit fares and parking costs since many jobs in those sectors are located downtown. Figure 6.2 Seven Mode Choice Model Parameter Estimate: Cost The influence of trip distance on the utility of non-motorized travel is found to match assumptions. For trips less than 3 kilometres, all parameter estimates are shown to be positive

112 96 indicating a willingness to walk or bike for short trips. The shortest trips induce the larger positive effect on the utility of non-motorized travel as expected (Figure 6.3). Figure 6.3 Seven Mode Choice Model Parameter Estimate: Effect of Trip Distance on Non- Motorized Utility The effect of travel time on the utility of all motorized modes is compared to the effect of transit walk and wait times. Long wait times are shown to be the most undesirable for travellers, followed by walk times. In-vehicle travel time has a negative effect on utility as anticipated but its disutility is smaller than those of walk time and wait time (Figure 6.4). People generally perceive in-vehicle travel times as less onerous than walk and wait times because they are shielded from the elements, seated or standing instead of walking, free to make use of their time, and perceive that they are approaching their destination rather than wasting time. Figure 6.4 Seven Mode Choice Model Parameter Estimate: Transit Level of Service Attributes

113 97 The effect of household auto ownership on mode choice is presented. For auto drivers, higher auto availability indicates a greater utility of driving. Interestingly, those in households with two or more cars are more likely to be passengers than those with only one car at home (Figure 6.5). While a scarcity of cars could be thought to induce the need to carry passengers, the availability of cars in which one could potentially travel as a passenger induces a larger contribution to the utility of the auto passenger mode. Figure 6.5 Seven Mode Choice Model Parameter Estimate: Auto Ownership The impact of household auto ownership on the utility of auto-accessed transit modes was also examined. For both modes - GO with auto access and other transit with auto access higher numbers of cars at home have a positive effect on the utility of the mode (Figure 6.6). The effect is shown to be larger for GO transit as compared to other transit such as subway, likely due to the fact that GO transit stations are much more sparsely distributed in space than subway stations and because GO transit serves a large, suburban area where the most common way to access a train station is by driving.

114 98 Figure 6.6 Seven Mode Choice Model Parameter Estimate: Effect of Auto Ownership of Transit Utility The effect of age on mode choice utility varies between modes. Note that all age parameters for the reference mode, auto driver, are set to zero meaning that positive parameters for other modes indicate a relative higher utility attached to the age group for that mode as compared to the auto driver mode. In addition, the model parameter for the age group between 35 and 55 years of age is used as a reference and is set to 0. For example, individuals under the age of 35 are shown to have a higher utility of using non-motorized travel as compared to driving, while those over 55 have a lower utility of using non-motorized travel. A similar pattern is observed for the auto passenger mode, and all transit modes except for GO transit. For GO transit, those under 25 and those over 55 have a higher added utility to use GO transit than other age groups. This is consistent with the observation that many GO train riders are either university students or established professionals.

115 99 Figure 6.7 Seven Mode Choice Model Parameter Estimate: Age AP 3-TWA 4-TAA 5-GTA 6-GAA 7-NMT < >55 Gender is shown to be correlated with mode choice. The data indicates that male travellers are less likely to choose the auto passenger mode than any other mode, followed by public transit, non-motorized travel, and GO with auto access. The only mode that induces a higher added utility for male travellers than the auto driver mode is GO transit without auto access (Appendix F) Validation of Mode Choice Model Seven Mode Version For the mode choice model validation, a subset of trips was taken from the full dataset used to estimate the model. The model was estimated again using the partial dataset, resulting in a mean log-likelihood of (similar to the model using the full dataset with ). The parameter estimates found using the partial dataset were very close to the estimates of the full dataset, with only an average deviation of 4%. The parameter estimates of the partial dataset were applied to calculate the predicted probabilities of selecting each travel mode for the remaining trips. The predicted mode split calculation is very close to the observed mode split (Figure 6.8 and 6.9).

116 100 Figure 6.8 Seven Mode Choice Model Validation: Mode Split Mode Split pred.proportion obs.proportion AD AP TWA TAA GTA GAA NMT Figure 6.9 Seven Mode Choice Model Validation 18% Predicted Mode Split 2% 0% 4% 1% AD AP 17% Observed Mode Split 2% 0% 5% 1% AD AP TWA TWA TAA TAA 9% 66% GTA GAA NMT 8% 67% GTA GAA NMT Mode Choice Model - Three mode version In order to combine the mode choice model with the existing departure time choice models, the mode choice model needed to be modified to represent the choice between three travel mode groups (Auto, Transit, Non-motorized) and to be estimated using the same dataset as was used for the departure time models (all 2006 TTS 24-hour home to work/school trips made by employed individuals). This is required because it is not possible to apply the parameter

117 101 estimates obtained from the seven-mode model using the 2006 peak hour dataset to forecast the behaviour of the 24-hour, home to work, trips made by employed people. In addition, policy analysis for mode and departure time choice must be done on the same dataset, so the mode choice model needed to be estimated using the same data as the departure time choice models. The level of service attributes in the 24-hour dataset vary over time, allowing for the analysis of dynamic policies Model Changes The code used to represent and estimate the mode choice model was modified to represent three travel modes with their corresponding utility functions (Appendix G). Only three mode choices are used because there is a departure time model for each of these three travel modes. In addition, the 24-hour dataset does not have alternate level of service attributes for various types of public transit, meaning that the choice between different transit sub-modes cannot be represented using this dataset. The revised utility functions can be represented by Table 6.2. Table 6.2 Mode Utility Functions Three Mode Version Mode Auto Transit Non-Motorized Utility of the Mode is a Function of Variables: auto'saivtt (auto's acost+(auto's park/2))*professional (auto's acost+(auto's park/2))*generaloffice (auto's acost+(auto's park/2))*sales (auto's acost+(auto's park/2))*manufacturing 2vehicles at home morethan2vehicles (accessaivtt + TIVTT) (fare + (park/2))*professional (fare + (park/2))*generaloffice (fare + (park/2))*sales (fare + (park/2))* manufacturing walk wait nveh male under over55 under1km 1-2km 2-3 km male under over55

118 102 The dataset used was composed of home-based work and school trips made by employed individuals from the 2006 TTS survey: 5888 using non-motorized travel, using public transit modes, and using auto a total of trips. Columns from the dataset were selected to match the variables used in the mode choice model estimation code. By limiting the choice to three modes, each cluster was defined to contain only one choice. Also, the variable representing average household income in the census tract of residence was changed to median income because the 24-hour dataset includes local median incomes but not averages Results of Mode Choice Model Three mode version The following figures depict the parameter estimates found upon estimating the mode choice model with three alternatives. The constant value for non-motorized travel was set to 0 in order to find auto and transit constant values relative to non-motorized travel (Figure 6.10). Figure 6.10 Three Mode Choice Model Parameter Estimate: Constant Next, the parameters representing the impact of travel cost on the utility of either the auto or the transit mode are all negative as expected (Figure 6.11). In this dataset, the professional workers are found to be more averse to high travel costs than manufacturing workers. The difference between the findings of this dataset and the previous peak hour dataset may be due to the fact that the 24-hour dataset considers only work trips or to the fact that only three modes are being studied.

119 103 Figure 6.11 Three Mode Choice Model Parameter Estimate: Cost For the effect of distance on the utility of non-motorized trips, this dataset also indicates that trips under 3 kilometres all have a positive effect on utility, with the shortest trips having the highest positive effect (Figure 6.12). Figure 6.12 Three Mode Choice Model Parameter Estimate: Effect of Trip Distance on Non-Motorized Utility The parameters for in-vehicle travel time and wait time are found to be positive for this dataset (Figure 6.13). Intuitively, longer travel and wait times should be correlated with an unwillingness to choose a certain travel mode although that effect may not have been observed in this dataset. Since this dataset considers only work trips, there may be a high degree of captive travellers who select a certain travel mode although it provides longer travel times and waits than another mode.

120 104 Since this dataset does not demonstrate the effect where longer travel and wait times induce travellers to choose another mode, policies that impose higher travel times and waits in an attempt to shift demand to other modes cannot be tested. Figure 6.13 Three Mode Choice Model Parameter Estimate: Transit Level of Service Attributes The effect of household auto ownership on mode choice shows intuituive patterns. The presence of more cars in a home induces a higher utility of choosing auto travel modes (Figure 6.14). Conversely, higher numbers of vehicles at home have a slight negative effect on the utility of choosing transit modes. ( ) Figure 6.14 Three Mode Choice Model Parameter Estimate: Auto Ownership The patterns between age and mode choice observed in this dataset indicate that those under 35 experience a relative higher utility to choosing transit and especially non-motorized travel

121 105 instead of auto modes. Those over 55 experience a disutility attached to transit modes as compared to auto modes and a larger added disutility for non-motorized travel (Figure 6.15). Figure 6.15 Three Mode Choice Model Parameter Estimate: Age In this dataset, male travellers experience an added disutility toward transit modes although they are shown to have an added utility for choosing non-motorized travel (Figure 6.16). This may be a representation of the prevalance of male bicyclists. Figure 6.16 Three Mode Choice Model Parameter Estimate: Gender Validation of Mode Choice Model Three Mode Version To validate the revised mode choice model, a subset of trips was taken from the trip dataset and the model was estimated on the subset. The parameters estimates were found to

122 106 be similar to those found with the full dataset (average 9% difference) and the mean log likelihood was also similar ( compared to from the full set). The observed and predicted mode splits are presented the fit of the model to the observed data is good and performs better than the null model (Figure 6.17 and 6.18). Figure 6.17 Three Mode Choice Model Validation: Mode Split Figure 6.18 Three Mode Choice Model Validation 6.2. Mode Choice Comparison with Previous Studies Long et al. (2010) found that mode choice differs between individuals with varying socioeconomic attributes. Similarly, in this study, income represents heteroskedasticity in mode