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Continuous Departure-Time Choice Models for Home-to-Work Commute

Permanent Link: http://ufdc.ufl.edu/UFE0022449/00001

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Title: Continuous Departure-Time Choice Models for Home-to-Work Commute
Physical Description: 1 online resource (86 p.)
Language: english
Creator: Komma, Abishek
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: commute, duration, hazard, traveltime
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This study contributes to the literature by developing continuous-time models for the home-to-work commute timing decisions of full-time workers with flexible and non-flexible work schedules using the hazard-duration structure. Further, the estimated departure time choice models include the effect of travel time at a fine temporal resolution of 15 minutes. In order to generate the travel time data at this resolution, a second set of regression models is developed. The models were estimated using data from the 2000 San Francisco Bay Area Travel Survey. The regression models for inter-zonal travel times produce smoothly time-varying travel duration profiles that capture the effects of temporal and spatial congestion appropriately. Both the hazard duration models indicated a statistically significant effect of commute speed/travel duration on the choice of departure time. Specifically, individuals are less likely to depart home at times when the commute speed is lower (or travel duration is higher). In addition, the model also captures the impact of several other explanatory factors such as individual and household socio-demographic characteristics, employment related characteristics and land use characteristics of the home and work zones on the choice of departure time to work.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Abishek Komma.
Thesis: Thesis (M.S.)--University of Florida, 2008.
Local: Adviser: Srinivasan, Sivaramakrishnan.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022449:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022449/00001

Material Information

Title: Continuous Departure-Time Choice Models for Home-to-Work Commute
Physical Description: 1 online resource (86 p.)
Language: english
Creator: Komma, Abishek
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: commute, duration, hazard, traveltime
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This study contributes to the literature by developing continuous-time models for the home-to-work commute timing decisions of full-time workers with flexible and non-flexible work schedules using the hazard-duration structure. Further, the estimated departure time choice models include the effect of travel time at a fine temporal resolution of 15 minutes. In order to generate the travel time data at this resolution, a second set of regression models is developed. The models were estimated using data from the 2000 San Francisco Bay Area Travel Survey. The regression models for inter-zonal travel times produce smoothly time-varying travel duration profiles that capture the effects of temporal and spatial congestion appropriately. Both the hazard duration models indicated a statistically significant effect of commute speed/travel duration on the choice of departure time. Specifically, individuals are less likely to depart home at times when the commute speed is lower (or travel duration is higher). In addition, the model also captures the impact of several other explanatory factors such as individual and household socio-demographic characteristics, employment related characteristics and land use characteristics of the home and work zones on the choice of departure time to work.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Abishek Komma.
Thesis: Thesis (M.S.)--University of Florida, 2008.
Local: Adviser: Srinivasan, Sivaramakrishnan.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022449:00001


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1 CONTINUOUS DEPARTURE-TIME CHOICE MODELS FOR HOME-TO-WORK COMMUTE By ABISHEK KOMMA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2008

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2 2008 ABISHEK KOMMA

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3 To my parents

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4 ACKNOWLEDGMENTS I thank m y advisor, Dr. Sivaramakrishnan Srin ivasan, Assistant Professor, Department of Civil Engineering, University of Florida, fo r his continuous support and. The learning process under him has been invaluable and I really enjoyed every brain storming session. I would also like to thank my committee members (Dr. Lily Elefteriadou, Associate Professor, and Dr. Yafeng Yin, Assistant Professor) for th eir guidance and feedback on the study. I express my deep sense of gratitude to my family members for their perennial moral support and encouragement. I also record my special thanks to my friends: Koustubh, Ramakrishna, Vipul, Karun, and Mayank for making my stay at UF very memorable.

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5 TABLE OF CONTENTS Page ACKNOWLEDGMENTS..............................................................................................................4 LIST OF TABLES................................................................................................................. .........7 LIST OF FIGURES........................................................................................................................8 ABSTRACT ...................................................................................................................... ......9 CHAP TER 1 INTRODUCTION ................................................................................................................10 1.1 Background ..................................................................................................................10 1.2 Motivations ..................................................................................................................10 1.3 Focus of Re search........................................................................................................11 1.4 Structure of the Thesis .................................................................................................12 2 LITERATURE REVIEW .....................................................................................................13 2.1 Methodological Issues .................................................................................................. 13 2.1.1 Model Structure Em ployed.............................................................................. 14 2.1.2 Temporal Resolution of the Choice Alternative.............................................. 14 2.1.3 Temporal Resolution of the Inter-zonal Travel Time Data.............................. 15 2.1.4 Incorporating the Concept of Schedule Delay ................................................. 15 2.2 Empirical Findings.......................................................................................................16 2.2.1 Individual S ocio-Economic Characteristics..................................................... 17 2.2.2 Household Socio-Econom ic Characteristics.................................................... 17 2.2.3 Employment Char acteristics............................................................................18 2.2.4 Transportation System Characteristics.............................................................18 2.2.5 Commute Characteristics .................................................................................18 2.3 Summ ary of the Literature........................................................................................... 19 3 INTER-ZONAL TRAVEL TIME MODEL ......................................................................... 26 3.1 Need for an Inter-zonal Travel Tim e Model................................................................ 26 3.2 Data..............................................................................................................................27 3.3 Econom etric Structure.................................................................................................. 29 3.4 Empirical Results......................................................................................................... 30 3.5 Summ ary......................................................................................................................32 4 COMMUTE-TIMING MODEL FOR F LEXIBLE SCHEDULE W ORKERS.................... 37 4.1 Data..............................................................................................................................37 4.2 Methodology ................................................................................................................39 4.3 Empirical Results......................................................................................................... 41

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6 4.3.1 Individual and Household Soci o-Econom ic Characteristics............................ 41 4.3.2 Individual E mployme nt Characteristics........................................................... 42 4.3.3 Day of the Week...............................................................................................43 4.3.4 Location Characteristics ...................................................................................43 4.3.5 Transportation System Characteristics.............................................................43 4.4 Model Application .......................................................................................................45 4.4.1 Aggregate P rediction of Departure Time Profiles........................................... 45 4.4.2 Aggregate S ensitivity to Changes in Time-Varying Characteristics............... 45 4.4.3 Aggregate S ensitivity to Changes in Non Time-Varying Characteristics....... 46 4.5 Summ ary......................................................................................................................47 5 COMMUTE-TIMING MODEL FOR FIXED SCHEDULE WORKERS ........................... 57 5.1 Data..............................................................................................................................57 5.2 Methodology ................................................................................................................58 5.3 Empirical Results......................................................................................................... 61 5.3.1 Individual and Household Soci o-Econom ic Characteristics............................ 62 5.3.2 Individual E mployme nt Characteristics........................................................... 62 5.3.3 Location and Commute Distance Characteristics ............................................ 63 5.3.4 Time-Varying Characteristics.......................................................................... 63 5.4 Model Application .......................................................................................................65 5.4.1 Aggregate P rediction of Departure Time Profiles........................................... 65 5.4.2 Aggregate S ensitivity to Changes in Time-Varying Characteristics............... 65 5.4.3 Aggregate S ensitivity to Changes in Non Time-Varying Characteristics....... 66 5.5 Summ ary and Conclusions...........................................................................................66 6 SUMMARY AND CONCLUSIONS ...................................................................................78 6.1 Summ ary of Empi rical Results.................................................................................... 79 6.1.1 Summ ary of empirical results fo r inter-zonal travel time models.................... 79 6.1.2 Summ ary of empirical results for commute-timing models............................ 79 6.2 Directions for Further Research ................................................................................... 80 LIST OF REFERENCES..............................................................................................................83 BIOGRAPHICAL SKETCH........................................................................................................86

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7 LIST OF TABLES Table Page 2-1 Overview of morning commute-timing models.................................................................... 21 2-2 Overview of other time-of-day choice models..................................................................... 24 2-3 Factors impacting morni ng commute-tim ing decisions........................................................ 25 3-1 Empirical results: Inter-zonal travel duration regression m odels......................................... 33 4-1 Sample characteristics of full-time workers with flexible work schedules .......................... 48 4-2 Empirical results: Covariate effects for the hazard duration m odel for departure tim e choice of flexible schedule workers.................................................................................................49 5-1 Sample characteristics of full-time workers with fixed work schedules.............................. 68 5-2 Empirical results: Covariate effects for the hazard duration m odel for departure tim e choice of fixed schedule workers.....................................................................................................69

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8 LIST OF FIGURES Figure Page 3-1 Distribution of depart ure tim es by time-of-day.................................................................... 34 3-2 Distribution of tr avel time duration ...................................................................................... 35 3-3 Variation of inter-zonal travel duration by tim e-of-day: Illustrative graphs........................ 36 4-1 Distribution of departure times for home-to-work commute by tim e-of-day of flexible schedule workers...................................................................................................................50 4-2 Estimated baseline hazard distri bution of flexible schedule workers ................................... 51 4-3 Observed vs predicted distribution of depa rture tim e patterns of flexible schedule workers 52 4-4 Impact of change in commuting speed in the morning peak period (7 AM to 9 AM) for flexible schedule workers .....................................................................................................53 4-5 Cumulative impact of change in commuting speed in the m orning peak period (7 AM to 9 AM) for flexible schedule workes........................................................................................ 54 4-6 Impact of change in % departures with work frequency less than or equal to four for flexible schedule workers ...................................................................................................................55 4-7 Cumulative impact of change in % departures with work frequency less than or equal to four for flexible schedule workers ........................................................................................ 56 5-1 Departure time distribution over time-of-day fixed schedule workers ................................ 70 5-2 Probability density function fo r the preferred w ork start time of fixed schedule workers... 71 5-3 Estimated baseline hazard dist ribution of fixed schedule workers .......................................72 5-4 Observed vs predicted distribution of depa rture tim e patterns of fixed schedule workers... 73 5-5 Cumulative impact of change in commuting speed in the m orning peak period (7 AM to 9 AM) for Model a for fixed schedule workers................................................................... 74 5-6 Cumulative impact of change in commuting speed in the m orning peak period (7 AM to 9 AM) for Model b for fixed schedule workers.................................................................... 75 5-7 Cumulative impact of change in % departures with change in work start time preference for Model a for fixed schedule workers................................................................................... 76 5-8 Cumulative impact of change in % departures with change in work start time preference for Model b for fixed schedule workers................................................................................... 77

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9 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science CONTINUOUS DEPARTURE-TIME CHOICE MODELS FOR HOME-TO-WORK COMMUTE By Abishek Komma August 2008 Chair: Sivaramakrishnan Srinivasan Major: Civil Engineering This study contributes to the literature by developing cont inuous-time models for the home-to-work commute timing decisions of fulltime workers with flexible and non-flexible work schedules using the hazard-duration structur e. Further, the estimated departure time choice models include the effect of travel time at a fi ne temporal resolution of 15 minutes. In order to generate the travel time data at this resoluti on, a second set of regressi on models is developed. The models were estimated using data from the 2000 San Francisco Bay Area Travel Survey. The regression models for inter-zonal travel tim es produce smoothly time-va rying travel duration profiles that capture the effects of temporal and spatial congesti on appropriately. Both the hazard duration models indicated a statistically signif icant effect of commute speed/travel duration on the choice of departure time. Sp ecifically, individuals are less likely to depart home at times when the commute speed is lower (or travel du ration is higher). In addition, the model also captures the impact of several other explanator y factors such as indi vidual and household sociodemographic characteristics, empl oyment related characteristics and land use characteristics of the home and work zones on the choice of departure time to work.

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10 CHAPTER 1 INTRODUCTION 1.1 Background Workers co nstitute a substantial fraction of the population and their commute to and from work constituted 16% of all travel undertaken. The average national commute travel times grew about 40 seconds from 21.7 minutes in 1980 to 22.4 minutes in 1990, with more than 22 million single occupant drivers added. This was followe d by a gain of three minutes to 25.5 minutes from 1990 to 2000, with an increase of another 13 million SOV users (Pisarksi, 2006). In addition, Pisarksi (2006) also reports a shift in commute trips away from the peak period. Specifically, the 6-9 AM period in 2000 constituted only 64% of all work travel in contrast to 67% of all work travel in 1990. These large volumes of commute tr avel along with their changing temporal patterns unde rscore the need to model the commute patterns of workers towards developing effective strategies for conges tion alleviation. The objective of this study is to broadly contribute towards this end by modeling the home-to -work commute timing decisions (i.e., choice of departure time) of workers. 1.2 Motivations In the context of m odeling the departure tim e choices for home-to-work commute travel, two issues are important. First, the models should recognize the continuous nature of the departure time choices. This is because evalua tion of policy actions such as dynamic pricing schemes and provision of real-time information re quire estimates of travel-demand patterns at a fine temporal resolution. Further, continuous-time models do not re quire apriori discretization of the day into periods and hence can be more flex ible in capturing the temporal shifts in the commute patterns into the future. Also, modeling the effect of vehicular emissions on the air quality can also benefit from continuous models for the choice of commut e departure time. Since

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11 the commute is typically the first trip made during the day, the departure times for commute travel provide information on the soak times (def ined as duration of time in which the vehicle's engine is not operating and that precedes a su ccessful vehicle start) in an area which can potentially be used as inputs to air-quality m odels (see for example, Nair et al. 2001). Second, disaggregate models that capture the impacts of changing life styles and emerging population trends on commuting should be developed. For instan ce, Pisarksi (2006) indi cates that increasing vehicle ownership levels esp ecially in African-American hous eholds, increasing fraction of women as a part of work force, alternate work arrangements such as compressed work week and telecommuting, increasing car-pool shares, increas ing trip chaining activity (stop making during commute), changing commuter flow patterns such as the shift from CBD to suburban for work, peak spreading phenomenon, etc can all impact the choice of departure time to work. Consequently, it is necessary to develop disaggregate, continuous-time models that control for these trends for accurate forecasting. 1.3 Focus of Research In the above section the importance of deve loping disaggregate, continuous-tim e models for the choice of commute depa rture times was highlighted. The objective of this study is to contribute to the literatu re in this area. Specifically, we de velop continuous-time models for the home-to-work commute (morning commute) tim ing decisions using the hazard-duration structure. These models include the effect of travel time at a fine temporal resolution of 15 minutes. In order to generate the travel time da ta at this resolution, a second set of regression models are developed. Further, this study also contributes to the understanding of the systematic differences in the commute timing decisi ons across population groups. Specifically, the empirical models incorporates several explanatory factors such as individual and household socio-economic characteristics, employment char acteristics, commute characteristics and land-

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12 use patterns to capture heterogeneity in the de parture time preferences. Separate models are developed for flexible and fixed-schedule (full-tim e) workers. Finally, a demonstration exercise is also presented for a better unde rstanding and also to hi ghlight the ease of application of these models in practice. 1.4 Structure of the Thesis The rest of this thesis is organized as follows. Chapter 2 gives a brief overview of the literature on departure time choice modeling for work trips. Chapter 3 discusses the development of the Inter-zonal travel time models which will serve as inputs to the commute-timing models. This is followed by the description of departur e time models of workers with flexible work schedules in Chapter 4. Chapter 5 discusses th e commute-timing models in the context of workers with fixed work schedules. Later Chapte r 6 summarizes the study, identifies the major conclusions, and highlights areas where this work can be extended and further developed.

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13 CHAPTER 2 LITERATURE REVIEW In recognition of the overall im portance of modeling commute timing decisions, there have been an increasing number of studies in this area es pecially in the recent pa st. In the next several sections, we present a synthesi s of literature on empirical modeling studies focused on commute departure choices using cross-sectional travel-s urvey data. For literature on the time-of-day choices for non-commute travel, see for example, Bhat and Steed (2002), Steed and Bhat (2000), Hunt and Patterson (1996) .For research on the day-to-day variability in the commute-timing decisions, the reader is refe rred to Mahmassani and Chang (1986), Mannering (1989), Hamed and Mannering (1989), and Saleh and Farrell (2005). Section 2.1 presents the synthesi s of the literature from a methodological standpoint. Later, Section 2.2 presents the empirical findings documented in the literature on departure time choice of individuals. This is followed by a summary Sec tion 2.3 that identifies th e shortcomings in the literature that this study intends to address. 2.1 Methodological Issues Table 2-1 lists several studies that have developed em piri cal models for home-to-work commute timing decisions. All these are disaggregat e models and capture the effects of several factors such as individual and household so cio-economic character istics, employment characteristics, residential and work location characteristics, and the transportation system characteristics. Four important dimensions of these studies are identified in this table and discussed below: The model structure used The temporal resolution of the choice alternatives The source and temporal resolution of th e inter-zonal travel-time data, and Incorporation of schedule de lay in the specifications.

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14 Table 2-2 lists several even ing commute and non-work studies that have relevantly contributed to the methodology of the departure time choice in our context. From the Table 2-1 and Table 2-2 several broad observations can be made. 2.1.1 Model Structure Employed On exa mining the model structure employed, we find that almost all studies have used the unordered discrete-choice methods (such as the multinomial and nested-logit models). These approaches do not capture the i nherently ordered nature of time and hence could lead to undesirable patterns (such as the equal proportional draws) in the departure-time shifts due to transportation system changes. Gadda and Kockelman (2007), however, develop continuous time models using the accelerated fa ilure time specification. Several studies modeled departure time using further advanced econometric frameworks such as hazard duration stru cture (see Bhat and Steed 2002) or OGEV models (see Steed and Bhat 2000) but in the context of non-work trips. For a comprehensive synthesis on the various other approaches to departure time the reader is referred to Xia and Chiao (2008). 2.1.2 Temporal Resolution of the Choice Alterna tive The second issue of interest is the temporal resolu tion of the choice a lternatives. Models developed by Purvis (1999) and Pendyala (2002) include few aggregate time periods as alternatives, but the a lternatives collectively span the entire day. On the other hand, models developed by Abkowitz (1981), Small (1982), He ndrickson and Planck (1984) and Chin (1990) incorporate a finer temporal re solution of the alternatives (5-15 minutes) but focus only on specific parts of the day. Thus all these models have rela tively less number of choice alternatives and hence could be estimated easily using the MNL structure. However, when the discrete departure time periods have fine temporal resolutions and, together, have to span the entire day, then the number of choice alternatives increase. This can be problematic to address

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15 within the MNL framework as it would involve the estimation of a large number of parameters. To address this, functional approximations to alternative-specific parameters have been employed (Hess et al. 2005; Vovsha and Br adley 2004, Cambridge Systematics 2004a; and Guo et al. 2005). 2.1.3 Temporal Resolution of the Inter-z onal Travel Time Data The third issue that needs to be addressed with increasi ng temporal resolution is the availability of inter-zonal travel time data at a fine temporal resolution. Some studies including the continuous-time models of Gadda and Ko ckelman (2007) did not include time-varying transportation system characteristics. Many of th e past studies have used peak and off-peak skims from equilibrium assignments. Thus, the trav el times are available only at an aggregatelevel even though departure time choice alternatives themselves are at a finer resolution. Other researchers have used methods su ch as interpolation between the peak and off-peak skims and explicit field data collection for developing the travel-time measur es at the required time-of-day resolution. The most rigorous methodology to da te involves the development of regression models of travel time as a function of time-of-day using data from household travel surveys (Cambridge Systematics, 2004b). 2.1.4 Incorporating the Concept of Schedule Delay One of the objectives of this cu rrent research is to also model fixed-schedule workers, and therefore incorporation of schedule-delay assumes cr itical importance. It is useful to note here that the past empirical models that account for schedule delay (using primarily the multinomiallogit structure) have had explicit data on the desire d work start times (see for instance, Coslett et al. 1977; Abkowitz 1981; Small 1982, and Hendricks on and Planck, 1984). However, such data are not commonly available from co nventional household travel surv eys (such as the one used in this study) that are most widely used for developing models for transpor tation planning purposes.

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16 Therefore, Ben-Akiva and Abou-Zeid (2007) have recommended a theoretical modeling approach assuming latent work-start-time prefer ences. One alternative approach was to use market segment specific utility functions of time-of -travel. The second one is to use a probability density function of the latent desired time-of-travel. Although there are few studies which incorporate the concept of schedule delay by using a stated prefer ence dataset (Hunt and Patterson 1996; Hess et al. 2004). 2.2 Empirical Findings Our prim ary focus is the departure time of mo rning home-to-work commute journeys. This section describes in de tail the factors that influence the departure time choice of morning commute. It is important to note that these studies have used different universal sets of timeof-day choice alternatives. Als o, difference exists in terms of modeling the journey to work as trips and as joint home-to-work and work-to-home tour while making the departure time choice decision. Moreover, differences in terms of modeli ng the departure time to work from home or modeling arrival time at work, data set used (Revealed preference da ta or Stated preference data) should also be noted. Due to thes e differences, it is not easy to generalize the impacts of the explanatory variables on the depart ure time choice of commuters. Table 2-3 presents a summary of the empirical factors included as e xplanatory variables in the literature of departure tim e choice of morning commute. These factors may be broadly classified into the following categories: (1) Individual Socio-Economic Characteristics, (2) Household Socio-Economic Charac teristics, (3) Employment Characteristics, (4) Transportation System Characteristics, and (5) Commute Characte ristics. In the next several paragraphs, the impacts of each category of factors are discussed in detail.

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17 2.2.1 Individual Socio-Economic Characteristics Am ong the individual socio economic characteris tics, age impacted departure time choice. Specifically, older workers (greater than 50) were found more inclined to depart so as to arrive earlier than the official work start time (Abkowitz 1982, Manneri ng 1988, and Bhat 2005). Female with kids was often involved in dropoff activities at school and hence chose early departures (Abkowitz 1982, Saleh and Farrell 2005) But on the contrary, Chin (1990) reported that employees with longer commute were generally male and hence chose early departures so as to get to work on time. According to Vovsha ( 2004) relative to children age 6-15, children of age 16+ tend to leave home earlier. Ve ry few studies explored the im pact of ethnicity; it was found (Bhat 2005) that more Afro Americans chose early departure to work. High income workers showed a tendency to choose early departures (Pendyala 2002). Students preferred later departures, which might be reflectiv e of the fact that most jobs taken up by students are part time jobs which are normally scheduled in the later periods of the day. 2.2.2 Household Socio-Economic Characteristics The next set of factors is the household leve l socio-econom ic characteristics. The presence of kids or higher household size favored earlie r departures (Pendyala 2002, Mannering 1988). It was expected that because of fewer family dema nds single workers are more flexible in their preference with regard to early arrival. But this could not be statistically established (Small 1982). Purvis (1999) and Cambridge Systematics (2004) implied that commuters from higher income households chose to travel in the p eak period (8 AM). Vovsha and Bradley (2004) indicated that tours made by high-income households (to CBD) were more likely to be of longer duration and are also less likel y to depart extremely early.

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18 2.2.3 Employment Characteristics On exa mining the employment related char acteristics it was found that longer work durations favored early departur es (Bhat 2005) and part time work ers chose later time periods to commute to work (night or evening shifts). Th e effect of part time or full time was more predominant for students (interac tion variables) as mentioned a bove. Similar effect was observed for work flexibility, availability of a flexible work schedule was considered important for people planning to arrive exactly on time and extremely im portant for those planni ng a late work arrival (Abkowitz 1982). Later departures were preferred by commuter s who have flexible work schedules (Hess et al. 2004, Cambridge System atics 2004, Guo et al. 2005). Occupation or the type of job played an importa nt role too, individu als employed in a professional, technical, management, or administration capacity typically a void departure such that arrival at work will be early (Abkowitz 1982). Small (1982) also conf irmed the affect that white collared employees were less averse to late arrival. 2.2.4 Transportation System Characteristics The effect of level of service variables was observed next. Longer travel tim es and travel cost in peak periods hindered commuters to depart in such periods. Small (1982) found that urban commuters were willing to alter their schedule s in order to save travel time to work. Chin (1990) further reinforced this issue by concl uding that commuters would not mind an early departure to work in order to avoid congestion. Si milar results were obtaine d in other studies as well. 2.2.5 Commute Characteristics Commute charac teristics like mode also infl uenced the departure time choice to work. Auto travelers were found more likely to plan on arriving at work exactly on time, while bus travelers were not likely to depa rt so as to arrive extremel y early for work. Small (1982)

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19 confirmed through his specifications that the need to match thei r schedules with other riders could make the car pool commuters to arrive ea rly at work. Moreover, Hendrickson and Planck (1984) concluded that departure time decisions were found to be more flexible than mode choice decisions which have large implications on policy measures. 2.3 Summary of the Literature The synthes is of literature presented in th is chapter highlights that commute-timing decisions have been predominan tly modeled using the MNL structure. However, the increasing need for finer temporal resolution has raised th e issues of identifica tion, interpretation, and computational effort involved in estimating the numerous parameters that go into the utility equations. To address this problem within the MNL framework, functional approximations have been suggested to reduce the number of alternativ e-specific parameters. An alternate approach for modeling commute-timing at a fine temporal resolution is to use continuous-choice methods such as the hazard-duration structure. However, such methods have not yet been adequately explored in the context of time-of-day decisi ons for commute. Hence, we contribute to the literature by developing continuous -time hazard-duration models for commute departure-time decisions. The second issue that needs to be addressed with increasing temporal resolution is the availability of inter-zonal travel time data as a continuous function of time-of-day. In the past, researchers have employed methods such as explic it field data collection, interpolation between the peak and off-peak skims, and regression m odels based on travel su rveys to develop the required time-of-day specific trav el time measures. In this stu dy, we develop and estimate interzonal travel time models which produce travel durations as a function of time-of-day using travel-survey data. These are further used as inputs to the commute-timing models.

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20 Further, this study also contri butes to the understa nding of systematic differences in the commute-timing decisions across population groups. Specifically, the empirical models developed incorporates several explanatory factors such as individual and household socioeconomic characteristics, employment character istics, commute characte ristics and land-use patterns to capture heterogeneity in the departure time preferences and also in the response to changes in transportation system characteristic s. Finally, this study presents the empirical analysis of modeling the departure time choice incorporating the c oncept of schedule delay in the absence of preferred work start times in the dataset.

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21Table 2-1. Overview of morning commute-timing models Choice Alternatives Inter-zonal Travel Time Sl.no Key Citation Dataset (Sample size) Model Type Arrival / Departure Temporal Resolution Temporal Resolution Data Source Schedule Delay incorporation 1 Man Mannering and Hamed (1988) 1987 Survey conducted in Seattle (117 commuters) Poisson regression Morning departure to work from home NA NA User provides information on travel time on the most frequently used/alternate route None 2 Pu Purvis C (1999) 1990 San Francisco Bay Area Household Travel Survey BL Departure time for home-work trips AM peak (6:30 8:30) or not Same as choice alternatives Network skims None 3 Ro Pendyala (2002) Tampa Bay Household Travel Survey (3208 HW trips) MNL Mid point time of home-to-work trips Morning peak (7:15 9:15), midday (9:15 to 3:15), afternoon peak (3:15 6:15), and off peak (6:15 PM to 7:15 AM) None None None 4 Ab Abkowitz, M D. (1981) 1972, San Francisco Bay area survey (425 commuters) MNL Arrival time at work Twelve 5 min intervals (42.5 min before to 17.5 min after work start time) Same as choice alternatives Linear interpolation between peak and off-peak skims Linearly 40 min early to 15 min late from official work start time 5 Sm Small, K A. (1982) 1972, San Francisco Bay area survey (527 commuters) MNL Arrival time at work Twelve 5 min intervals (42.5 min before to 17.5 min after work start time) Same as choice alternatives Floating car observations on major expressways Linearly SDE and SDL and its interactions on family type, occupation, flexibility 6 HP Hendrickson, Chris, and Edward Plank. (1984) Pittsburg, Pennsylvania (1800 commuters) MNL Departure time for home-work trips Seven 10-minute discrete periods (from 6:40 to 7:40) with four modes Same as choice alternatives Quadratic travel time function estimated using several vehicle trips to the CBD Quadratic terms for later and early arrival

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22Table 2-1. Continued Choice Alternatives Inter-zonal Travel Time Sl.no Key Citation Dataset (Sample size) Model Type Arrival / Departure Temporal Resolution Temporal Resolution Data Source Schedule Delay incorporation 7 SF Saleh and Farrell (2005) 2002 SP Survey conducted in Edinburgh (658 observation) MNL Morning departure to work from home No change, depart earlier than usual, depart later than usual NA Travel time savings given in the stated preference experiment Single linear SD term 8 Ch Chin, Anthony T. H. 1983 household survey in Singapore (956 commuters) Nested Logit Departure time for home-work trips Eleven 15 min intervals from 6 am to 8.45 am classified into "very early", early", and "morning" nests Peak and off-peak Network skims Single linear SD interacted with gender, occupation, income, CBD dummy 9 HPB Hess, S., Polak, J.W., Bierlaire, M. (2005) 2000, Dutch National System (1000 travelers) MNL with functional approximations to alternative specific constants Departure time for home-work trips 24 one hour time periods (full day) Unknown Unknown None 10 VB Vovsha, P., and Bradley, M. (2004) 1999, Mid-Ohio region household travel survey (6005 work tours) MNL with "continuous shift" specification of the utilities Departure-fromhome and arrivalback-home time for each tour 19 one-hour periods (5 AM 11 PM) with a total of 190 departure/arrival combinations) 4 discrete periods ( am peak, midday, pm peak and night) Network skims None 11 CS Cambridge Systematics, Inc (2004) 2000, San Francisco Bay area survey (21675 person-days) MNL with functional approximations to coefficients on alternative specific variables Departure time for work tours 35 time periods (33 half hour and 2 extreme long duration intervals) with a total of 630 departure /arrival combinations) Same as choice alternatives Travel time regression by time of day using household travel survey None

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23Table 2-1. Continued Choice Alternatives Inter-zonal Travel Time Sl.no Key Citation Dataset (Sample size) Model Type Arrival / Departure Temporal Resolution Temporal Resolution Data Source Schedule Delay incorporation 12 BhCS Guo, J.Y., S. Srinivasan, N. Eluru, A. Pinjari, R. Copperman, and C.R. Bhat (2005) 1996 Dallas Fort worth household travel survey MNL with functional approximations to coefficients on alternative specific variables Arrival time at work 32 time periods (with a total of 528 arrival / departure combinations) Peak and off-peak Network skims None 13 HPDH Hess, Polak, Daly & Hyman (2006) 3 SP surveys conducted in UK & Holland Error component logit Segmented models for commute, business, other tours Base, retime early, late, switch mode, no travel Unknown Unknown Linear SDE, SDL terms 14 BhHD Bhat, C.R., Srinivasan, S., and Guo, J. (2002) 1996 Dallas Fort worth household travel survey Hazard-duration model Arrival time at work Full day was discretized into 32 time periods None None None 15 GK Gadda, Shashank and Kara Kockelman (2007) 1996, Austin, Texas survey (1717 home-work trips) Bayesian estimates using accelerated failure time specification Departure time for home-work trips Continuous time None None None 16 KL2 Kumar and Levinson (1993) 1990 Montogomery county, Maryland data Binomial logit Full day: Work and Non work trips Peak (3.30 pm to 6.30 pm) and shoulder Same as choice alternatives Network equilibrium skims with feedback NA

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24Table 2-2. Overview of othe r time-of-day choice models Choice Alternatives Inter-zonal Travel Time Sl.no Key Citation Dataset (Sample size) Model Type Arrival / Departure Temporal Resolution Temporal Resolution Data Source Schedule Delay incorporation 1 MH McCafferty and Hall (1982) 1997,Survey in Hamilton, Ontario (<200 households) MNL Departure from Work to home Peak/off-peak; Pre, peak & Post peak; Peak (4.30 pm to 5.15 pm), shoulder, off-peak Same as choice alternatives Speed and delay studies (Constant travel times in each time period) None 2 MC Mahmassani & Chang Simulation experiment with different values of parameters in the simulation Macroscopic traffic simulation Dynamics of departure to work Departures on a 14 min time interval Continuous time scale (measured as departure rate or veh/hr departing) From simulation and heuristics (myopic and learning models) Assumed distributions for SD with mean (5 10 15 min) and constant desired work arrival time of 8 AM 3 Jot Jotinsaka, Hess and Polak (2004) Simulated data sets MNL, Mixed Logit Modeling departure time of a generic trip 1 min to 30 min levels of aggregation (6.30 am to 9.30 am departures) Same as choice alternatives Weights for generating congested skims from free flow skims Constant desired arrival time of 9 am assumed 4 BhSt1 Steed and Bhat (2000) 1996 Dallas Fort worth household travel survey MNL and OGEV Social recreation (3178 trips) and Shopping trips (2056 trips) Morning, am peak (6.30 am to 9 am), am, off-peak, pm, pm peak (4 pm to 6.30 pm), evening Peak and off-peak Network skims None 5 HPa Hunt & Patterson (1996) Stated preference experiment, Calgary, Canada (635 observations) Exploded Logit for arrival at the movies Departures such that travel time, SD are certain chosen values NA NA Expected travel time values (10, 15, 30 min) Expected SD (5, 10, 30 min) and the prob of that SD (5, 10, 20 %) 6 BhSt2 Bhat and Steed (2002) 1996 Dallas Fort worth household travel survey Hazard-duration model Departure time for Shoppin g trips Continuous time (15 min resolution empirically) Peak and off-peak Network skims None 7 HaM Mannering and Hamed (1989) Survey conducted in Seattle (204 commuters) MNL for occurrence, Poisson regression for frequency, hazard duration for duration of delay Occurrence, frequency and duration of departure delay from work to home (pm commute) No change, depart early, depart later NA Network skims None

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25Table 2-3. Factors impacting morning commute-timing decisions KEY Explanatory Factor Pu Man Ro Ab Sm HP SF Ch HPB VB CS BhCS HPDH BhHD GK KL2 Individual Socio-Economic Characteristics Age Yes Yes Yes Yes Yes Gender Yes Ethnicity Yes Yes Individual income Yes Education level Yes Yes Student Yes Yes Household Socio-Economic Characteristics Mother Yes Yes Presence/Number of kids Yes Household structure/size Yes Yes Yes Yes Household income Yes Yes Yes Yes Yes Employment Characteristics Work Duration (Part-time/Full time) Yes Yes Yes Yes Yes Yes Flexibility Yes Yes Yes Yes Yes Yes Yes Occupation Type Yes Yes Yes Yes Industry Type Yes Yes Self employed Retired Transportation System Characteristics Travel Time Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Travel Cost Yes Yes Yes Yes Yes Transit Seat Availability Yes Distance Yes Yes Yes Yes Schedule Delay Late / Early Arrival at Work Yes Yes Yes Other factors Mode/Number of vehicles Yes Yes Yes Yes Yes Yes Land-use at origin / destination Yes Yes Yes Yes Season of the year Yes

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26 CHAPTER 3 INTER-ZONAL TRAVEL TIME MODEL The contents of this chapter describe the modeling of inter-zonal travel times which will serve as inputs to the commutetiming model discussed in the late r chapters. Section 3.1 presents the need for estimating the inter-zonal travel times as a function of time of day from survey data. Section 3.2 describes the dataset that has been used for the estimation. Section 3.3 presents the econometric modeling framework followed by a disc ussion of the empirical results in Section 3.4. Section 3.5 concludes this chapter with a summary. 3.1 Need for an Inter-Zonal Travel Time Model Usually, th e level-of-service variables (peak and off-peak travel time and costs) are obtained by performing equilibrium assignments on the transportation network for the peak and off-peak periods. Treating time of day as merely two discrete peak and off-peak time periods limits our ability to capture the variation of traffi c congestion over the entire day. This limits the estimation of advanced continuous-time models, whic h require inter zonal travel times at a finer temporal resolution. One solution to counter this problem is to run the equilibrium assignment for several time periods. But this would give ri se to several problems. Firstly, the travel time profiles may not be continuous across the time periods. Secondly, running so many static equilibrium assignments is a very time consumi ng process. Thirdly, as the temporal resolution increases there will be demand spillover across ti me periods (i.e. all the demand in a single timeof-day discrete time period may not be assigne d to that time period) which require dynamic assignment techniques which are even more time c onsuming. An alternative approach to address is to develop models using reported travel time s from household travel survey data. Further we can also use the free flow and peak period tr avel time obtained from the aggregate time equilibrium assignments as the independent variables. This will be discussed later in this chapter.

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27 Therefore the objective of this chapter is to model travel time duration of a trip between any two zones as a function of network characteris tics and time-of-day of departure of the trip. These estimated travel time durations functions (ins tead of just the aggregate peak and off peak travel time measures obtained from equilibrium assignment on the network) are incorporated into the continuous time models to better capture the effects of congesti on across different time periods in a given day. 3.2 Data The San Francisco Bay Area Travel Surv ey (BATS) conducted in the year 2000 by MORPACE Intern ational Inc. for the Bay Area Metropolitan Transportation Commission (MTC) is been used in this study. The nine county San Francisco Bay Area was divided into 1000 traffic analysis zones (TAZs) for this purpose. Activity information for two days was recorded from each of the respondent using an activity diary and the Computer Assisted Telephone Interview (CATI) method for recruitment and retrieval. The information was finally structured into four files namely the household file, person file, vehicle file and activity file. The household file provides information on the household level soci o-economic characteristics like household size, number of children in the household, household income, location of the household, number of vehicles in the household and family struct ure of 14529 households. On the other hand, the person file provides information on individual level socio-demographi c characteristics like gender, age, employment stat us, ethnicity for the 33402 member s who participated in this survey. The vehicle file comprises information li ke make, model, year, and odometer reading for each vehicle owned by the surveyed households. Lastly, the activity file provides detailed information on activity purpose, location of ac tivity participation (inc luding latitude and longitude), start and end time of the activity.

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28 These data were further augmented with land-u se and level-of-service files obtained from MTC. The zonal characteristics of the TAZs lik e employment density, ho usehold density, area type (CBD, urban, suburban and rural), land-use mix index were included in the land-use file. The network characteristics like peak and off-peak travel time, travel cost and distance between zones were provided in the level-of-service file. The data assembly for the estimation of the inter-zonal travel time models included the following steps: First, weekday, inter-zonal, auto trips were extrac ted from the survey. The auto trips refer specifically to those in whic h the corresponding respondent i ndicated that he/she was the driver of the vehicle.Each trip is characterized by the start and end times (on a continuoustime scale), and the origin a nd destination locations (in te rms of the Traffic Analysis Zones, TAZs). The reported trip duration was calculated as the difference between the endand start-times of the trip. Second, for each trip, the corresponding inter-zonal free-flow and peak-period travel times and distances were added from th e level-of-service file. Third several consistency checks were performed to remove outliers and inconsistent information. Specifically, we removed trips for which the reported trip durations were less than one fourth or greater than four-times the corresponding free-flow travel times. The travel times in surveys are often reported fo r door-to-door travel whereas the free-flow travel times (obtaine d from network skims) represent the travel time between zonecentroids. Therefore, there could be consider able mismatch between the reported and freeflow travel times depending on the size of the zones. The threshold values of the ratios used here are what we think as empirically reasonable for the BATS data and the Bay Area Zoning system used in this study. In addition, we also removed long trips (reported travel times > 2 hours or distance > 50 miles). However, it is useful to point out that these checks did not result in a substantial reduction in the size of the data sample. Fourth, the 24-hour day was divided into 96 15-minut e intervals (2:52 AM 3:07 AM, 3:07 AM 3:22 AM, 3:27 AM 3:37 M, and so on) i.e. th e midpoint of each interval is an integral multiple of 15 minutes. All trips between th e same origin-destination (OD) pair and departing within the same discrete time interv al were aggregated to obtain average values of travel times between the corresponding OD pair and the departure time period. This averaged travel time is used to construct th e dependent variable in the inter-zonal travel time model. Fifth details on the land-use at the origin and de stination locations were added. The resulting estimation sample comprises 68,801 records. Each record represents travel between a particular OD pair and departing at on e of the 96 discrete time periods.

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29 Figure 3-1 presents the plot of % departur es by time-of-day. Since there were not enough observations before 5.45 AM and after 10.30 PM th ey were removed from the estimations. The morning peak period occurs between 7 AM to 9 AM (18 % departures) and the evening peak occurs between 3 PM to 6 PM (35 % of departures ). It can be observed fr om the Figure 3-1 that a more people round of their departure times to th e nearest 30 minute than to the nearest 15 minute time slot. Hence the relatively higher percentage observed for time slot which are integral multiples of 30 minute than the adjacent time slot s. Figure 3-2 plots of the distribution of trips based on the travel duration. It can be observed th at 42.65 % of all the trip s have travel duration between 7.5 to 17.5 minutes. 3.3 Econometric Structure The em pirical structure for the inter-zonal tr avel-time model is drawn from the earlier work of Cambridge Systematics (2004b). The tr avel duration for a trip from origin zone i to destination zone j when departing at time t ( Tijt) is related to the free-flow travel time between the zones (fftij), peak-period travel ti me between the zones ( pktij), time-of-day of travel ( t ), and other factors ( X ) as given by the following structure: 2 212 12 12 12 0 12 12 12 12n nttt sin sin sin n ij ijt ij ttt cos cos cos ij nijtee +....e pkt lnTlnfftX fft ee....e 2 ijtWhere, )~N( 0, (Equation 3.1) In the above equation, 0 represents the constant term in the regression equation. X is the set of independent variables char acterizing the trip. For example, this set of variables could include trip distance and land-use characterist ics at the origin and destination locations. Is the vector of coefficients on the explanatory variables X. The impact of time-of-day on the travel

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30 time is captured via a set of sin and cosine terms. 1,2,.., n and 1,2,.., n are the coefficients on these trigonometric terms. The number of such terms to be included (i.e., n) is determined empirically based on the mode l fits and the reasonabl eness of the profiles implied by the specifications with different values of n. The peak-period travel time is obtained from static equilibrium assignment using the peakperiod OD trip-table. Whereas, the free flow travel time is a function of the distance and the transportation system characteristics. The ratio of the peak to the free-flow travel times is included in the model to capture the effect of time-varying travel-demands between the zonalpair on the variation of travel times over the day. As mentioned earlier, if the peak-period travel time were available at a finer temporal resolution (say 4 time periods) they can be incorporated into the estimations too. The ln of the ratio ensures that the predicted travel times are always positive. An alternate piecewise linear specificati on (dummies from time-of-day) was also estimated. That specification did not provide smooth and continuous plot for travel time by timeof-day (kinks in the plot) which could have implications on the commute-timing models. 3.4 Empirical Results A segm entation approach was adopted to allo w for the travel durat ion profiles (over the day) to vary spatially and based on trip lengths. For this purpose, the data were first divided into the following four subsets based on inter-zonal di stance: 0-5 miles, 5-15 miles, 15-30 miles, and 30-50 miles. Within the second and third distance categories, data were further segmented into four groups based on the trip-end location characteristics. That is we identify whether the trips

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31 (1) originate and end in the urban region (density1 > 30), (2) originate in an urban region and end in a suburban region (density < 30), (3) originate in a suburba n region and end in an urban region, or (4) originate and end in a suburban region. Such segmentation was not possible in the fourth distance category because of lack of data and deemed unn ecessary in the first distance category (0-5 miles) because of very limited varia tions in travel times ov er the day. However, the trip-end location characteristics were included as explanatory variables in the models estimated for the first and fourth distance categories which yielde d statistically insignificant coefficients. Overall, ten regression models we re estimated and the best specifi cations are presented in Table 3-1. Note that thet statistics have been suppres sed in the table to avoi d clutter and all reported estimated are statistically significant at at-least 90% level. The impact of time-of-day on the travel time is captured via a set of sin and cosine terms. As the coefficients on these sin and cosi ne terms cannot be interpreted individually, we present the variability of travel time by time-of-d ay as implied by the models in the form of four illustrative graphs (Figure 3-3). In Case 1 (short distance trips with distance = 2.2 miles, free flow travel time = 7 minutes and peak travel ti me = 8 minutes) we find practically no variation in the travel duration over the entire day. Parameters from the first column in Table 3-1 are used in this plot. Cases 2 and 3 represent longer tr ips (distance = 9 miles and free flow time = 15 minutes, and peak travel time = 30 minutes) exhi bit more variability (up to about 10 minutes over the day). Further, the trips from suburban to urban regions (case 2) ha ve higher travel times during the morning peak period compared to an identical (i.e., equal length) trip from urban to suburban regions (case 3). In c ontrast, the duration for travel from urban to suburban regions is higher during the evening peak co mpared to an identical trip in the opposite direction. Finally, 1 Density is defined as (Total population in the zone + 2.5 Employment in the zone) / ( Residential + Commercial/Industrial Acreage)

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32 case 4 represents a trip identical in all aspects to case 3 (9 mile tr ip from urban to suburban with free flow time = 15 minutes) excep t for a higher peak travel time (45 minutes). In this case we find a larger variation in travel time over the day compared to case 3. Parameters from the third and fourth columns in Table 3-1 were used to pl ot the graphs as shown in Figure 3-2 for travel from urban to suburban and suburban to urban respectively. 3.5 Summary The need for developing the Inter-zonal trav el tim e models was presented. Later the econometric structure of the mode l was presented. The models were estimated using data from the 2000 San Francisco Bay Area Travel Survey. Th e regression models for inter-zonal travel times produce smoothly time-varying travel duration pr ofiles that capture the effects of temporal and spatial congestion ap propriately. The empirical specifications were discussed in detailed. These models will serve as inputs to the commute timing models which will be discussed further.

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33Table 3-1. Empirical results: Inter-zona l travel duration regression models 5-15 miles 15-30 miles 0-5 miles OriginUrban & Dest-Urban OriginUrban & DestSuburban OriginSuburban & Dest-Urban OriginSuburban & DestSuburban OriginUrban & Dest-Urban OriginUrban & DestSuburban OriginSuburban & Dest-Urban OriginSuburban & DestSuburban 30-50 miles 0 1.295 1.135 1.152 1.076 1.051 1.032 1.059 1.057 0.955 1.088 distance -0.044 -0.007 -0.007 -0.005 -0.007 -0.001 -0.004 -0.003 -0.002 -0.002 1 -0.066 -0.067 -0.085 -0.056 -0.052 -0.056 -0.074 -0.040 -0.045 -0.019 2 ------------------------------------------0.022 ---------------------3 0.086 0.088 0.101 0.092 0.082 0.071 0.077 0.057 0.080 0.023 4 ----------------------------------------------------------------------1 ------------------------------------------0.028 0.025 --------------2 0.086 0.120 0.108 0.133 0. 137 0.073 0.119 0.063 0.148 -------3 -------------------------------------------0.048 ---------------------4 -0.079 -0.108 -0.098 -0.121 -0. 113 -0.061 -0.097 -0.054 -0.118 0.017 Number of cases 35463 2656 4081 4010 10436 834 2321 2106 3932 2962 Adjusted R2 0.956 0.980 0.980 0.980 0.974 0.984 0.986 0.986 0.984 0.987 Note1: Only statistically significant variables are reported at 90 % CI Note2: The high Adjusted R2 values are due to absence of a cons tant term in the model specification

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34 0 0.5 1 1.5 2 2.5 3 3.5 45 0 0 6 0 0 7.00 8.00 9.00 1 0 0 0 1 1 0 0 1 2 0 0 13.00 14.00 15.00 16.0 0 17 0 0 1 8 0 0 1 9 0 0 2 0 0 0 2 1 0 0 22.00 23.00Time of day% Departures Figure 3-1. Distribution of departure times by time-of-day

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35 13.71 20.84 21.81 11.48 6.03 11.03 2.78 2.36 3.34 6.62 0.00 5.00 10.00 15.00 20.00 25.000 < TD <= 7.5 7.5 < TD <= 12.5 12.5 < TD <= 17.5 17.5 < TD <= 22.5 22.5 < TD <= 27.5 27.5 < TD <= 32.5 32.5 < TD <= 37.5 37.5 < TD <= 42.5 42.5 < TD <= 47.5 47.5 < TD <= 120Duration in minutes% of Total trips Figure 3-2. Distribution of travel time duration

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36 0 5 10 15 20 25 30 35 40 455 0 0 6 0 0 7.00 8.00 9.00 1 0 0 0 1 1.00 12.00 13.00 14.00 15.00 16.00 17.00 1 8 0 0 1 9 0 0 2 0 0 0 2 1 0 0 2 2.00 2 3.00Time of the dayTravel time (min) Case 1 Case 2 Case 3 Case 4 Figure 3-3. Variation of inter-zonal travel du ration by time-of-day: Illustrative graphs

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37 CHAPTER 4 COMMUTE-TIMING MODEL FOR FLEXIBLE SCHEDULE W ORKERS This chapter describes in detail the methodology behind the comm ute timing model for workers with flexible work schedules. Section 4.1 describes the sample that has been used for the estimation of the hazard duration structure. Section 4.2 presents the modeling framework followed by a discussion of the results in S ection 4.3. Section 4.4 summarizes the chapter. 4.1 Data As m entioned the primary source of data is the San Francisco Bay Area Travel Survey (BATS) conducted in the year 2000. The proced ure for assembling the dataset for estimating commute-timing models comprised four major tasks. In the first task, the home-to-work commute was extracted from the overall activity-diary of the respondent. The home-to-work commute includes the entire journey from home to work including any possible intermediate stops. This extrac tion began with identifying and characterizing (location, start ti me, mode of travel to episode, etc.) the first and last out-ofhome work episodes. This was followed by id entifying and characterizing (location, start time, etc.) the last in-home activity episode before the first work episode (the LHBFW episode). Next, all activity episodes before the LHBFW episode and those after the first out-of-home work episode were removed. The re tained activity episodes constitute those undertaken during the home-t o-work commute. Further processing was done on the commute activities to determine additional char acteristics of the commute such as number of stops, activity type at the intermediate stops, and journey duration. All commute characteristics were then compiled into a home-to-work commute file. In this file each record represents a commute journey and is completely characterized by home location, work start location, departure tim e to work, work start time, m ode used in various legs of the journey, number of stops, and activity type during the stop making. In the second task, relevant household-, indi vidual-, residential-, and level-of-service characteristics from the appropriate data files were adde d to the home-to-work commute file. The third task involved cleaning to remove reco rds with missing, outlier, and/or inconsistent data. For example, working spending less than 30 minutes at an out-of-home location for work or traveling for more than 2 hours to work were removed. In addition, only cases that had the complete data on all the relevant explanatory variable s were retained. In the final fourth task, restrictions were im posed to define the empirical scope of the study. Specifically, only weekday auto-based commute s of full time, workers aged 18 years or older are retained in the final estimation sa mple. Further, we also retain only those

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38 individuals who had two or fewer work epis odes during the day and a single out-of-home work location. That is, we do not include work ers who undertake a lot of work-based travel in our analysis. It should also be noted th at we restricted to only inter-zonal commute journeys. All the above tasks were performe d for all workers i.e. workers with both flexible and fixed work schedules. This chapter is focused on a subset of the above data that reports fully flexible workers. A user is said to have full flexible work schedule when the individua l has complete freedom to start and end work at will. On the other hand a fixe d schedule worker does not have any freedom to alter the work start and end times. The co rresponding dataset comp rises of 4008 commute journeys to work obtained fr om 2742 persons and 2536 households. 15 % sample (615 records) of the 4661 commute journeys is set aside for the demonstration exercise which is discussed in the later sections. This leaves 3393 commute j ourneys to work obtained from 2496 persons and 2328 households for the estimation. Descriptive statis tics on selected explan atory variables from the above estimation dataset are presented in Table 4-1. Note that the mean and standard deviation are presented for c ontinuous variables (such as ag e, work duration, and household income) and the sample shares (percentages) ar e provided for categorical variables (such as ethnicity and household structure). In general we find that the fu lly-flexible, full-time workers analyzed in this study are middle-age d, more likely to be men, and hold executive/managerial/professional positions. The sample also includes considerable numbers of single-person households and indi viduals of Asian ethnicity. The commute timing profile (i.e., the percentage of departures to work in the estimation sample during each discrete time-of-day period) is presented in Figure 4-1. The mid-point times of the discrete periods are presented in the X-axis That is, 5:30 refers to departures between 5:23 AM and 5:38 AM; 5:45 refers to departures be tween 5:38 AM and 5:53 AM, and so on. The bulk of the departures (60.5%) are concentrated in the 7-9 AM pe riod with peaks at 7:30 and 8:00 AM. Few people leave before 5:30 AM or after 10:30 AM. The reader will also note that

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39 departures at half-hour periods (i.e., 6:30, 7:00, 7:30, 8:00, and so on) are generally higher perhaps reflecting inherent biases in the report ing of departure times in travel surveys. 4.2 Methodology This section presents the hazard -duration structure for modeling the commute-timing (i.e., departure time) decisions. The model has a pr oportional-hazard structure incorporating the effects of the exogenous covariates in a multip licative form, a non-parametric baseline-hazard distribution, and a parametric (gamma distri bution) control for unobserved heterogeneity. Further, the model structure captu res the impact of time-varying c ovariates (in this context, the home-to-work travel times vary as a function of time-of-day). Overall, the model structure adopted here is similar to the one adopted in Bhat and Steed (2002) However, we do not incorporate time-varying coefficien ts as these authors do. In this rest of this section, the model structure is presented in our application context. The hazard for departing to work at any time of the day u (measured on a continuous scale, say in minutes from 3 AM) is defined as the probability that a worker will depart immediately after time u conditional on not departing until time u. This hazard is assumed to have the following functional form: 0()()exp uuXZuw (Equation 4.1) In the above equation, 0()u is the baseline hazard. X and Z(u) are vectors of non-time varying and time varying covariates respectively. For example, X could include the sociodemographic characteristics of the worker whereas Z(u) includes the travel times / speeds between home and work locations at time u. and are the vectors of coefficients on the nontime varying and time varying covariates respectively. w is the unobserved heterogeneity term assumed to follow a gamma distribution (with variance = 2 ) and independent of the covariates.

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40 As already indicated, we adopt a non-parametri c distribution for the ba seline hazard (i.e., 0() u ) in our specification. For this purpose, we discretize the continuous time into K unique time intervals. Let p denote the index for the time intervals (p = 1, 2,, K) and pa represent the upper bound time corresponding to discrete interval p. Therefore discrete period p represents the time interval [1 pa, pa] and the duration of this discrete period is given by, p = 1 ppaa The baseline hazard is then assumed to be a cons tant within each of th ese discrete periods (i.e., 0()u = exp(p ) if u element of discrete period p). In addition, we assume that the value of timevarying covariates remain constant within each discrete time period (i.e., Z(u) = p Z if u element of discrete period p). The survival function, S(u), is defined as the probability th at the worker did not depart to work until time u and is given by the following expression: ()exp() pa pSa udu (Equation 4.2) 0()expexpexpp pjjj jSa XZw (Equation 4.3) The probability that a worker de parts in discrete time period p conditional on the unobserved heterogeneity term w is therefore given by: 1 1Prob[]|Prob[ ]| ()|()|pp pptpwauaw SawSaw (Equation 4.4) The unconditional probability of departure in interval p is given by (See, Bhat and Steed, 2002 for details)

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41 2 21 2 0 2 0Prob[]1exp 1expp jjj j p jjj jtp XZ XZ (Equation 4.5) Where 0 and K 4.3 Empirical Results The em pirical results of the hazard duration mo del for departure time choice are presented in Table 4-2. The set of explanatory factors incl uded in the model specification can be broadly classified as follows: (1) I ndividual and Household SocioEconomic Characteristics, (2) Individual Employment Character istics, (3) Day of the Week, a nd (4) Location Characteristics, and (5) Transportation System Characteristics. Each of these sets of variables is discussed in detail below. Consistent with the notation speci fied in the formulation, a positive coefficient on a time invariant covariate increases the hazard and hence increases the like lihood of departure at any time. Therefore, a positive coefficient can be interpreted, in general, as favoring earlier departures. The interpretation of the coefficients on time varying c ovariates is described later. 4.3.1 Individual and Household Soci o-E conomic Characteristics Among the set of individual-level socio-economic characteristics, only age impacts the choice of departure time. The coefficient on age is positive which means that older individuals are more likely to depart in the earlier time pe riods. Other characteri stics like ethnicity and gender were also tested but we re found to be insignificant. The income of the household as well as th e household composition is found to impact commute departure time choice. Specifically, we find that flexible full-time workers from higher income households depart later compared to iden tical individuals from lower income households. Workers in single-person househol ds are found to be most likely to depart the latest. Workers

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42 from couple households depart earlier than the ab ove persons but later th an individuals from nuclear family, single parent, or any other type of household. Thus, it may be observed that individuals in households with ch ildren depart the earliest for work. This is perhaps because of their need to chauffer children to school on the wa y to work. In fact, we did explore the inclusion of a variable indicating whet her the individual undertakes a drop-off activity during the commute. However, this was found to be insi gnificant after contro lling for the household structure (but was significant with the positive sign in anot her model without the household structure variables). Finally, the commute departure time decisions of flexible workers are also influenced by the presence of other non flexible commuters in the household. Specifically, the flexible worker is likely to depart earlier if another inflexible worker is also present in the household. This intrahousehold interdependency might be broadly capturing the desire of household members to synchronize their work timings perhaps to facilita te joint leisure pursuits during the later part of the day. 4.3.2 Individual Employment Characteristics Work duration, work frequency, and the occ upation type are indivi dual-level em ployment characteristics found to determine the departure time choice for commute travel. Individuals who work long hours during the day also depart earlier for work, perh aps reflective of the overall time-budget constraints. Persons who do not travel to the out-of-home work location all five days of the week are found be more lik ely to depart later in the day. This is possibly reflecting a greater degree of flexibility in the work schedules of such pe rsons among all flexible full-time workers. Finally, the occupation type of the person strongly in fluences the choice of commute departure time. Specifically, indi viduals employed in a professiona l, technical, management, or

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43 administration capacity are more likely to depart later in the day. However, those employed as executives or managers depart earlier. 4.3.3 Day of the Week Individuals are m ore likely to depart earlier to work on Fridays compared to other four days of the work week. Perhaps, this is a manifestation of a desire to comp lete work earlier so as to have the evening available for the pursuit of leisure activities. 4.3.4 Location Characteristics The residentialand work-location characteristic s were tes ted in the specifications. It was found that only work location characteristics imp acted the departure time choices of individuals. Individuals working in the CBD are more likely to leave earlier. This is perhaps because of the overall higher congestion prevailing in CBD area dur ing the morning period. 4.3.5 Transportation System Characteristics The effect of tim e-varying transportation system characteristics on the choice of departure time is captures via the commute speed variable The commute speed when departing at time u is calculated as the ratio of commute distance to th e travel time between home and work zones at time u (this is determined from the inter-zonal tr avel time model discussed in Chapter 3). The model also allows heterogeneity in the sensitiv ity to speed by interacting it with a categorical distance variable. For short distance trips, we find that the choice of departure time does not depend on the transportation system characteristic s as indicated by a statistically insignificant coefficient on speed for distance = 0 5 miles For greater distances, we find a positive sign on the speed variables indicating that the probabi lity of departing home at a certain time (conditional on not departing earlier) is higher if the speed at that time is higher. Further, the sensitivity to speed is also greater for longe r commutes possibly reflec ting the potential for greater time savings.

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44 Note from equation 4-5 that the probability of departing during any discrete time interval is a function of commute speeds prevailing at all times until the discrete time interval under consideration and does not depend on the commute speed after the time interval under consideration. However, it is reas onable to expect that the probab ility that a person departs at a certain time is also dependent on future commute speeds. To captu re this effect, we introduced measures of future commute speeds as a s econd time-varying covariate in our model. Specifically, this future speed variable correspondi ng to any discrete period is calculated as the difference between the commute speed during the next time period (say 15 or 30 minutes) and the current period as a percentage of the curren t speed. A negative coefficient on this variable could be expected implying that as the commute speed in the future increase relative to the currently prevailing times, the hazard for departure decreases (or a person is less likely to depart at a certain time if the commute speed in the futu re will be greater than the currently prevailing speeds). We explored the effect of this futu re speed variable at both 15 minute and 30 minute resolutions. However, these effects were not st atistically significant. Additional empirical research on how to capture the effects of futu re travel times on the departure time choice is required. The standard deviation of the unobserved hetero geneity term (gamma in Table 4-2) is estimated to be statistically different from zero. Th is reflects the strong pr esence of factors other than those controlled for in the model that infl uence the departure time choices of individuals. The baseline hazard for the estimated model is as shown in the Figure 4-2. It can be seen that the longer an individual wait s to depart for work, the more likely he/she is to depart. In other words, there is general positive duration dependence in the hazard function for departure to work.

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45 4.4 Model Application This section dem onstrates an application of the commute timing model in predicting the aggregate departure time patterns of a sample of individuals. For this exercise, we use the validation sample containing the 615 observations. Section 4.4.1 presents the aggregate predictions on the choice of departure time on the validation sample. Sections 4.4.2 and 4.4.3 describe the aggregate sensitivity of changes in non time-varying and time-varying characteristics to the departure time choice. 4.4.1 Aggregate Prediction of Departure Time Profiles We predict the averag e probability of the samp le choosing different choice alternatives across time-of-day from the estimates obtained and compare it against the observed distribution of departure time choice. It can be noted from Fi gure 4-3 that the distribution predicted from the model closely approximates the observed distri bution for the departure time choice of the individuals on an aggregate level. However, it can be found that the highest over-prediction is recorded at 6 AM at 1.65 % and the highest under-prediction of 2.24 % occurs at 8.30 AM. Overall, across the full day, the average over-p rediction and under-prediction were 0.57 % and 1.06 % respectively. It should be noted that the above numbers are calculated by taking the difference of the predicted and observed percentages. 4.4.2 Aggregate Sensitivity to Changes in Time-Varying Characteristics Further, we also test the im p act of change in commuting sp eed (during the peak hour 7 AM to 9 AM) on the departure time choice of the indi viduals. The various scenarios for the change in the commute speed during 7 AM and 9 AM (we call this time period as policy time period) include doubling the speed and re ducing the speed by half. The d ecrease in the commuting speed during the morning peak period may be due the in creased congestion effects and the decrease in speed might occur in the case of reversible lanes. Here again th e average predicted probabilities

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46 of all the individuals calculated for all the choice alternatives across the day are plotted. This is compared against the base case of no change in the speed variable. Figure 4-4 shows the impact of the change in a time varying covariate, in th is case the travel time. Figure 4-5 presents the cumulative departures as a function of time-of-day. Several observations can be made from the figures. Firstly the predictions pa ttern before start of the policy time period does not change. This as mentioned earlier is manifestation of the fact that hazard duration imp licitly doesnt recognize the impact of future time periods. The second observation that can be made is when the commuting speed in the morning peak period d ecreases in the policy time period, which is reflective of the increasing conge stion during the peak period, the fraction of people choosing to depart at the start of the conge sted morning peak period decrease s relative to base case of no change in the speed. In other wo rds individuals tend to move aw ay from the congestion as one would expect. Similarly if the commuting speed increases which may be reflective of a new reversible lane introduced in the direction of th e congested traffic in the morning peak period, the fraction of people choosing to depa rt at the start of the congested morning peak period increases as compared to the case when the speed doesn t change? However a hi gher fraction of the individuals have already departed at the start of the policy period increases (due to the increased speeds), we would expect lower de partures at the later time pe riods. These overall effects are more discernible in Figure 4-5 where the cumulative departures are plotted. It is clear that as the speed increases the fraction of people who have depa rted after the start of policy period is always higher than the base case of no change in the commute speeds. 4.4.3 Aggregate Sensitivity to Changes in Non Time-Varying Characteristics We also test the sensitivity of a non-tim e va rying covariate on departure time patterns of the individuals. The variable chos en for the purpose of demonstrati ng the impact of the change in a non time-varying covariate on the departure time pattern of the individuals is the binary

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47 variable for work frequency less th an or equal to four per week. In order to simulate the change in the data we randomly pick 15 % of the indivi duals whose frequency to work is greater than equal to four per week and convert these individuals to individuals with work frequency less than or equal to four per week. Since the percentage of population with increased flexibility to depart to work has increased in the population sample, we expect a general in creasing trend for later departures during the time-of-the-day. The effect can be observed from Figure 4-6 and Figure 47 (% departures and % cumulative departures as a function of time-of-day respectively). As the aggregate flexibility of the workers in the sample increases, it is easier to note from Figure 4-7 that at any given time across the time-of-day the fraction of individua ls that have already departed for work is lower than the base case. 4.5 Summary This chapter described the developm ent of continuous-time model for the home-to-work commute timing decisions of flexible full-time workers using the hazard-duration structure. Further, the estimated departure time choice model includes the effect of travel time at a fine temporal resolution of 15 minutes. In order to gene rate the travel time data at this resolution, the regression models developed for th e Inter-zonal travel times are used. The hazard duration model indicates a statistically significan t effect of commuting speed on the choice of departure time. Specifically, individuals are less likely to depart home at times when the commute speeds are lower. In addition, the model also captures the impact of several other explanatory factors on the choice of departure time to work. Further we al so presented a demonstration on how this model can be used for predicting the depa rture time patterns. This model application exercise also tries to present the sensitivities of the departure time patterns to the changes in the time varying transportation system and non-tim e varying characteristics.

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48 Table 4-1. Sample characteristics of full-time workers with flexible work schedules Attribute Statistic Attribute Statistic Individual Char. Household Char. Age 42.69(10.48)Number of persons Gender 1 18.42 Male 64.93 2 40.88 Female 35.07 3 16.00 Ethnicity 4 17.86 Caucasian 75.04 >=5 6.84 African American 2.30Number of vehicles Hispanic 3.92 1 22.40 Asian/Pacific islander 13.14 2 52.20 Other 5.60 3 19.07 Work duration in hours 8.46(2.41) >=4 6.34 Work frequency Number of children <5 days per week 8.58 0 64.87 >=5 days per week 91.42 1 14.85 Occupation 2 15.30 Exec/Managerial 29.33 >=3 4.98 Professional 44.50Presence of another fixed schedule worker Other 26.17 No 82.58 Transportation System and Land Use Char. Yes 17.42 Commute free flow time (mins) 18.77(10.33)Household structure Commute distance in miles 12.96(10.28) Single person 18.42 Area type of home zone Single parent 1.80 CBD (density >100) 1.18 Couple 34.04 Urban (density 30-100) 20.90 Nuclear Family 27.73 Suburban (density 6-30) 72.86 Other 18.01 Rural (density >6) 5.07 Area type of work zone Household Income in 1000s of $ 12.23(2.27) CBD (density >100) 10.88 Urban (density 30-100) 47.54 Suburban (density 6-30) 39.23 Rural (density >6) 2.36 The values mentioned are the mean (standard deviation) for conti nuous variables and the percentage shares for the categorical variables

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49 Table 4-2. Empirical results: Covariate effects fo r the hazard duration model for departure time choice of flexible schedule workers Variable Parameter Estimate t-statistic Individual and Household Socio-Economic Characteristics Age 0.0202 7.423 Household Income -0.0422 -3.469 Household structure Nuclear, Single parent, Other (Base) ------------Single person household -0.2956 -3.687 Couple married or unmarried -0.2167 -3.479 Presence of a non-flexible worker in the household 0.1261 1.751 Individual Employment characteristics Work duration 0.3112 19.009 Work frequency less than 4 days a week -0.5363 -5.519 Occupation Executive/Managerial 0.2025 2.731 Professional -0.1824 -2.784 Other ------------Day of the Week Day is Friday 0.1324 1.826 Location Characteristic Work location is CBD 0.1235 2.185 Transportation System characteristics Commute Speed (miles/hr) For distance = 0 5 miles -0.0049 -0.705 For distance = 5 -1 5 miles 0.0129 3.22 For distance = 15 30 miles 0.0211 6.642 For distance = 30 50 miles 0.0248 8.361 Gamma 0.8334 16.434 Number of cases 3393 Log Likelihood at convergence -9621.67 Log Likelihood at convergence for constants only model -10107.8

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50 0 2 4 6 8 10 12<= 5 1 5 AM 5.3 A M 5 4 5 AM 6 AM 6 1 5 AM 6.3 A M 6 45 AM 7 A M 7 1 5 AM 7.3 AM 7 4 5 AM 8 A M 8 1 5 AM 8.3 A M 8.45 AM 9 AM 9 1 5 AM 9.3 A M 9 45 AM 1 0 A M 10.15 AM 1 0 3 AM >= 1 0.45 AMTime of day% Departures Figure 4-1. Distribution of departure tim es for home-to-work commute by time-of-day of flexible schedule workers

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51 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 5.006.007.008.009.0010.00Time of the Day (AM)Hazard Figure 4-2. Estimated baseline hazard di stribution of flexib le schedule workers

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52 0.00 2.00 4.00 6.00 8.00 10.00 12.005 1 5 A M 5 3 A M 5 4 5 A M 6 A M 6 1 5 A M 6 3 A M 6 4 5 A M 7 A M 7 1 5 A M 7 3 A M 7 4 5 A M 8 A M 8 1 5 A M 8 3 A M 8 4 5 A M 9 A M 9 1 5 A M 9 3 A M 9 4 5 A M 1 0 A M 1 0 1 5 A M 1 0 3 A M 1 0 4 5 A MTime of Day (AM)% People choosing the time-of-day alternative Predicted Observed Figure 4-3. Observed vs predicted distribution of departure time patte rns of flexible schedule workers

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53 0.00 2.00 4.00 6.00 8.00 10.00 12.005 1 5 A M 5 3 A M 5 4 5 A M 6 A M 6 1 5 A M 6 3 A M 6 4 5 A M 7 A M 7 1 5 A M 7 3 A M 7 4 5 A M 8 A M 8 1 5 A M 8 3 A M 8 4 5 A M 9 A M 9 1 5 A M 9 3 A M 9 4 5 A M 1 0 A M 1 0 1 5 A M 1 0 3 A M 1 0 4 5 A MTime of Day (AM)% People choosing the time-of-day alternative Predicted Predicted with 100 % Inc Speed Predicted with 50 % Dec Speed Figure 4-4. Impact of change in commuting speed in the morni ng peak period (7 AM to 9 AM) for flexible schedule workers

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54 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.005 1 5 A M 5 3 A M 5 4 5 A M 6 A M 6 1 5 A M 6 3 A M 6 4 5 A M 7 A M 7 1 5 A M 7 3 A M 7 4 5 A M 8 A M 8 1 5 A M 8 3 A M 8 4 5 A M 9 A M 9 1 5 A M 9 3 A M 9 4 5 A M 1 0 A M 1 0 1 5 A M 1 0 3 A M 1 0 4 5 A MTime of Day (AM)% Cumulative People choosing the time-of-day alternative Predicted Predicted with 100 % Inc Speed Predicted with 50 % Dec Speed Figure 4-5. Cumulative impact of change in commuting speed in the morning peak period (7 AM to 9 AM) for flexible schedule workes

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55 0.00 2.00 4.00 6.00 8.00 10.00 12.005 1 5 A M 5 3 A M 5 4 5 A M 6 A M 6 1 5 A M 6 3 A M 6 4 5 A M 7 A M 7 1 5 A M 7 3 A M 7 4 5 A M 8 A M 8 1 5 A M 8 3 A M 8 4 5 A M 9 A M 9 1 5 A M 9 3 A M 9 4 5 A M 1 0 A M 1 0 1 5 A M 1 0 3 A M 1 0 4 5 A MTime of Day (AM)% People choosing the time-of-day alternative Predicted Predicted with 15 % Inc WRKFRE4l Predicted with 100 % Inc WRKFRE4l Figure 4-6. Impact of change in % departur es with work frequency less than or equa l to four for flexible schedule workers

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56 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.005 1 5 A M 5 3 A M 5 4 5 A M 6 A M 6 1 5 A M 6 3 A M 6 4 5 A M 7 A M 7 1 5 A M 7 3 A M 7 4 5 A M 8 A M 8 1 5 A M 8 3 A M 8 4 5 A M 9 A M 9 1 5 A M 9 3 A M 9 4 5 A M 1 0 A M 1 0 1 5 A M 1 0 .3 A M 1 0 4 5 A MTime of Day (AM)% People choosing the time-of-day alternative Predicted Predicted with 15 % Inc WRKFRE4l Predicted with 100 % Inc WRKFRE4l Figure 4-7. Cumulative impact of change in % departures with work frequency less than or equal to four for flexible schedule workers

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57 CHAPTER 5 COMMUTE-TIMING MODEL FOR FIXED SC HEDULE WORKERS This chapter presents the description of co mmutetiming models for workers with fixed work schedules in detail. Section 5.1 describes the dataset used for the estimations. Section 5.2 presents the modeling framework followed by a disc ussion of the results in Section 5.3. Section 5.4 presents an application of the commute timing model in the case of workers with fixed work schedules. Finally the chapter conclu des with a summary in Section 5.5. 5.1 Data Again, the S an Francisco Bay Area Travel Su rvey (BATS) conducted in the year 2000 by is the source of data used in this set of estim ations. The estimation dataset for the departure-time choice model comprises of 3600 weekday auto-bas ed commute journeys of 2528 fixed-schedule full-time workers from 2262 house holds. The overall data processi ng procedure is similar to the one adopted in the context of modeling departure time choices of flexible-schedule workers. The commute timing profile (i.e., the percentage of departures to work in the estimation sample during each discrete time-of-day period) is presented in Figure 5-1. The mid-point times of the discrete periods are presented in the X-axis That is, 5:30 refers to departures during the fifteen minute period from 5:23 AM to 5:38 AM; 5:45 refers to de partures between 5:38 AM and 5:53 AM, and so on. The bulk of th e departures (61 %) are concentr ated in the 6:30 to 8:00 AM period. This occurs a little early as compared to the bulk of depa rtures occurring between 7 and 9 PM as in the case of flexible schedule workers reflecting the constraint to get to work early. Departures before 4 AM or afte r 12:15 PM were relatively few and hence not included in this analysis. The reader will also note that departures at half-hour periods (i.e., 6:30, 7:00, 7:30, 8:00, and so on) are generally hi gher perhaps reflecting inherent biases in the reporting of departure times in travel surveys.

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58 Descriptive statistics on chosen explanatory variables from the above estimation dataset are presented in Table 5-1. In general we find that the fully-flexible, full-time workers analyzed in this study are middle-aged, equally likely to be male or female (as opposed to male slightly male dominate in case of flexible workers), a nd hold position in private profit making firm. The sample also includes considerable numbers of si ngle-person households and individuals of Asian ethnicity like in the case of flexible schedule work ers. It can also be observed that the average work duration of the fixed schedul e workers is slightly more than that of the flexible schedule workers. The area type, household size, number of vehicles and children in the household distributions are pretty similar amongst both fixed and flexible schedule workers. 5.2 Methodology The econometric structure presented in this se ction draws from earlie r research of Steed and Bhat (2002) and Ben-Akiva and Abou-Zeid (2007). Specifically, we adopt the form er researchers approach to incorporate time-var ying covariates in a hazard-duration framework (proportional-hazard structure with a non-pa rametric baseline-hazard distribution and a parametric control for unobserved heterogeneity ) and the methodology prescribed by the latter researchers on accommodating latent work-start-time preferences. The hazard for departing to work at any time of the day u (measured on a continuous scale, say in minutes from 3 AM) is defined as the probability that a worker will depart immediately after time u conditional on not departing until time u. This hazard is assumed to have the following functional form: 0123()()exp ()()() uuXSpeeduSDEuSDLu (Equation 5.1) In the above equation, 0()u is the baseline hazard. X is a vector of non-time varying and covariates such as the socio-demographic characteristics of the worker and is the

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59 corresponding vector of coefficients. Speed(u) represents the commuting speed prevailing at time u and is defined as th e ratio of distance and TT(u). Where TT(u) is the travel time prevailing precisely at time u. SDE(u) and SDL(u) represent schedule delay terms as defined below: otherwise 0 0)( if )( )( otherwise 0 0)( if )( )( )()( uSDuSD uSDL uSDuSD uSDE WSTuTTuuSD (Equation 5.2) SD(u) represents the schedule-delay or the di fference between the ac tual arrival time at work when departing at time u [i.e., u + TT(u) ] and the preferred work start time (WST). Recognizing that earlier-than-pr eferred arrivals and later-than -preferred arrivals may be perceived differently by decision makers, the schedule delay term is further divided into early schedule delay (SDE(u)) and late schedule delay (SDL(u)). Note that both these schedule delay terms are always positive by definition. 3 21 and ,, are the coefficients on the time-varying covariates (i.e.., the travel time and schedule-delay variables).A lternatively the schedule delay terms can also be defined as a fraction of free fl ow travel time or distance. The normalization is introduced to capture the sensitivity of delay te rms to the commuting distance. In other terms a 5 min delay might imply different penalties to an individual commuting 10 m iles (or 10 minutes of free flow time) and an individual commuting 20 mile s (or 20 minutes of free flow time) to get to work. This allows us to estimate three different specifications based on how the schedule delay terms are specified. This will be disc ussed further in the next section. The final term in equation 2 is th e unobserved heterogeneity term (w) which is assumed to follow a gamma distribution (with variance = 2 ) and independent of the covariates.

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60 As already indicated, we adopt a non-parametri c distribution for the ba seline hazard (i.e., 0() u ) in our specification. For this purpose, we discretize the continuous time into K unique time intervals. Let p denote the index for the time intervals (p = 1, 2,, K) and pa represent the upper bound time corresponding to discrete interval p. Therefore discrete period p represents the time interval [1pa, pa] and the duration of this discrete period is given by, p = 1ppaa The baseline hazard is then assumed to be a cons tant within each of th ese discrete periods (i.e., 0()u = exp(p ) if u element of discrete period p). In addition, we assume that the value of timevarying covariates remain constant within each discrete time period (i.e., () and ()ppSpeeduSpeedSDuSD if u element of discrete period p ) and are evaluated at the mid-point time of each discrete period. The probability of departure in interval p conditional on knowing the preferred work start time (WST) is given by (See, Bhat and Steed, 2002 for details): 2 21 2 123 0 2 123 0[|]1exp 1expp jj jjj j p jj jjj jprobtpWST XSpeedSDESDL XSpeedSDESDL (Equation 5.3) Where 0 and K As the preferred work start times (WST) ar e not directly known from the traditional household travel surveys, we assume that the wo rk-start-time preferences are latent and follow a discrete probability density function f(WST). In this research, we determine this density function

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61 from the distribution of work start times obser ved in the estimation data. Now, the unconditional probability of departure in a disc rete period p can be obtained as: )(]|[][ WSTfWSTptprob ptprob (Equation 5.4) Therefore the model parameters can be estimated by maximizing the following likelihood function: qpM NK q=1p=1L=Prob[t=p] 0qp1 if individual q's trip begins in period p M otherwise (Equation 5.5) 5.3 Empirical Results As described in the model formulation, the work-start-time preferences are assumed to follow a discrete probability density function de termined from the distribution of work start times observed in the estimation data. This profile is presented in Figure 5-2. Note that work start times in our estimation sample range from 3:45 AM to 2:45 PM (there were relatively few very early or very late work starts and these are ignored in our anal ysis). This temporal range is divided into 43 equal 15-minute disc rete periods and the probability of choosing to start work in any discrete period is determined as the fraction of the sample observed to start work during this period. The results of our empirical specification of the hazard duration model for the departure time choice of the fixed schedule workers is as shown in Table 5-2. Three difference model specifications were developed. In Model (a), the schedule dela y terms (SDE and SDL) were defined as in Equation 5.2. The schedule dela y terms were normalized by distance in Model (b) and by free-flow travel time in Model (c) We now discuss the interpre tation of the variables

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62 (remains same for any of the thr ee specifications). We have cla ssified the set of explanatory factors into the following f our categories: (1) Individual and Household Socio-Economic Characteristics, (2) Individual Employment Characteristics, (3 ) Location and Commute Distance Characteristics, and (4) Time-Varying Characteristics. 5.3.1 Individual and Household Soci o-E conomic Characteristics Among the set of individual-lev el socio-economic characterist ics, age and gender impacts the choice of departure time. The coefficien t on age is positive which means that older individuals are more likely to depa rt in the earlier time periods. Note that from equation 5.1, a positive coefficient on a time-invariant coefficien t increases the hazard and hence increases the likelihood of departure at any time. Similarly men also chose to depart early relative to women. Other characteristics like ethnic ity were also examined but we re found to be statistically insignificant. A positive coefficient on the number of childre n in the household indicates that workers with children depart earlier. This might be because of the need to drop off the children at school on their way to work. Household structure variab les and the presence of other workers in the household were also tested but were found to be insignificant after cont rolling for number of children in the household. The number of vehicles in the household was also found not to impact the departure time decisions of fixed-schedule workers. 5.3.2 Individual Employment Characteristics Work duration, work frequency, and the wo rk type are individual-level employment characteristics found to determine the departure time choice for commute travel. Individuals who work long hours during the day also depart earlier for work, perh aps reflective of the overall time-budget constraints. Persons who travel to th e out-of-home work location on all the five days of the week were found more likely to depart earli er in the day (relative to those who work less

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63 than five days a week). This is possibly re flecting a greater degree of fixity in the work schedules of such persons among all non-flexible full-time workers. This effect was only observed in Model a. The dummy for work fre quency greater than four was found insignificant in the Models b and c. Finally, the occupation ty pe of the person strongly influences the choice of commute departure time. Sp ecifically, individuals employed in a governmental organization depart the earliest followed by those who work for private non-profit organizations. Self employed individuals depart the latest to work. 5.3.3 Location and Commute Distance Characteristics The residentialand work-location characte ristics were found to be insignificant in determining the departure-time choice of fixe d schedule workers. However, we find that individuals who have to travel longer distances leave ea rlier in the day. The coefficients on the commute distance dummies were significant in Model a where the schedule delay was introduced as an absolute term. But in Models b and c where it was introduced relative to (fraction of) the distance and free-flow time some of the coefficients on the distance dummies turned insignificant. This might be due to the correlation that might exist between the relative schedule delay terms and the commute distance dummies. 5.3.4 Time-Varying Characteristics The coefficient on the Speed (in miles per hour ) variable was found to be statistically significant. The positive coefficient on the speed va riable suggests that the individual is more likely to depart at a time with higher commuting speeds which is as expected. The results show a negative coefficient on the early schedule delay terms. This indicates that an individual is less likely to depart at a certain time with increasing early schedule delay. Alternatively, this means that an individual w ho would get to work 30 minutes earlier than the desired work start time is less likely to depart at a certain time comp ared to an identical

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64 individual who would get to work only 20 minutes earlier than the desired work start time when departing at the same time. The coefficient on the late schedule delay term s is positive and significant. This indicates that an individual is more likely to depart at a certain time with increasing late schedule delay. That is, a person who would get to work 30 minutes later than the desired work start time is more likely to depart at a certain time compared to an identical individual who would get to work only 20 minutes later than the desired work start time when departing at the same time. Note that these probabilities are conditional on not departing earlier. Overall, the coefficients on the schedule de lay terms indicate that commuters choose their departure times so as to arrive at work as cl ose as possible to the pr eferred work start times. Another alternate specification to capture the sensitivity of the delay terms to commuting distance was estimated. The delay terms were pa rtially segmented base d on the four commute distance categories. We found that the coeffi cients across the dist ance categories were approximately the same. Hence this specification was deemed unnecessary. The standard deviation of the unobserved hete rogeneity term (gamma in Table 5-2) is estimated to be statistically different from zero. This reflects the strong presence of factors other than those controlled for in the model that infl uence the departure time choices of individuals. The baseline hazard for the estimated model is as s hown in the Figure 5-3. It can be seen that the longer an individual waits to depart for work, the more likely he/she is to depart. In other words, there is general positive durati on dependence in the hazard function for departure to work. On the overall, Model a performed the best in terms of the likelihood f it measure. But if we have to capture the differential sensitivities on the delay term base d on the commute distance Model b or Model c can be used. The results (sig n of the coefficients) ar e same irrespective of

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65 whether the schedule delay is introduced into the specification as a fraction of distance of freeflow time. But amongst these two, Model c performed slightly be tter in terms of the likelihood fit. 5.4 Model Application Similar to the structure in Chapter 4, we demonstrate an application of the commute timing model in predicting the aggregate time patterns of a sample of individuals. For this exercise, we use the validation sample containing the 612 obser vations. Section 5.4.1 presents the aggregate predictions on the choice of departure time on the sample followed by a description of the aggregate sensitivity of changes in time-varyi ng and non time-varying characteristics to the departure time choice in Sections 5.4.2 and 5.4.3 respectively. 5.4.1 Aggregate Prediction of Departure Time Profiles First, we predict the aggregate departure time choice patterns based on the estimates of the Model a and Model b respectively as show n in Figure 5-4. We find that, on an aggregate level the predicted departure choice patterns from both the models approximate to the observed departure time pattern in the sample. The maxi mum over and under prediction recorded were at around 1 % (at 7 AM) and 2 % (at 5.45 AM) respectiv ely. Again, it should be noted that the reported numbers above are calculat ed as a difference of the obser ved and predicte d percentages. 5.4.2 Aggregate Sensitivity to Changes in Time-Varying Characteristics Secondly, we try to understand the influen ce of the sensitivity of the time-varying characteristics on the predictions of the departur e choice patterns on an aggregate level. For this we consider two scenarios in which the commuting speeds during the peak period (7 AM and 9 AM) are doubled and halved respectively similar to the exercise in Chapter 4. The sensitivities of the departure time to the commuting speeds for Mode l a and b can be observed in the Figures 5-5 and 5-6 respectively. The time of the day is plotted on the X-axis and the cumulative

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66 percentage of departures is plotted on the Y-axis. Model a suggests the highest number of departures in the case of reduced speed in the pe ak period, which is agai nst our expectations (as compared to the base case of no change in sp eed and doubling the speed). This might be the manifestation of the trade-off between the co mmuting speed and schedule delay terms in the specification. Reduced speeds might be getting peopl e closer to their work start times as opposed to higher speeds result ing in being at work much earlier than the preferred work start times. This suggests that the schedule delay dominates over the effect of commuting speed in the specification of Model a. The opposite effect is observed in the case of Model b i.e. doubling the speeds increases the departures and reduci ng the speed in the p eak period reduces the departure in that period. This suggests that the commuting speed dominates over the schedule delay terms in the specification of Model b. 5.4.3 Aggregate Sensitivity to Changes in Non Time-Varying Characteristics Finally, we depict the sensitivity to non-time varying covariates on the choice of departure time. The variable chosen for the purpose of dem onstration is the assumed aggregate distribution of the work start time. Specifica lly, we adjust the probabilities of the individuals to reflect a generic preference to start work earlier, than the base case (adjustmen t done in the 7 9 AM period). Models a and b predict an increase in the departures in the earlier time periods (before 7 AM) and also a decrease in the time pe riods after 9 AM as compared to the base case. These results observed in Figures 5-7 and 5-8 is as expected due to the increased generic preference to depart in earlier time periods. 5.5 Summary and Conclusions In this chapter, a continuous-time model for the choice of departure time for the home-towork commute for fixed schedule workers was formulated and estimated. A hazard-duration structure is adopted that accounts for latent work start time preferences. The model was

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67 estimated using data from the 2000 San Francisco Bay Area Travel Survey. The empirical results capture the strong effect of sc hedule delay on departure time d ecisions. Specifically, the model highlights that fixed-schedule commu ters are likely to choose departure times so as to arrive at work as close as possible to their preferred work start times. The model also captures the effects of several socio-economic and employment ch aracteristics variables on the commute timing decision. An application of the commute timing m odels that were estimated was also presented. The sensitivities of the time-varying and non time-varying factors on the prediction of the departure time choice patterns were analyzed.

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68 Table 5-1. Sample characteristics of fulltime workers with fixed work schedules Attribute Statistic Attribute Statistic Individual Char. Household Char. Age 43.37 (11.33) Number of persons Gender ` 1 15.00 Male 49.08 2 39.17 Female 50.92 3 17.25 Ethnicity 4 18.44 Caucasian 74.31 >=5 10.14 African Ameri can 3.50 Number of vehicles Hispanic 6.78 1 19.472 Asian/Pacific islander 8.81 2 46.361 Other 6.61 3 23.972 Work duration in hours 8.68(1.95) >=4 10.194 Work frequency Number of children <5 days per week 6.78 0 65.19 >=5 days per week 93.22 1 15.14 Occupation 2 13.75 Private non-profit 10.36 >=3 5.92 Private profit 63.00 Presence of another fixed schedule worker Governmental organizatio n 23.22 No 59.86 Self employed 3.42 Yes 40.14 Transportation System and Land Use Char. Household structure Commute free flow time (mins) 18.34(11.15) Single person 15.00 Commute distance in miles 12.57(10.43) Single parent 2.17 Area type of home zone Couple 30.97 CBD (density >100) 0.67 Nuclear Family 21.81 Urban (density 30-100) 18.11 Other 30.05 Suburban (density 6-30) 76.03 Rural (density >6) 5.19 Area type of work zone CBD (density >100) 6.64 Urban (density 30-100) 33.83 Suburban (density 6-30) 55.14 Rural (density >6) 4.39 The values mentioned are the mean (standard deviation) for conti nuous variables and the percentage shares for the categorical variable

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69Table 5-2. Empirical results: Covariate e ffects for the hazard duration model for depa rture time choice of fixed schedule worke rs Model a: Speed, SDE, SDP, discat Model b: Speed, SDEd, SDPd, discat Model c: Speed, SDEf, SDPf, discat Attributes Estimates t-statistic Estimates t-s tatistic Estimates t-statistic Individual and Household Socio-Economic Characteristics Age 0.0161 8.21 0.0129 8.926 0.0131 8.018 Male 0.6946 11.77 0.4892 13.292 0.5785 13.015 Number of kids in the household 0.0908 4.716 0.0688 4.399 0.0671 3.901 Individual Employment characteristics Work duration 0.0049 15.391 0.0039 24.146 0.0042 20.78 Work frequency is >= 5 days per week 0.1481 1.871 0.0008 0.014 0.056 0.818 Work type (Self employed is Base) Private non-profit 1.4662 9.665 1.1751 11.267 1.2451 10.338 Private profit 1.1241 8.128 0.9378 8.638 0.9475 7.748 Governmental organization 1.5824 10.704 1.3496 12.812 1.3405 11.195 Location and Commute Di stance Characteristic Commute Distance 0 5 miles ------------------------------------------5 -1 5 miles 0.1176 1.66 0.0466 0.766 -0.1009 -1.446 15 30 miles 0.4007 3.652 0.3124 3.899 0.1021 0.996 30 50 miles 1.1858 7.471 0.9927 9.325 0.7554 5.463 Time Varying characteristics Speed (miles/hr) 0.0107 2.925 0.013 4.624 0.0141 4.889 Schedule Delay on the early side (min) -0. 0157 -8.751 -0.009 -4.807 -0.0506 -5.576 Schedule Delay on the late side (min) 0.0142 2.072 0.0893 7.684 0.2959 4.603 Gamma 0.6957 9.084 0.7727 25.53 0.8638 22.45 Number of cases 3600 3600 3600 Loglikelihood at Convergence -30670.6788 -30692.6604 -30680.8956

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70 0 2 4 6 8 10 12 144.00 AM 4.15 AM 4.30 AM 4.45 AM 5.00 AM 5.15 AM 5.30 AM 5.45 AM 6.00 AM 6.15 AM 6.30 AM 6.45 AM 7.00 AM 7.15 AM 7.30 AM 7.45 AM 8.00 AM 8.15 AM 8.30 AM 8.45 AM 9.00 AM 9.15 AM 9.30 AM 9.45 AM 10.00 AM 10.15 AM 10.30 AM 10.45 AM 11.00 AM 11.15 AM 11.30 AM 11.45 AM 12.00 AM 12.15 PMTime of Day% Departures Figure 5-1. Departure time distribution over time-of-day fixed schedule workers

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71 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.164.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00Time of the Da y Probability Figure 5-2. Probability density functi on for the preferred work start time of fixed schedule workers

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72 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 4.005.006.007.008.009.0010.0011.0012.00Time of the DayHazard Model a Model b Model c Figure 5-3. Estimated baseline hazard distribution of fixed schedule workers

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73 0 2 4 6 8 10 12 144. 00 A M 4.15 AM 4. 30 A M 4.45 AM 5. 00 A M 5.15 AM 5. 30 A M 5.45 AM 6. 00 A M 6.15 AM 6. 30 A M 6.45 AM 7. 00 A M 7.15 AM 7. 30 A M 7.45 AM 8. 00 A M 8.15 AM 8. 30 AM 8.45 AM 9. 00 A M 9.15 A M 9. 30 AM 9.45 AM 1 0. 00 AM 10.1 5 A M 10. 30 AM 10. 45 A M 1 1. 00 AM 11.1 5 A M 11.30 AM 11. 45 A M 1 2. 00 AM 12. 15 P MTime of day% Departures Observed Predicted Model A Predicted Model B Figure 5-4. Observed vs predicte d distribution of departure time patterns of fixed schedule workers

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74 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.004.00 AM 4 .15 AM 4 .30 A M 4 .4 5 A M 5 00 AM 5.15 AM 5 .30 AM 5 .4 5 A M 6 .0 0 A M 6.15 AM 6.30 AM 6 .45 AM 7 .0 0 A M 7 15 A M 7.30 AM 7 .45 AM 8 .00 AM 8 .1 5 A M 8.30 AM 8.45 AM 9 .00 AM 9 .1 5 A M 9 30 A M 9.45 AM 1 0 .00 AM 10 .15 A M 10 3 0 A M 10.45 AM 1 1 .00 AM 1 1 .15 A M 11 .30 A M 11 45 AM 12.00 AM 1 2 .15 PMTime of day% Departures Model A -Double Speed Model A Half Speed Predicted Model A Figure 5-5. Cumulative impact of change in commuting speed in the morning peak period (7 AM to 9 AM) for Model a for fixed schedule workers

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75 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.004.00 AM 4.15 A M 4 .3 0 AM 4 .4 5 AM 5. 0 0 AM 5.15 AM 5 .3 0 A M 5 .4 5 AM 6 .0 0 AM 6.15 AM 6.30 AM 6 .4 5 A M 7 .0 0 AM 7. 1 5 AM 7.30 AM 7.45 AM 8 .0 0 A M 8 .1 5 AM 8.30 AM 8.45 AM 9 .0 0 A M 9 .1 5 AM 9. 3 0 AM 9.45 AM 10.0 0 A M 1 0 .15 A M 1 0 .30 A M 1 0 .45 AM 11.00 A M 11 1 5 A M 1 1 .30 A M 1 1 .4 5 A M 12.00 AM 12.1 5 P MTime of day% Departures Predicted Model B Model B Double Speed Model B Half Speed Figure 5-6. Cumulative impact of change in commuting speed in the morning peak period (7 AM to 9 AM) for Model b for fixed schedule workers

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76 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.004.00 A M 4.15 A M 4. 30 A M 4. 45 AM 5.00 AM 5.15 A M 5 30 A M 5. 45 AM 6. 00 AM 6.15 AM 6.30 A M 6. 45 A M 7. 00 AM 7. 15 AM 7.30 A M 7.45 A M 8. 00 A M 8. 15 AM 8.30 AM 8.45 A M 9 00 A M 9. 15 AM 9. 30 AM 9.45 AM 10.00 AM 1 0. 15 AM 10. 30 A M 10. 45 A M 11.0 0 AM 11.15 AM 11. 30 AM 11. 45 A M 12. 00 A M 12.1 5 PMTime of day% Departures Predicted Model A Model A wst change Figure 5-7. Cumulative impact of change in % departures with change in work start time preference for Model a for fixed sched ule workers

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77 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.004.00 AM 4.15 A M 4 .3 0 AM 4 .4 5 AM 5. 0 0 AM 5.15 AM 5 .3 0 A M 5 .4 5 AM 6 .0 0 AM 6.15 AM 6.30 AM 6 .4 5 A M 7 .0 0 AM 7. 1 5 AM 7.30 AM 7.45 AM 8 .0 0 A M 8 .1 5 AM 8.30 AM 8.45 AM 9 .0 0 A M 9 .1 5 AM 9. 3 0 AM 9.45 AM 10.0 0 A M 1 0 .15 A M 1 0 .30 A M 1 0 .45 AM 11.00 A M 11 1 5 A M 1 1 .30 A M 1 1 .4 5 A M 12.00 AM 12.1 5 P MTime of day% Departures Predicted Model B Model B wst change Figure 5-8. Cumulative impact of change in % departures with change in work start time preference for Model b for fixed sched ule workers

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78 CHAPTER 6 SUMMARY AND CONCLUSIONS A detailed understanding of de partu re time choice of commuter s is necessary in the wake of increasing volumes of commut e travel along with their cha nging temporal patterns due to increasing availability of work start flexibility, telecommuting behavior, sh ared ride services and increasing HOT/HOV lanes during the peak hour. Fu rther, it is important to evaluate policy implications of introducing time-varying road pricing or congestion pricing schemes on the departure time patterns. Hence disaggregate de parture time models for full-time fixed and flexible schedule workers were estimated. The emphasis in the commute-timing models was to incorporate the effects of time-vary ing transportation system covariates. For this a separate set of inter-zonal travel time regression models were estimated. Econometric models which adopted a hazard duration structure were estimated for both the commute-timing models. For the fixed schedule commuter, the constraint of being at work at a specified time was captured but introduced the concept of schedule delay. Se veral other factors found to impact commute departure time such as individual and househol d socio-economic characteristics, employment characteristics and land use charact eristics were also introduced. Further an application of the commute timing models was also demonstrated indicating the ease of implementing these models in practice for policy ev aluation. Data from the 2000 San Francisco Bay Area Travel Survey (BATS) were used in this study. Section 6.1 will provide a brief summary of the empirical results followed by the limitations and directions for furt her research in Section 6.2.

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796.1 Summary of Empirical Results Section 6.1.1 will summarize the empirical re sults for the inter-zonal travel time models. Later, Section 6.1.2 will provide a brief summary of the empirical implications for the commutetiming models. 6.1.1 Summary of empirical results for inter-zonal travel time models Inter-zonal travel time models were segm ented based on the four commute distance categories. Further segmentation based on origin and destination land use categories was done. A total of 10 models were estimated. This segmenta tion was not possible in the case of very short distance trips (0-5 miles) and very long distance trips (30-50 miles) due to lack to variation in the observed travel time and data amongst different categories respectively. Our empirical results on the inter-zonal travel time models indicate the influence of timeof-day and distance. In general longer the distan ce/ free flow time longer the travel duration. The variability across the time-of-day was very apparent in the case of long di stance (5-30 miles) and very long distance trips. The travel times show ed two smooth peaks indicating the morning (7 AM to 9 AM) and evening (3 PM to 6 PM) peak periods. It could also be observed that the travel durations were higher for a trip from a sub-urban region to urba n regions when compared to that for a trip from sub-urban to urban re gion in the morning time period. The vice-versa was observed during the evening peak pe riod. This indicated that the directionality effects of the congestion are appropriately captur ed by the model specifications. 6.1.2 Summary of empirical results for commute-timing models Our empirical results on the commute-timing models reinforce several intuitive conceptions also documented in th e literature. For example, work ers in households where kids are present (or nuclear households ) were found to depart later th an workers in households with no children (single-person or c ouple households). Also early depa rtures were observed when the

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80 commute distances grew or when individuals have to stay at wo rk for longer durations. Further, people chose to depart in periods experiencing highe r speeds (or lower travel times) or at times which could get them as close as possible to th e preferred work start tim es. Another interesting variable we tested was the day of the week. The effect was however statis tically insignificant for fixed schedule workers. This is in contrast to the result obtaine d in the case of flexible-schedule workers. Overall, this result reinforces that fixed schedule workers have very tight time constraints and hence travel at the same time i rrespective of the day of the week. It was also found that presence of another fixed schedule worker in the h ousehold affected the departure time of only flexible schedule workers and not a fixed schedule worker. This effect is the manifestation of tighter constraint s to start work at a specified time for a fixed schedule worker. Several other employment characteristics such as occupation and industry type impacted departure time of commuters. Apart from the a bove mentioned variables several variables such as ethnicity, dummy variable fo r student, origin and destinat ion land use characteristics and several interaction variables between time vary ing covariates and demographic variables (to capture response heterogeneity) were te sted but found to be insignificant. For a better understanding of the model applic ation for forecasting purposes, a separate set of demonstration exercises were carried for both the commute timing models highlighting the sensitivities of the de parture time patterns to time varying and non-time varying covariates. Through this exercise, we found that the departure time patterns predicted compared very closely to the observed departure time patte rn on an aggregate time scale. 6.2 Directions for Further Research There are several directions for further resear ch that can be explored in this area of research. In this section, we identify empirical and methodologi cal enhancements:

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81 Conventional revealed preference travel survey data do not collect data on the preferred or desired work start time of the individuals. This was dealt by simply assuming the observed work start time distribution in the dataset. A bette r approach would be to enhance the survey instrument to collect additional data on preferred work start times. Further, the inter-zonal travel time models estimated and forecasted from survey data seem to be th e easiest way to produce travel times by time-of-day. With the available technology, travel time data by time-of-day can also be collected by instrumented vehicle experi ments on the transportation network (to be used in building the travel time models). This essentially will eliminate the error in the travel times reported by individuals in the survey data. Also if data on time-of-day specific data were available for travel/parking costs they can also be incorporated into empirical modeling. For example, policy evaluation on the impacts of commu te departure time in response to congestion pricing can be evaluated by additi onal the appropriate costs such as travel costs and parking costs. The models developed in this research could be enhanced methodologic ally is several of the following ways. 1. The hazard duration structure does not recogn ize the effect of future travel times (departure at time t conditional on not departing until time t ) on departure time choice. We tried to overcome this limitation by introduci ng the future travel times into the model as explanatory variables. These variables were found to be insignificant in our estimations possibly due the presence of high co rrelation (less variability in travel times) across the adjacent time periods. More research on how to appropriately capture these future effects still needs to be addressed. 2. The main advantage of using a hazard dur ation type framework is the parsimonious structure it provides at fine temporal resoluti ons of choice alternatives as opposed to the MNL type models. At the same time, it lead to an overall restrictive relationship between the departure time choice and the explanat ory factors. On the other hand, MNL or Ordered response type advanced formulati ons such as OGEV or the mixed multinomial logit type structures provide the flexibility to specific elaborate correlation structures. This will again have the issue of exploding al ternatives at finer temporal resolutions. Studies which can quantify the trade-offs be tween using the hazard duration structure and OGEV type specifications need to be explored.

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82 3. This study mainly focused on developing cont inuous departure time choice models for commuters. A broader perspective would be look at how these models fit into the current comprehensive demand forecasting frameworks.

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83 LIST OF REFERENCES Abkowitz, Mark D. (1981) An Analysis of the Comm uter Departure Time Decision. Transportation, Vol. 10, pp. 283-297. Bates, J.J.: Time Period Choice Modeling: a Pr eliminary Review. HETA Division, Department of Transport, UK (1997) Ben-Akiva, M and Aboud Zeid, M (2007) Methodol ogical Issues in Modeling Time-of-Travel Preferences. Presented at the 11th Wo rld Conference on Transportation Research. Bhat, C.R. and Steed, J.L. (2002) A Continuous-Time Model of Departure Time Choice for Urban Shopping Trips, Transportation Res earch Part B, Vol. 36, pp. 207-224. Cambridge Systematics, Inc. (2004) Forecasting Person Travel by Time of Day: Tour Based Time of Day Choice Modeling, unpublished report prepared for the Federal Highway Administration. Chin, A. T. H. (1990) Influences on Commuter Trip Departure Time De cisions in Singapore. Transportation Research A, Vol. 24, No. 5, pp. 321-333. Ettema, D.F. and H.J.P. Timmermans (2003), Mode ling departure time choice in the context of activity scheduling behavior, Transpor tation Research Record, 1831, 39-46. Gadda, S, Kockelman, K.M. and Damien, P. (2007) Continuous Departure Time Models: A Bayesian Approach. Meeting Compendium of the Transportation Research Boards 86th Annual Meeting, Washington, DC. Guo, J.Y., S. Srinivasan, N. Eluru, A. Pinjar i, R. Copperman, and C.R. Bhat (2005) "ActivityBased Travel-Demand Analysis for Metropo litan Areas in Texas: CEMSELTS Model Estimations and Prediction Procedures, 4874 Zone System CEMDAP Model Estimations and Procedures, and the SPG Software Details," Report 4080 -7, prepared for the Texas Department of Transportation. Hamed, Mohammed M., and Fred L. Mannering. (1993) Modeling Travelers Postwork Activity Involvement: Toward a New Methodology. Transportation Science, Vol. 27, No. 4, pp. 381-394. Hendrickson, C. and Plank, E (1984) The Flexib ility of Departure Times for Work Trips. Transportation Research A, Vol. 18, No. 1, pp. 25-36. Hensher, David A., and Fred L. Mannering. ( 1994) Hazard-Based Duration Models and their Application to Transport Analysis. Transpor t Reviews, Vol. 14, No. 1, pp. 63-82. Hess, S., Polak, J.W., Bierlaire, M. (2005) F unctional approximation to alternative-specific constants in time-period choice modeling, CT S Working paper, Centre for Transport Studies, Imperial College London.

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84 Hess, S., Polak, J.W., Daly, A. & Hyman, G. (2004), Departure Time and Mode Choice, paper presented at the European Tran sport Conference, Strasbourg. Hess, S., Polak, J.W., Daly, A.J., and Hyman, G. (2004) Flexible substitution patterns in models of mode and time of day choice: New evid ence from the UK and the Netherlands, Paper submitted to Transportation. Hunt, J. D., and D. M. Patterson (1996). A Stated Preference Examination of Time of Travel Choice for a Recreational Trip, Journal of Advanced Transportation, 30, 3, 17-44. Jotisankasa, A. and Polak, J.W., 2005, Experimental investigation of day-to-day traveler learning and adaptation in route and departure tim e choice behavior, paper presented at the 37th UTSG Annual Conference, Bristol. Jou, R. and Kitamura, R. (2002) Commuter Departure Time Choice: A Reference Point Approach. Mimeograph Mahmassani H. S., Chang G. L. (1986). Experiments with departure time choice dynamics of urban commu ters. Transportation Research, vol. 20B, pp. 297-320. Kiefer, N.M. (1988). Economic Duration Data and Hazard Functions, Journal of Economic Literature, 27, June, 646-679. Kumar, A., and D. Levinson (1995) Temporal Variations on Allo cation of Time, Transportation Research Record 1493, TRB, National Rese arch Council, Washington, D.C., 118-127. Levinson, David, and Ajay Kumar. (1993) Inte grating Feedback Into Transportation Planning Model: Structure and Applica tion. In Transportation Re search Record 1413, TRB, National Research Council, Washington, D.C., pp. 70-77. Levinson, David. and Ajay Kumar (1994). Oper ational Evidence for Changing Travel Patterns. ITE Journal, April, 1994 pp.36-40 Mahmassani H. S., Chang G. L. (1986). Experi ments with departure ti me choice dynamics of urban commuters. Transportation Re search, vol. 20B, pp. 297-320. Mannering, F L. (1988) Poisson Analysis of Commuter Flexibility in Changing Routes and Departure Times. Transportation Research B, Vol. 23, No. 1, pp. 53-60. Mannering, Fred L., and Mohammed M. Hamed. (1989) Occurrence, Frequency, and Duration of Commuters Work-to-Home Departure Delay. Transportation Research B, Vol. 24, No. 2, pp. 99-109. McCafferty, Desmond, and Fred L. Hall (1982) The Use of Multinomial Logit Analysis to Model the Choice of Time to Travel. Economic Geography, Vol. 36, No. 3, pp. 236-246. Nair, H.S., Bhat, C.R., and Kelly, R.J. (2001) Modeling Soak-Time Distribution of Trips for Mobile Source Emissions Forecasting: Techniques and Applications, Transportation Research Record, Vol. 1750, pp. 24.

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85 Pendyala, R (2002) Time of Day Modeling Procedures for Implementation in FSUTMS: Final report submitted to the Florida De partment of Transportation. Pisarski, A.E. 2006. Commuting in America II I. National Cooperative Highway Research Program Report 550. Washington D.C.: Th e National Academies, Transportation Research Board. 196 p. Purvis C (1999) Peak Spreading Models: Promises and Limitations. Paper presented at the 7th TRB conference on Application of Tran sportation Planning Methods, Boston, Massachusetts. Saleh, W., and Farrell, S. (2005). Implications of congestion charging fo r departure time choice: work and non-work schedule flexibility. Tran sportation Research A, Vol. 39, pp. 773791. Small, Kenneth A. (1982) The Scheduling of C onsumer Activities: Work Trips. The American Economic Review, Vol. 72, No. 3, pp. 467-479. Steed, J., and C.R. Bhat, On Modeling the Departure Time Choice for Home-Based Social/Recreational and Shopping Trips", Tran sportation Research Record, Vol. 1706, pp. 152-159, 2000. Vovsha, P., and Bradley, M. (2004) A Hybrid Discrete Choice Depart ure Tim e and Duration Model for Scheduling Travel Tours. Transportation Research Record 1894, 46-56. Xia Jin and Chiao, Kuo-Ann (2008) Synthesis of Time-of-Day Modeling Research Meeting Compendium of the Transportation Research Boards 87th Annual Meeting, Washington, DC.

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86 BIOGRAPHICAL SKETCH Abishek Komma was born in Ind ia, in 1983. He received his dual degree (bachelors and masters degree) in civil engine ering from the Indian Institut e of Technology Madras, Chennai, India in 2006, also receiving a minor degree in financial management. Mr. Komma is currently a masters candidate and research assistant in the Transportation Research Center, at the University of Florida, Department of Civil and Coastal Engineering, and he will be receiving his Master of Science degree in August 2008.