Transportation Systems Planning Methods and Applications 02

Transportation Systems Planning Methods and Applications 02 Transportation engineering and transportation planning are two sides of the same coin aiming at the design of an efficient infrastructure and service to meet the growing needs for accessibility and mobility. Many well-designed transport systems that meet these needs are based on a solid understanding of human behavior. Since transportation systems are the backbone connecting the vital parts of a city, in-depth understanding of human nature is essential to the planning, design, and operational analysis of transportation systems. With contributions by transportation experts from around the world, Transportation Systems Planning: Methods and Applications compiles engineering data and methods for solving problems in the planning, design, construction, and operation of various transportation modes into one source. It is the first methodological transportation planning reference that illustrates analytical simulation methods that depict human behavior in a realistic way, and many of its chapters emphasize newly developed and previously unpublished simulation methods. The handbook demonstrates how urban and regional planning, geography, demography, economics, sociology, ecology, psychology, business, operations management, and engineering come together to help us plan for better futures that are human-centered.

2 Time Use and Travel

Behavior in Space

and Time

CONTENTS

2.1 Introduction2.2 Time Use and Travel: A Descriptive Analysis2.3 Example Application 1: Modeling Time–Space Prisms2.4 Example Application 2: Structural Equations Modeling

of Household Activity and Travel Durations2.5 Example Application 3: Two Dimensions of Time Use–Activity Episode Timing and Duration

Causal Structure D → T • Causal Structure T → D • Time of Day Affects Activity Duration • Activity Duration Affects Time of Day

2.6 Example Application 4: Time Use Patterns and Quality-of-Life Measures

2.7 Summary and ConclusionsReferences

Further Information

2.1 Introduction

Transportation systems are planned and designed to provide people with the ability to engage in activities at locations and times of their preference When people cannot engage in activities at locations and times of their preference, the transportation system is deemed to provide a poor level

of service Transportation models are aimed at modeling and forecasting where and when the demand for travel will occur so that the transportation system can be planned and designed to meet the projected travel demand and ensure a high quality of life for the residents and visitors of a geographical region Thus the analysis of travel behavior is inextricably linked to the concepts of space and time, and there is a growing body of literature that makes a strong case for the development of transpor-tation models and planning methods that explicitly recognize the role of space and time dimensions

in people’s travel behavior

The traditional approach to travel demand analysis and forecasting has relied on models of travel demand that are based on computing four major aspects of travel behavior:

1 How many trips are made? (trip generation)

2 Where are trips made? (trip distribution)

3 By what means of transportation are trips made? (modal split)

4 On what route or path are trips made? (network assignment)

Ram M Pendyala

University of South Florida

The spatial element of travel plays an important role in all steps of the modeling process, but is mostly captured in the second step, trip distribution In this step, trip origin and destination locations are identified using measures of zonal attractiveness or activity levels and degree of separation to determine trip interchanges between zone pairs The spatial characteristics of trips in turn influence the choice of mode and route in the subsequent two steps of the four-step modeling process.

The time element of travel is less explicitly captured in the current transportation modeling process, although it is at least as important as the spatial element The timing of travel is often addressed through transportation models that are formulated or adjusted to obtain peak hour or peak period travel demand, and the duration of travel is often addressed by the inclusion of different forms of travel time variables

in trip distribution, modal split, and network assignment models

Significant changes in the past few decades in sociodemographic characteristics of households, urban structure, industrial composition, and transportation systems have resulted in increasingly complex activity engagement and travel patterns Consequently, although infrastructure expansion continues to play a major role in transportation planning and analysis, there is a growing emphasis being placed on transportation systems management and, more recently, on the role and impacts of various travel demand management (TDM) strategies and transportation control measures (TCMs) Although current travel models capture several fundamental aspects of transportation demand, they are based on sets of assump-tions and paradigms that do not adequately reflect the spatiotemporal interdependencies that are inherent

in the organization of activities and travel This realization has led to the growing interest in travel forecasting methods that incorporate activity participation and time allocation behavior It has been increasingly realized that transportation is a derived demand in that the way individuals and households organize their lives dictates when and where they travel Recent developments in the transportation modeling field have paid considerable attention to the notion of time use with the belief that under-standing the mechanisms of activity participation and time allocation will lead to increased capability

in forecasting travel demand and evaluating planning options (Kitamura et al., 1997b)

As an example of the importance of recognizing time and space dimensions in models of activity and travel demand, one may consider the case of telecommuting When a worker telecommutes (from home), the commute to and from the work location is eliminated Therefore, the worker now has additional time available for pursuing activities The elimination of the commute trip influences the duration of travel or activity engagement Besides influencing duration, telecommuting may influence the timing and location of activity engagement Whereas a worker may have pursued nonwork activities in combi-nation with the commute when traveling to and from work, the worker may now choose to engage in nonwork activities at other times of the day and at locations closer to home In the absence of the commute trip, the worker no longer has the need or opportunity to link nonwork activities to the commute trip and the work location Analyzing these spatial and temporal shifts in activity engagement patterns is important for accurately assessing the impacts of telecommuting on travel demand

The role of time in travel behavior analysis is further amplified by the fact that it is a finite and critical resource that is consumed in the engagement of activities and travel All activities and trips consume time, and regardless of the time span under consideration, there is only limited time within which an individual can pursue activities and trips In turn, the spatial dimension is very closely related to the temporal dimension as the distance traversed and the set of possible destination opportunities are dictated

by timing and time availability Thus, there is only a finite spatiotemporal action space in which an individual can pursue activities and travel Moreover, there may be additional personal, work- and school-related, household, institutional, and modal constraints that limit the size of the spatiotemporal action space of an individual

In recent years, the state of the art in travel demand modeling has moved in the direction of developing and implementing activity-based models of travel demand that explicitly recognize the important role played by time and space in shaping activity and travel patterns of individuals In the new planning context where TDM strategies and TCMs are inherently linked to time and space dimensions, activity-based approaches that capture the relationships between time use and travel behavior in space and time offer a stronger behavioral framework for conducting policy analyses and impact studies

This chapter aims to provide a general overview of the role of time use in analyzing travel behavior

in space and time It includes several specific examples that demonstrate how the explicit recognition of the notion of time can offer valuable insights into human activity and travel behavior

2.2 Time Use and Travel: A Descriptive Analysis

Activity-based travel analysis is increasingly being recognized as a powerful methodology to model human travel behavior Activity-based travel analysis recognizes that individuals’ activity and trip patterns are a manifestation of their decision to allocate time to various activities during a day Travel is then derived from an individual’s desire to perform an activity at a location away from the previous activity location Recent research has argued that information on individual activity engagement behavior offers the potential to enrich our understanding of the complex and dynamic nature of travel executed by people Benefits of the activity-based approach include the determination of (1) spatial and temporal constraints

on activity and travel choice, (2) scheduling and sequencing of activities in time and space, (3) interactions between activity and travel decisions, and interactions between individuals, and (4) roles played by members of a household in accomplishing household activities and tasks

Time use research is playing an increasingly important role in activity and travel behavior research because of the recognition that many travel choices are governed by time, which is a limited resource that is consumed according to one’s needs and preferences Activity data are often derived from time use studies that record all in-home and out-of-home activities and all trips performed during the survey period in a sequential manner Potentially, the explicit representation of time use in travel demand models will further help to explain people’s travel choices over the course of a day

Time use and activity studies have focused on the examination of various aspects of activity and travel behavior, including:

1 Daily time allocation: In these studies, the total time allocated to various activity categories or purposes is examined or modeled at the day level In these studies, individual episodes are not explicitly considered As such, while these studies focus on daily time use and allocation behavior, they are unable to consider issues such as activity timing, frequency, episode duration, or activity scheduling and sequencing On the other hand, they provide strong insights into daily time allocation and the trade-offs associated with having to allocate time among various activity types

in a typical 24-h day

2 Activity episode duration: Studies of episode duration analysis have focused on modeling the duration of individual activity episodes by purpose or category These analyses provide a powerful mechanism for understanding the factors that influence individual activity episode durations and the probability that a certain activity will be terminated given that a certain duration has elapsed Episode duration models have traditionally taken the form of hazard-based duration models and Tobit models that help explain time use in the context of a single activity episode Within the context of these models, it is often possible to reflect the interdependence among activity episodes and the timing of activities, as the end of one activity episode reflects the beginning of another activity episode On the other hand, issues associated with daily time allocation to activities, sequencing of activities, and scheduling of activities are more difficult to capture explicitly in models of episode duration

3 Activity timing and scheduling: Activity timing and scheduling models focus on identifying when

a certain activity or trip will be pursued Hazard-based duration models, time-of-day period-based discrete choice models, and heuristic algorithms have been used to model activity timing and scheduling behavior Although these studies do not necessarily capture time use behavior, they do examine the role of time in activity–travel behavior, as timing and scheduling decisions are, by definition, temporal in nature

4 Activity sequencing: Activity sequencing studies are concerned with the sequence in which various activities and trips are linked Thus, activity sequencing studies directly capture the essence of trip

chaining because trip chaining is simply a manifestation of activity sequencing decisions Various methods, including sequence alignment techniques, discrete choice models, and heuristic rule-based algorithms, have been used to model activity sequencing decisions While activity sequencing does occur along the time dimension and is closely related to activity timing and scheduling, these studies have incorporated time use behavior only in a limited way.

5 Activity frequency: Activity frequency models focus on the number of occurrences of various types

of activities These models often take the form of Poisson or negative binomial regression tions, discrete choice models, or other models suitable for representing count phenomena In general, these models do not explicitly capture the time dimension, as they are exclusively focused

equa-on the number of times an activity is pursued, regardless of the duratiequa-ons of the episodes.Among the five types of studies noted above, the first three are directly related to the notion of time use and its role in travel behavior Therefore, only examples of models pertaining to these three aspects

of time use (i.e., daily time allocation, activity episode duration, and activity timing) are presented in this chapter The examples presented in this chapter serve as applications of the usefulness of the notion

of time use in transportation demand and policy analysis

Over the past several years, there have been several activity-based time use and travel surveys taken in the transportation planning, modeling, and survey research arenas However, time use research and studies have been undertaken in the social sciences for many years These surveys have afforded the opportunity to quantify the activity and time use behavior of individuals in the context of their travel The remainder of this chapter provides descriptive analysis and statistics on activity and time use patterns that have been obtained in some recent surveys

under-When examining activity and time use patterns, it is very important to note that activity and time use behavior varies considerably by demographic segment and by survey method Demographic character-istics that may contribute to differences in time use and activity patterns include employment status, age, sex, education, income, household composition, and land use–transport environment Besides demographic factors, the survey methodology may also result in differences in activity and time use patterns For example, the design of the survey instrument may have important implications for the reporting of activities and time While some instruments are sequential in nature, collecting information

on each activity pursued by an individual in a sequential fashion, other instruments utilize the time diary format, where individuals enter their activities in various time intervals, similar to a day planner or personal calendar Also, whether the survey is self-administered (e.g., mail-out mail-back survey) or interviewer administered (e.g., computer-assisted telephone interview (CATI)) may have an important bearing on the activity and time use data collected in a survey Within the scope of this chapter, it is not possible to provide a rigorous analysis and description of time use and activity patterns by demographic segment while controlling for survey method Therefore, the statistics presented here distinguish only between commuters and noncommuters and are derived from CATI surveys

The data presented in this section are derived from three different surveys conducted in the past decade All of the surveys may be regarded as activity-based time use and travel surveys administered by CATI techniques The three surveys include the 1996 San Francisco Bay Area activity survey, the 1998 Miami activity survey of commuters, and the 1994 Washington, D.C., activity survey of commuters Among these three surveys, only the 1996 San Francisco Bay Area survey includes a sample of noncom-muters; therefore, the sample derived from this survey is split into commuter and noncommuter samples for describing time use and activity characteristics Even though all surveys were administered by similar means, they used different activity categories As such, any comparison of statistics across the three surveys must be done with caution, recognizing that the activity categories may not be exactly equivalent.The 1996 San Francisco Bay Area activity survey was a 2-day time use and travel survey conducted in the nine counties of the San Francisco Bay Area Detailed information on both in-home and out-of-home activities and trips undertaken by an individual was recorded in the survey While information on all trips and trip segments (in the case of chained trips) was collected, in-home activity information was requested only for those activities that were longer than 30 min in duration However, many of the

respondents provided detailed information on all in-home activities, regardless of duration On the other hand, information on all out-of-home activities was collected irrespective of their duration.

The CATI survey elicited a favorable response from 14,431 persons residing in 5857 households in the bay area They provided detailed household and person level socioeconomic and demographic data The survey intended to collect detailed activity and trip information for all individuals residing

in a household However, not all individuals who provided demographic data furnished complete activity and trip information Only 8817 individuals residing in 3919 households provided detailed activity and trip information over a 48-h period After extensive data checking, cleaning, and merging and organizing, the final data set included 7982 persons residing in 3827 households Among the 7982 persons, 4331 were commuters and the remaining 3651 were noncommuters Full-time or part-time workers who had at least one work activity outside the home during the survey period were treated

as commuters Individuals reporting activities performed out of the study area and individuals who provided activity trip information for 1 day or less during the survey period were not included in the final sample

The Miami–Dade County activity-based travel behavior and time use survey was conducted in Florida

in 1998 The survey collected detailed information on both in-home and out-of-home activities and on all travel associated with these activities Unlike the San Francisco Bay Area survey, the Miami survey collected activity and travel behavior data for only a 1-day (24-h) period In addition, the sample consisted exclusively of commuters who were defined as individuals who commuted to a regular work or school location at least 3 days a week Only one randomly selected commuter was chosen to participate from each household

Similar to the Bay Area survey, the Miami survey was administered using the CATI technique economic and demographic information about the household and about persons residing in the house-hold was collected first Information regarding the usual commute to and from work was collected from the randomly selected commuter Activity and time use data were collected only from eligible commuter respondents Unlike the Bay Area survey, the Miami survey did not have any duration threshold for reporting of activities All activities, regardless of their length, were recorded in the data set Similar to the Bay Area survey, the Miami survey included information on all trips, including individual trip segments of chained trips

Socio-Socioeconomic and demographic data were collected for 2539 persons residing in 1040 households

As mentioned earlier, activity and trip data were collected only from commuters, with the constraint that each commuter must be drawn from a different household A total of 803 commuters provided detailed information on their usual commute to and from work; of these, 640 provided detailed activity and trip information for the 24-h survey period The analysis presented here, however, is performed only on a sample of 589 commuters, as the remaining respondents included full-time students with

no work Even though the omitted respondents were considered commuters from a survey standpoint,

it was felt that they should not be included here for reasons of compatibility and comparability across the surveys

Finally, a very detailed activity-based travel survey was administered using CATI techniques to a random sample of 656 commuters in the Washington, D.C., metropolitan area in 1994 This survey was conducted as part of a larger study to develop an activity-based travel demand forecasting system and policy evaluation tool called AMOS — Activity Mobility Simulator As is typical with most travel surveys, the survey gathered information on the socioeconomic and demographic characteristics of the commuters In addition, commuters were asked to provide data on their typical travel patterns over the duration of an average week The survey then collected very detailed and revealing preference information on all out-of-home and in-home activities that one randomly chosen commuter in a household pursued over a 24-h period

Table 2.1 provides a summary of the socioeconomic characteristics of the households, while Table 2.2 provides a summary of the person characteristics in each of the survey samples An examination of Table 2.1 shows that the survey samples exhibit both similarities and differences with respect to household characteristics It should be noted that the Miami and Washington, D.C., samples include only households

that have at least one regular commuter who works outside the household Some of the differences across the survey samples are simply a manifestation of the difference in sampling scheme In the San Francisco survey sample, 16.5% of the households have no worker who commutes to a workplace outside home This is reflected in the smaller average household size and number of workers in the household for the San Francisco sample Auto availability, represented by the percent of households where the number of vehicles is greater than or equal to the number of commuters, is quite high in the San Francisco and Washington, D.C., samples, where about 90% of the households fall into this category For the Miami sample, the corresponding percentage is only about 65%, reflecting a lower level of auto availability relative to the San Francisco and Miami samples.

The person characteristics summarized in Table 2.2 once again show that there are similarities and differences across the survey samples Once again, it should be noted that the Miami and Washington, D.C., samples are pure commuter samples As expected, whereas the commuter samples show relatively strong similarities in person characteristics, the noncommuter sample in the San Francisco survey shows substantial differences in age, license holding, and student status

Table 2.3 shows the average activity and travel characteristics of the person samples with a view toward providing insights into average time use patterns Differences and similarities in time use patterns across the survey samples should be viewed in the context of the differences and similarities in their household and person sociodemographic characteristics seen in Tables 2.1 and 2.2

TABLE 2.1 Household Characteristics of Survey Samples

2.1 64.4

2.0 90 Number of workers

Zero worker household

1.4 16.5%

2.5 n.a.

1.7 n.a.

Note: n.a = not applicable or not available.

TABLE 2.2 Person Characteristics of Survey Samples

Characteristic

San Francisco

Miami

Washington, D.C.

14.5%

31.5%

41.5 18.8%

An examination of the statistics presented in Table 2.3 shows that commuters generally exhibit similar characteristics across the three survey samples As expected, noncommuters tend to have activity and time use characteristics that are substantially different from those of commuters While some of the differences in time use characteristics can be related to differences in socioeconomic characteristics, one should be careful in trying to explain differences in time use patterns as a function of differences in socioeconomic characteristics One may postulate that many sociodemographic factors, often considered explanatory variables of time use, are in fact endogenously determined by an individual’s or household’s long-term lifestyle choices and short-term activity decisions Thus, one may be able to infer lifestyle choices by noting time use patterns exhibited by an individual or household.

In addition to the statistics derived from activity-based travel surveys, as shown in Table 2.3, the literature offers additional insights into time use patterns of individuals Kitamura et al (1997a) provide

a comparative description of time use patterns of survey samples drawn from The Netherlands, California, and the United States (a nationwide sample) Descriptive time use statistics provided in their paper account for sex (male or female), working status (working or not working on survey day), and type of day (weekday or weekend day) Table 2.4 offers a summary of the time use statistics derived from their tabulation

The Dutch and California data sets represent time use patterns of randomly chosen individuals The Dutch time use survey included home interviews from a sample of 2964 individuals, with a response rate of 54% The time use survey conducted in California had a response rate of 62% and yielded a

TABLE 2.3 Time Use and Activity Characteristics of Survey Samples

Characteristic

San Francisco

Miami

Washington, D.C Noncommuters Commuters

Sample Size 3651 4331 589 656

Daily Activity Durations Work 00:00 (0%) 06:41 (28%) 07:00 (29%) 07:44 (32%) Sleep 09:23 (40%) 07:57 (32%) 07:56 (32%) 07:13 (30%) In-home maintenance 03:43 (15%) 02:28 (11%) 02:29 (11%) 02:25 (10%) Personal care/child care 01:16 (5%) 01:08 (5%) 01:24 (6%) n.a Out-of-home maintenance 00:47 (3%) 00:44 (3%) 00:45 (3%) 01:00 (4%) Shopping/personal business 00:34 (2%) 00:23 (2%) 00:24 (2%) n.a In-home recreation 03:46 (16%) 02:12 (9%) 01:51 (8%) 01:47 (7%) Out-of-home recreation 01:10 (5%) 00:46 (3%) 00:40 (3%) 00:26 (2%) Eating/meal preparation 01:46 (7%) 01:24 (6%) 01:23 (6%) n.a School 02:21 (10%) 00:07 (1%) 00:00 (0%) 00:00 (0%) Missing (unaccounted time) 00:05 (0.5%) 00:07 (1%) 00:15 (1%) 00:18 (1%) Total 00:59 (4%) 01:34 (7%) 01:41 (7%) 02:00 (8%)

Daily Travel Durations Work 00:00 (0%) 00:29 (32%) 00:34 (34%) 00:45 (38%) Out-of-home maintenance 00:18 (32%) 00:17 (19%) 00:26 (26%) 00:26 (22%) Shopping/personal business 00:08 (14%) 00:07 (8%) 00:10 (10%) n.a Child care/serve child 00:01 (2%) 00:01 (1%) 00:06 (6%) n.a Other 00:09 (16%) 00:09 (10%) 00:10 (10%) n.a Out-of-home recreation 00:08 (14%) 00:07 (8%) 00:06 (6%) 00:07 (6%) Eat meal (out of home) 00:03 (5%) 00:05 (5%) 00:06 (6%) n.a Return home 00:23 (39%) 00:34 (36%) 00:28 (28%) 00:42 (35%) School 00:06 (10%) 00:00 (0%) 00:00 (0%) 00:00 (0%)

Note: For the San Francisco and Miami samples, the in-home and out-of-home portions of the eating and meal preparation

activities are not available For the Washington, D.C., sample, these portions have been added to the in-home and home maintenance categories All durations are represented in hours and minutes in the format hh:mm Figures in parentheses indicate the percentage of the day (1440 min) dedicated to the activity, except in the case of travel durations, where the figures represent the percent of total travel time dedicated to each travel purpose n.a = not applicable or not available.

out-of-TABLE 2.4 Activity Durations by Activity Type, Sex, and Working Status for Weekday and Weekend

Activity Category Day Type Survey Area

Overall Average

sample of 1564 individuals Whereas the Dutch time use survey employed a weekly time use diary format with 15-min time intervals and closed activity categories, the California survey adopted a sequential activity diary format in which all information about in-home and out-of-home activities and travel was collected sequentially for a 24-h period using an open activity category structure The overall U.S data set was obtained from a nationwide sample of 3047 individuals residing in 44 states Time use information

is available for a 1-day period for this sample of individuals All of the surveys utilized similar activity categorization schemes, thus facilitating comparative tabulation of time use patterns across the surveys

In all of the survey samples, about 55% of the individuals are female With respect to age distributions, the Dutch and California data sets are quite similar, while the U.S national data set has a larger proportion

of elderly individuals The U.S and California samples differ from the Dutch sample with respect to marital status; in general, the Dutch sample includes a larger proportion of married persons and persons who have never been divorced or separated

This chapter has provided a descriptive analysis of time use statistics from recent activity-based and time use surveys conducted in various areas of the United States and the Netherlands As mentioned

in the earlier parts of this chapter, activity and time use studies have focused on various aspects of behavior, including such items as the frequency, scheduling, timing, and sequencing of activities While

TABLE 2.4 (CONTINUED) Activity Durations by Activity Type, Sex, and Working Status for Weekday and

Weekend

Activity Category Day Type Survey Area

Overall Average

opment of an activity-based traveler benefit measure, in Activity-Based Approaches to Travel Analysis, Ettema, D.F and

Timmermans, H.J.P., Eds., Pergamon, Elsevier Science Ltd., U.K., 1997 With permission.

some of these items will be addressed in the context of the examples and applications furnished in subsequent sections of this chapter, this section has focused mainly on daily time use behavior for the sake of emphasis and clarity in presentation Even though a detailed presentation and discussion of the frequency, scheduling, and sequencing of activities is beyond the scope of this chapter, it is very important to note that daily time use patterns and time allocation behavior are inextricably linked to such aspects of activity behavior.

Time use and activity surveys have been conducted around the world over the past several decades The measurement and research of time use is quite complex, and extreme care must be exercised in the design and administration of time use and activity surveys In general, a time use survey collecting information on in-home and out-of-home activities should yield a total of about 20 to 25 activities per person per day, with about one fifth of these activities constituting trips (i.e., four or five trips per day per person) These general values may be used as broad guides to ensure that an activity and time use survey is yielding information consistent with past experience These figures may vary considerably, depending on the nature and composition of the sample, the level of detail regarding activities and trips that is captured in the survey instrument, and the design and administration of the survey As pointed out by Harvey (2002), there is a merging of traditions between travel and time use studies that bodes well for the transportation planning profession as time use surveys become increasingly amenable to collecting detailed travel information

2.3 Example Application 1: Modeling Time–Space Prisms

The notion of time–space prisms was introduced by Hägerstrand (1970) to describe the spatiotemporal constraints in which people make activity and travel decisions Since then, many researchers in the travel behavior arena have addressed or utilized the concept of time–space prisms for modeling activity and travel engagement patterns of individuals The representation of spatiotemporal constraints in the mod-eling of human activity and travel behavior is very important In any given day, a person has only 24 h available and much of that time may be spent on basic subsistence activities, including sleeping, working (to earn a living), and personal and household care The temporal aspects of these types of activities tend

to be rigid and impose constraints on an individual’s potential activity–travel engagement pattern Similarly, in a spatial context, one can postulate that fixed home and work locations (coupled with various temporal constraints) limit the range of spatial choices for a person Thus, it can be seen that time–space constraints play an important role in shaping people’s activity–travel patterns

The accurate and complete representation of time–space prisms has taken on added importance in the context of the emergence of microsimulation approaches to travel demand forecasting Whereas in the traditional zone-based four-step travel demand modeling approaches one did not focus on the individual traveler, microsimulation approaches attempt to simulate activity and travel patterns at the level of the individual traveler When dealing with individual travelers and their potential behavioral responses to evolving transportation policy scenarios, it is imperative that a mechanism be developed by which individual time–space prisms can be accurately modeled

This section is aimed at developing a methodology by which temporal vertices of time–space prisms

of individuals can be effectively represented in a comprehensive framework that encompasses both home and out-of-home activity engagement and time use The approach involves the use of recent activity and time use data to model temporal vertices of time–space prisms for each individual as a function of his or her socioeconomic and demographic characteristics

in-Thus, this section presents an attempt to define the beginning and ending point (called a vertex) of Hägerstrand’s prism While a trip is observable and is by definition always contained in a prism, the prism itself can rarely be defined based on observed information Although the vertices of a prism are often determined by coupling constraints (e.g., one must be at a certain place by certain time), such constraints are often unobserved or not well defined For example, consider a commuter who must report

at work by 9:00 A.M In this case a prism has one of the vertices located at the workplace at 9:00 A.M in

the space–time coordinates The other vertex, which designates the beginning point of the prism, is not defined, except that it is located at the home base somewhere prior to 9:00 A.M along the time axis.

In this section, models are developed to locate prism vertices along the time axis The models are formulated as stochastic frontier models, which are used to estimate the location of an unobservable frontier (or an upper or lower bound) based on the measurement of an observable variable that is governed by the frontier In this study, the location on the time axis of a prism vertex is the unobservable frontier, and the starting or ending time of a trip is the observable quantity governed by the frontier In particular, this section focuses on three items of interest:

1 Formulation and estimation of time vertices using stochastic frontier models

2 Comparison of space–time prism vertices between geographic areas

3 Investigation of day-to-day variability in time vertices

By definition, a trip in a prism always starts at or after the origin vertex of the prism, and ends at or before its terminal vertex While the beginning and ending times of a trip are almost always available from travel survey data, the origin and terminal vertices of a prism are normally unobserved A modeling approach, therefore, is adopted in this study to estimate the location of prism vertices using observed variables

Adopted in the modeling approach are the following inequalities:

at origin vertex: τo≤ to

where τo is the location along a time axis of the origin vertex of a prism, τt is the location of the terminal vertex, to is the beginning time of a trip in the prism, and tt is the ending time of the trip It is assumed that τo and τt are unobserved From the inequalities,

to = τo + uo, tt = τt – ut (2.2)where uo and ut are nonnegative random variables

A possible model that applies to these relationships is the stochastic frontier model, whose general form can be presented as

Yi = β′Xi + εi = β′Xi + vi – ui (2.3)where i denotes the observation; Yi is the observed dependent variable (in this case a trip beginning or ending time); β is a vector of coefficients; Xi is a vector of explanatory variables; and vi and ui are the random error terms, –∞ < vi < ∞ and ui > 0 In the context of this study, β′Xi + vi can be viewed as the location of the terminal vertex of a prism with the random element, vi The observed trip ending time (Yi in the above notation) will not exceed β′Xi + vi because ui is nonnegative A model for an origin vertex can be formulated similarly as Yi = β′Xi + vi + ui

In the econometric literature on stochastic frontier models, vi is typically assumed to be normal and

a truncated (half) normal distribution is often used for ui In this case, the distribution of εi is given as (subscript i is suppressed below)

2 2Φ

2 2

This formulation is adopted with an observed trip starting or ending time as Yi and selected attributes

of the individual and household, including person commute characteristics, as Xi Because of the way the model is constructed, the inequalities of Equation (2.1) are always satisfied Yet, there remains the question of whether β′Xi + vi in fact represents the prism constraint in the strict sense of Hägerstrand One could argue that β′Xi + vi may represent a threshold that an individual subjectively holds as the earliest possible starting time or the latest possible ending time for a trip, but may not coincide with actual constraints that are governing travel For example, a commuter may believe that he or she cannot possibly leave home before 6:30 A.M in the morning; thus the origin vertex of his prism before the work starting time is located subjectively at 6:30 A.M But it is not likely that this is an objectively defined constraint In fact, the same commuter may leave home before 6:00 A.M for a business trip

Models of prism vertices are estimated in this study with empirical data without any information on the individual’s beliefs or perceptions of prism constraints Yet observed travel behavior is governed by subjective beliefs and perceptions, e.g., “I must return home by midnight” or “I cannot possibly leave home before 6:30 A.M.” Thus some ambiguity is unavoidable about the nature of β′Xi + vi; it is unlikely that it represents a prism vertex in the strict sense of Hägerstrand It is yet reasonable to assume that β′Xi + vi is nonetheless a useful measure for the practical purpose of determining the earliest possible departure time or latest possible arrival time for a trip

It is often considered that workers’ daily activities are regulated by their work schedules It may then

be assumed that the work starting time defines the terminal vertex of a worker’s morning prism before work, and the work ending time defines the origin vertex of his or her evening prism after work The prism during the lunch break is determined by the beginning time and ending time of the break Work schedules that define these prism vertices are determined primarily by institutional factors, and personal

or household attributes are expected to have relatively small effects There is therefore little room to apply such a model as described above to prism vertices that are defined by a work schedule Therefore, stochastic frontier models are presented in this section for the origin vertex of workers’ morning prisms and the terminal vertex of workers’ evening prisms For those prism vertices that are defined by work schedules, different approaches (e.g., using observed frequency distributions of work starting or ending times by industry and occupation) may be more effective

Commuter samples from the Miami and San Francisco Bay Area surveys (described earlier in this chapter) were used to estimate stochastic frontier models of prism vertices Pendyala et al (2002a) present models of the following prism vertices:

• Origin vertex of the commuters morning prism — Miami and San Francisco

• Terminal vertex of the commuters evening prism — Miami and San Francisco

As data are available for a 2-day period in the San Francisco data set, separate models are estimated for each day and for the pooled data set so that day-to-day variability in time vertex locations can be explored.The dependent variables of the models presented in this section are defined with the time of day expressed in minutes, with 12:00 A.M (midnight) being 0; so 6:00 A.M is expressed in the model as 360, and 6:00 P.M as 1080 All models assume that vi has a normal distribution and ui has a half-normal distribution The expected value of ui is evaluated as

(2.6)

where is an estimate of σu

For the sake of brevity, this section presents two tables that are representative of the model estimation results that can be accomplished using econometric software such as LIMDEP The model for the origin vertex of the Miami commuter’s morning prism is presented in Table 2.5 The model is a cost frontier model and is formulated as β′Xi + vi + ui The model is found to offer plausible indications The model shows that a full-time worker has a origin vertex about 86.5 min earlier than a nonworker, while the corresponding

figure for a part-time worker is about 57 min On the other hand, those who work at home have origin vertices about 87 min later than those who work outside the home Similarly, the variable representing students also has a negative coefficient, though not as much as those associated with full- or part-time workers The origin vertex of the Miami commuters’ morning prism is pushed earlier as commute time increases — about 30 min for every hour of commute Greater car availability and the possession of a driver’s license provide for origin vertices that are later in the morning; this is presumably because of the faster travel times and flexibility associated with the ability to drive alone Older individuals and those in families with children have slightly earlier origin vertices than other groups E[u] is 141 min, indicating that the first time of departure from home is, on average, about 2 h 20 min after the origin vertex.Table 2.6 shows the results of the model estimation effort for the terminal vertex of the commuter’s evening prism of the San Francisco sample For the San Francisco commuters, 2 days’ worth of data is available Therefore, model results are shown by day and for the pooled sample as a whole The work end time and the final time of arrival at home for the San Francisco commuter sample show distributions that have high variance and less well-defined patterns This is also evidenced in the model estimation results For example, the effect of a working day for a full-time worker is minimal (and not significant for the second day) On the other hand, the working day of a part-time worker and working multiple jobs shifts the terminal vertex by about 30 min later in the day Similarly, school also shifts the terminal vertex later in the day For every hour of commute, the vertex is shifted later by about 25 min This result

is found to be very symmetric with that of the origin vertex of the morning prism, where 1 h of commute shifted the origin vertex 25 min earlier in the day (table not presented in this chapter) Being older or

of minority status (Hispanic or Black) is associated with relatively earlier terminal vertices for the commuter’s evening prism On the other hand, being a single person and having a driver’s license are both associated with later terminal vertices This may be because of the greater flexibility for final home arrival that these individuals may have relative to those who have families and those who cannot drive

A greater number of workers or cars is associated with marginally later terminal vertices, once again presumably due to the flexibility afforded by these variables

E[u] is found to be about 2 h 45 min, indicating that commuters in the San Francisco sample, on average, arrive home about 2 h 45 min prior to the terminal vertex For both survey samples, it was found that the goodness of fit of the model of the evening prism terminal vertex is substantially poorer than that found for the morning prism origin vertex The greater variability in the final arrival times at home may be contributing to this poor fit

TABLE 2.5 Stochastic Frontier Model of Miami Commuters’ Morning

Prism Origin Vertex

Overall, it is seen that the stochastic frontier modeling methodology is capable of representing the terminal vertices associated with beginning or ending points of space–time prisms, at least for commuters who tend to have more structured weekdays Further research is warranted in the context of estimating vertex locations for nonworkers.

Pendyala et al (2002a) present comparisons for two items of interest:

• Comparisons between Miami and San Francisco commuter samples with respect to origin vertex

of morning prism and terminal vertex of evening prism

• Comparisons between first and second days of the San Francisco commuter sample with respect

to origin vertex of morning prism and terminal vertex of evening prism

For the sake of brevity, two comparisons are shown in this section The first comparison, shown in Figure 2.1, pertains to distributions of expected vertex locations and observed final home arrival times The peak home arrival time for the Miami sample appears to be about 7 P.M., while that for the San Francisco sample appears to be about 30 min earlier at 6:30 P.M The distributions of expected vertex locations peak for both samples at about 9:30 P.M., with the Miami sample showing a more pronounced peak than the San Francisco sample Greater household obligations (child care, etc.) associated with larger household sizes in the Miami area may be contributing to this difference Thus it is found that most individuals arrive home about 2.5 to 3 h prior to their vertex location

The second comparison, shown in Figure 2.2, examines day-to-day variation in origin vertex of the morning prism and the first time of departure from home for the San Francisco Bay Area survey sample.The distributions are strikingly similar The peaks of the observed distributions are shifted about 2 h

to the right (later in the day) of the peaks associated with the distributions of the expected vertex locations The distributions of the expected vertex locations are very similar between the 2 days, as are the distri-butions of observed home departure times

TABLE 2.6 Stochastic Frontier Model of San Francisco Commuters’ Evening Prism Terminal Vertex

Variable

FIGURE 2.1 Distribution of expected vertex locations and final arrival at home.

FIGURE 2.2 Distribution of expected vertex locations and first departure from home: comparison between day 1

and day 2 for San Francisco commuters.

Overall, the analysis and model estimation results showed that similarities across geographic areas are more pronounced in the case of origin vertices associated with the morning prism of commuters The greater variability in home arrival times contributes to greater differences across geographical areas when one considers the terminal vertex locations of the evening prism Also, comparisons between 2 days of travel show striking similarities between the distributions of expected vertex locations and observed departure and arrival times The stochastic frontier modeling method is effective for modeling temporal extremities Estimation results provide strong indications that the temporal vertices associated with space–time prisms are significantly influenced by people’s socioeconomic, demographic, and commute characteristics.

2.4 Example Application 2: Structural Equations Modeling

of Household Activity and Travel Durations

Recent advances in activity-based approaches involve the microsimulation of individual activity–travel patterns in the space–time continuum The individual person is typically considered the decision or choice maker, and model system components attempt to represent various aspects of the activity–travel behavior of the individual traveler These models are becoming increasingly sophisticated in their ability

to reflect the effects of various types of constraints on activity–travel patterns In this context, household interactions and the constraints and opportunities that such interactions bring about can also play a big role in influencing individual activity–travel patterns Household members allocate tasks among one another, make trade-offs, or join together in activity participation, and often may depend on one another for undertaking activities and travel (particularly in the case of children who depend on adults for their transport) As the use of cell phones, e-mail, and other technology becomes increasingly common, one can only expect that the amount of interaction (especially real-time interaction) will increase over time (Meka et al., 2002)

Considering that there is a wide array of possible interactions among household members that merit investigation, the analysis in this section focuses on nonwork activity and time allocation among house-hold members consistent with the notion of time use discussed in this chapter For an individual, the amount of work activity and travel may have an effect on nonwork activity engagement and travel As a person spends more time at work or traveling to work, he or she is likely to spend less time at nonwork activities These intraperson trade-offs are often clear and well captured in models of activity and travel behavior Similar trade-offs may occur at the interperson level As one individual in the household spends more time at work or traveling to work, it is possible that the other individual will spend more time taking care of the household obligations and other nonwork activities Thus, in modeling household activity and travel behavior, it is important to represent such trade-offs to accurately capture household-level trip-making patterns

The data set used in this study is derived from a traditional household travel survey conducted in southeast Florida (Broward, Palm Beach, and Miami–Dade Counties) during the 1999 calendar year The travel survey consisted of three steps, including a computer-assisted telephone interview recruit-ment, a mail-out of survey instruments and travel diaries, and a CATI retrieval of the survey responses

Of the 7500 households that agreed at first to participate, 5168 households actually responded to the survey The 5168 households were approximately evenly split among the three counties in the region and provided a respondent sample of 11,426 persons reporting a total of 33,082 trips In general, the respondent sample exhibited socioeconomic, demographic, and travel characteristics consistent with the population in the region

For the analysis reported in this section, it was necessary to extract a suitable sample that would facilitate the modeling of interperson interactions and activity allocations in a focused manner In order

to do this, households that had two or more adults (18 years or older) of which at least one adult worked outside the home were extracted to form a multi-adult worker household sample This sample consisted

of 1262 households All of the analysis and model estimation reported in this section has been conducted

on this sample of 1262 households

In order to make comparisons between two adult household members meaningful and easy to interpret, the adults were numbered (given a person ID) based on work duration and age The following method was used to assign identification numbers:

• Adults were assigned numbers in descending order of their total daily work activity duration The adult with the longest work duration is person 1, and the adult with the next longest work duration

a poor response rate, with more than one quarter of the households not providing income information Considering the nature of the selected household sample, the rather high proportion falling in the high-income category ($80,000 and above) is not surprising On average, the households have about one child per household, with nearly one half reporting no children About 60% of the households have two workers; once again, this is consistent with the nature of the sample

With respect to person attributes, the average age is very similar between person 1 and person 2 However, person 2 has a higher proportion of elderly (greater than 60 years) individuals While only 1% of those classified as person 1 are not employed, the corresponding percentage among those classified as person 2

is 23% Consistent with the employment pattern, the income distribution shows a higher personal income for person 1 Among those who commute, about 85% choose to drive alone to work, while about 10 to 12% choose to car- or vanpool to work Very small percentages use transit or other modes

Table 2.7 provides average activity frequencies, activity durations, and travel durations for persons 1 and 2 The table makes a distinction between the entire sample of 1262 persons and the subset of persons who actually participated in the activity The latter set is considered the nonzero set, and the sample size for each activity is in parentheses under the respective average For example, 98 persons (among the 1262 classified as person 1) pursued shopping The average shopping activity frequency for this set of 98 persons is 1.07

With respect to activity durations, the average work duration for those classified as person 1 is about

8 h 20 min As expected, the average for those classified as person 2 is considerably lower because of the higher incidence of noncommuters among the person 2 sample However, in line with the higher activity frequencies they exhibited, those classified as person 2 spent more time at nonwork activities Even if one were to focus on the nonzero samples, those classified as person 2 show consistently higher daily average activity durations for nonwork activities

Average travel durations show trends that are similar to those shown by activity frequencies and activity durations Those classified as person 1 spend about 40 min traveling to work, while those classified as person 2 spend about 30 min traveling to work However, among the nonzero observations, those classified as person 2 spend more time traveling to work than those classified as person 1 On average, those classified as person 2 spend more time traveling to nonwork activities than those classified as person

1 One anomaly is found in the context of travel to school Among those who actually participated in school activity, those classified as person 1 spent more time traveling to school than those classified as person 2 In general, the person samples spend an average of about 110 min traveling to various activities This is quite high, but consistent with expectations given the larger household size and multiworker, multiadult, and multivehicle nature of the sample

The modeling of within-household interactions in activity engagement involves dealing with multiple endogenous variables in a simultaneous equations framework Work and nonwork activity frequencies,

activity durations, and travel durations are all activity- and travel-related endogenous variables that are interconnected with one another When modeling the interactions among several interdependent endog-enous variables, simultaneous equations systems offer an appropriate framework for model development and hypothesis testing In this application, the structural equations methodology is adopted for estimating simultaneous equations systems that capture the interdependencies among household members’ activity engagement patterns.

A typical structural equations model (with G endogenous variables) is defined by a matrix equation system, as shown in Equation (2.7):

(2.7)

This equation can be rewritten as

(2.8)or

(2.9)

TABLE 2.7 Daily Time Use and Activity–Travel Frequencies on Travel Survey Day

Person 1 (Nonzero) Person 2 (All)

Person 2 (Nonzero) Activity Frequencies

Return home (includes final home stay, but

not initial home stay)

a Significantly different from person 2 (all) at the 0.05 significance level.

b Significantly different from person 2 (nonzero) at the 0.05 significance level.

ε

Y=BY+ΓX+ε

Y= −I B− X+( ) (1Γ ε)