Unravelling the Relationship between Travel Time

Investigating the Non Linear Relationship between Transportation System Performance and Daily Activity-Travel Scheduling Behaviour

Khandker Nurul Habib Department of Civil Engineering, University of Toronto [email protected] Ana Sasic Department of Civil Engineering, University of Toronto [email protected] Claude Weis IVT, ETH, Zurich [email protected] Kay Axhausen IVT, ETH, Zurich [email protected]

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Abstract: The paper presents an econometric investigation of the behavioural relationship between transportation system performance in terms of travel time changes and daily activity-travel scheduling processes. Innovative survey data on the complete daily activity-scheduling adaptation process is used jointly with revealed scheduling information. The survey, conducted in Zurich, Switzerland, collected daily scheduling information together with stated adaptation responses corresponding to four adaptation scenarios. The four scenarios are defined by applying hypothetical increases in travel time of 50, 100, and 200 percent and a 50 percent decrease in travel time. Stated adaptation responses are collected in the context of 24-hour activity scheduling. Data are used to estimate RUM based daily travel activity scheduling models. Models are estimated for one revealed schedule and four stated scheduling datasets. In addition, a joint model is estimated for pooled revealed and stated scheduling data. In the joint model, separate scale/variance parameters are estimated for revealed and stated information. Results clearly identify the non-linear responses of activity-travel scheduling to the changes in travel time. Asymmetric responses are shown for travel time increases and decreases. People become more conservative with time expenditures when scheduling activities subject to increased travel times. However, beyond a certain limit of travel time increase, scheduling behaviour becomes more unpredictable. The lessons learned from this investigation have implications in the application of activity-based models for forecasting and policy analyses. Models developed using only a revealed preference dataset should not be used to extrapolate to situations where travel times changes by large margins. The results also prove that significant improvements in capturing behavioural responses in the activity scheduling process are possible by pooling revealed preference and stated preference data sets and jointly modelling with an explicit representation of RP scale/variance differences.

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Introduction: It is well known that travel conditions imposed by the performance of the transportation system influence travel demand. All growing cities have experienced periods of change in their transportation systems and the ways that people travel. Over time, development, technology and changing social and economic environments in urban areas have had major impacts on both travel patterns and development of the transportation system. In turn, the usage of transportation and the operational attributes of the system have a reciprocal effect on each other. For many transportation policy decisions, it is vital to have an understanding of the forces motivating travel demand patterns in a city. The effect of system performance attributes such as travel times, wait times and costs on travel demand is of specific interest to all those involved in the design of a sustainable transportation system. However, the nature and extent of the influence of transportation system performance on our travel behaviour is not yet fully understood (Weis et al 2010). One of the main reasons is the traditional tendency to rely only on Revealed Preference (RP) travel survey data. Although RP data are less subject to error and bias than Stated Preference (SP) data, RP data may not always contain information on a wide range of scenarios. Transportation system performance does not change drastically at the system scale level very frequently. Therefore, RP data often fail to present information on a wide variety of transportation system performance levels and the resulting influence on activity-travel demand. Travel demand models developed using RP data may fail to capture changes in travel demand trends due to variation in transportation systems over time (Roorda et al 2008). However, such models are often used to forecast medium to long term forecasting and policy scenario analyses. RP data used in developing activity-based travel demand models often describe stable/equilibrium interactions between transportation demand and supply. Travel activity scheduling decisions are made on a daily or even weekly basis. Changing traffic congestion, economic and social conditions may lead to increasing complexities in our activity-travel behaviour. Many such changes are unprecedented and create significant challenges for modelling activity-based travel demand (Bifulco et al 2010). Such challenges are mostly related to increasing the sensitivity of travel demand models to previously unobserved conditions. RP survey based activity-travel data often fail to provide sufficient information for modelling these. In such cases, SP data are valuable because they provide a unique way to evaluate the expected response to potential future system changes. An RP activity-travel survey is very unlikely to contain observations from a wide variety of transportation system performance scenarios and the resulting activity-travel behaviour adaptations. Even a six-week RP travel survey may not show significant variations in activity travel scheduling process behaviour if significant changes in transportation system performance do not happen during the survey time (Axhausen et al 2002). Failing to capture a variety of system states limits our ability to forecast demand patterns and/or predict reactions to new policies that may affect transportation system performance significantly by using activity-based travel demand models. One way to overcome this basic limitation in activity-based analysis is to use Stated Preference (SP) survey data. A properly designed SP survey (involving pivoting the SP scenarios to the RP responses) can present a rich set of information for developing comprehensive activity scheduling models. Such models would be capable of predicting a wide range of transportation demand-supply interaction scenarios. In this investigation, we use such a 3

dataset that contains RP activity scheduling information together with four Stated Adaptation (SA) responses corresponding to four transportation system states. SA scenarios are created to collect SP responses in activity scheduling decisions by pivoting to the RP scheduling information to generate a complete 24-hour response pattern. Both RP and SP data are used independently and jointly to develop dynamic RUM based daily activity scheduling models. Comparisons of the model parameters highlight the complexities of activity-travel scheduling behaviour and its relationship with transportation system performance. The paper is arranged as follows: the next section presents a literature review followed by a description of the scheduling model based on random utility theory, a description of the Stated Adaptation survey and the datasets and discussions on empirical models. The paper concludes with recommendations for further investigations.

Literature Review: The complexities of the relationship between daily activity-travel scheduling decisions and transportation system performance have long been of interest to researchers. Recker et al (1986) summarize the efforts of various researchers in conceptualizing this issue in the early 80’s, when the concept of an activity-based approach was first recognized as a legitimate theory for modelling travel demand. Since then, the theoretical understandings on the dynamics and complexities of activity travel behaviour have been complemented by many researchers from various disciplines of science and engineering (Han et al 2008, 2011). It is now well recognized that modelling activity-based travel demand requires consideration of the interactions among multidimensional activity planning horizons, psychological processes of planning and decision making, intra and inter-household interactions, effects of social networks, as well as the dynamics of transportation system performances (Garling et al 1994, Lin et al 2008). Various approaches of modelling such complex activity-travel behaviour are evident in literature. Some researchers consider hybrid mixing of behavioural rules and econometric choice models for capturing behavioural complexities (Arentze and Timmermans 2000, Roorda et al 2008, Auld and Mohammadian 2009). Some researchers apply discrete choice models for modelling activitytravel patterns (Ben-Akiva and Bowman 1998,, Bowman et al 1998, Shiftan 2008). Hybrid approaches of activity-based travel demand models often try to capture activity-travel rescheduling and/or adjustments by directly addressing the rescheduling process in the modelling structure. On the other hand, discrete choice model based activity pattern choice modelling captures rescheduling behaviour indirectly through utility feedback from lower level decisions (such as activity start time, activity durations etc.) to upper levels decisions (such as choice of specific tour pattern, etc.) in activity travel pattern choices. In any type of modelling approach, dynamics of transportation system performance needs to be accurately captured into the activitytravel pattern dynamics and vice versa. This is very important for maintaining the behavioral realism of activity-based travel demand modelling. In order to capture the dynamic relationship between activity-travel scheduling processes and transportation system performance, researchers are now focussing on integrating activity-based travel demand models with dynamic traffic assignment (Lin et al 2008, Feil et al 2010). However, it is difficult to capture induced demand for urban transportation created by unexpected changes 4

in travel time or cost (Weis et al 2010). Making demand forecasting models sensitive to changing travel times and costs is important for policy analysis. An efficient way of observing travel demand adaptation behaviour is to use a stated preference (SP) or stated adaption (SA) survey. The use of SP surveys for observed activity adaptation behaviour is not new in the literature. Researchers are often interested in the activity-travel rescheduling process in response to changes in transportation system performance. An early attempt of capturing travel-activity rescheduling behaviour is presented in Jones (1979). Jones (1989) developed a computer-based stated preference survey to capture the reactions of the travellers while taking public transit. Using SP surveys, the effects of many explanatory variables on travel patterns were studied. The specific issues addressed were: transit service changes (Van Knippenberg and Clarke (1984)), fuel shortages (Lee-Gosselin (1989, 1990)), automobile usage reduction scenarios (Doherty and LeeGosselin (2000) and Doherty et al (2002)), congestion pricing (Arentze et al (2004)), travel time increases and household auto availability (Roorda et al (2005)). Most recently Weis and Axhausen (2010) conducted a comprehensive stated adaptation survey to understand daily activity scheduling behaviour in response to travel time and cost changes. In this survey, the RP scheduling information is collected first. Pivoting on the 24-hour RP scheduling information, a set of alternative scenarios is created by considering different travel time information. Respondents were allowed to change the activity schedules freely in response to changes in context and situations. The survey was conducted in Switzerland and the collected dataset is used in this investigation. Similar other studies on activity rescheduling behaviours are reported by Roorda and Andre (2007); Nijland et al (2009) and Clark and Doherty (2010). In most cases, data collected through SA based SP surveys are used to understand how people modify their decisions under enforced changes in travel time, cost, auto availability etc. Data are used for descriptive analyses or for investigating single or multiple facets of activity-travel rescheduling decisions. Roorda and Andre (2007) present a comprehensive literature review on the investigation of personal activity rescheduling decisions by using datasets from both an activity-travel survey and a stated adaptation survey. Although stated adaptation surveys are now becoming common practice, the potential of such surveys in providing useful information for modelling activity-travel demand is largely unexplored. There are no known prior uses of SA survey data for comprehensive modelling of activity-travel scheduling. So, comparative performances of models developed by using SP and RP datasets are unknown. In a bid to fill this gap in literature, this paper presents comprehensive activity-travel scheduling models developed using both RP and SP data separately as well as in combination. Rather than focusing on a specific component/dimension of activity-travel scheduling behaviour, this paper focuses on the complete daily activity scheduling processes. The importance of modelling 24hour activity travel scheduling considering RUM is now well recognized. Recently, Cirillo and Axhausen (2010) used RUM based discrete choice models for 24-hour activity-travel scheduling. Habib (2011) develops a RUM based discrete-continuous model for 24-hour activity-travel scheduling. However, all such modelling efforts are developed for RP scheduling information. This study uses RP as well as SP data to develop a RUM based daily activity scheduling model for improving our understanding on the relationship between a wide range of transportation system performance and corresponding activity-travel scheduling behaviour. The next section explains the econometric modelling approach used in this study. 5

RUM Based Model for Activity Scheduling: The RUM based scheduling model used in this paper assumes that individuals gain utility (U) for scheduling an activity type, j:

U j  Vj   j   j x j   j

; j  1,2,3,.........A

(1)

The total utility of activity scheduling, Uj is composed of two components: the systematic utility component (Vj) and the random variable component (εj). The systematic component is assumed to be a linear-in-parameter function of a set of explanatory variables, (xj), and corresponding parameters (βj). While scheduling an activity, individuals face a trade-off in deciding the amount of time to be spent on the activity and the amount of time that will remain available for rest of the day. In a utility-based framework, an individual maximizes the total utility of these two scheduling decisions. At any scheduling step, if the total time is budget is T, the total utility of scheduling decisions becomes:

U (T ) 

1

j



exp( j z j   /j ) (t j j  1) 

1

c



exp( c zc   c/ ) (tc c  1)

(2)

t j  tc  T

(3)

Here the subscript, j, indicates the activity to be scheduled and the subscript c indicates the time left over for the composite activity under the available time budget constraints. In this formulation (dropping the subscripts for simplicity), t indicates allocated time, exp(ψz+ ε/), is the baseline utility function; z indicates a vector of explanatory variables; ψ indicates a vector of coefficient corresponding to z; ε/ is the unobserved random error component of the random utility function; α is the satiation parameter. The Lagrangian function of the time allocation decisions is:

l

1

j



exp( j z j   /j ) (t j j  1) 

1

c





exp( c zc   c/ ) (tc c  1)   t j  tc  T



(4)

In the above Lagrangian function, λ is the Lagrangian multiplier. By using first order differential condition non-zero time allocation, we can write that: exp( j z j   /j ) t j

 j 1

 exp( c zc   c/ ) tc

c 1

Taking the logarithm of both sides:



j



z j  ( j  1) ln t j    /j   c zc  ( c  1) ln tc    c/

 V    V   / j

/ j

/ c

/ c

(5)

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The above condition of equality applies to an expenditure of tj amount of time on the given activity. Similarly, for the case where tj < tc

V j/   /j  Vc/   c/ To derive the probability function of spending a specific amount of time, we can further modify as)

 /j   c/  Vc/  V j/

for t j  0

 /j   c/  Vc/  V j/

for t j  0

(6)

If we assume that the random error component, ε/j, follows a Type I Extreme-Value (Gumbel) distribution with a mean value of 0 and a scale parameter of σ, the probability distribution function (PDF) and cumulative distribution function (CDF) of ε/j become (Johnson et al., 1995):

   (Vc/  V j/ )   Pr   (V  V   )  1  exp      



/ j

/ c

/ j

/ c



1

(7)

To ensure model identification, the specification of V/ji and V/ci can be further specified as (Bhat, 2008):





V j/   j z j  ( j  1) ln t j  and Vc/  ( c  1) ln(tc )

(8)

Here V/ci indicates the composite activity for the corresponding chosen activity type under the remaining time budget constraints. Now, according to the change of variables theorem, the probability distribution function (PDF) can be determined as follows:

 1   j 1  c  1   (Vc/  V j/ )    (Vc/  V j/ )       Prt  t j    exp 1  exp       t  t   c      j 

2

(9)

The previous formulations for activity scheduling decisions consider a specific chosen activity for scheduling. In order to integrate the activity type choice within time allocation decisions, let us assume that an individual chooses a specific activity (j) out of a number of possible activity types for scheduling. According to RUM theory, an alternative activity, j, will be chosen if the utility of that alternative activity is the maximum of all considered alternatives.

Uj 

max n  1,2,3...... A, n  j

Un

So,

Pr(U j

max n  1,2,3...... A, n  j

U n )  PrVn  V j  ( j   n ) 

(10) 7

In the above formulations, the systematic utility of a chosen alternative is a function of the difference between two random error terms: the error term of the chosen alternative, εj, and the error term of the second best alternative, εn. Let us assume that the random variable, εj, has the Independently and Identically Distributed (IID) Type I Extreme-Value (Gumbel) distribution with a mean value of 0 and a scale parameter of 1. According to the properties of IID Type I Extreme-Value distribution with scale parameter μ, the maximum over an IID Extreme-Value random variable is also extreme-value distributed, and the difference of two IID Extreme-Value random terms is logistically distributed (Johnson et al., 1995). Hence, it can be written as:

Pr(( n   j )  (V j  Vn ))  Pr( n  (V j  Vn   j )) 

exp(  j x j )

exp(  j x j )   exp(  n xn )

(11)

n j

Joint estimation of RUM-based activity type choice and time expenditure requires the assumption that the random error terms of the models have an unrestricted correlation. One means of specifying the unrestricted correlation between these two random variables is to transform both random variables into an equivalent standard normal variable and specify the joint distribution as an equivalent bivariate normal distribution (Lee, 1983). In transforming these marginal distributions into equivalent standard normal variables, it can be shown that (Lee, 1983):

 *j  J1 ( j )   1[( n   j )  (V j  Vn )]  k*  J 2 ( /j )   1[( /j   c/ )  (Vc/  V j/ )]

(12)

Here, Φ-1 indicates an inverse of the cumulative standard normal variable. The joint decision process of activity type choice and time expenditure now can be described by considering that the transformed standard normal variables are bivariate normal (BVN) distributed with correlation ρjt: BVN[J1(εj ), J2(ε/j), ρjt]. Hence, the joint probability of observing that any individual (ignoring the individual identifier, i) choosing an alternative activity j, and corresponding time expenditure, tj can be expressed as follows (Habib, 2011):

Pr(Time  t j  Activity Type  j )  Pr(Time  t j    J1 ( j )) 2  J ( )   J ( / )]  (13)  1   j 1  c  1   (Vc/  V j/ )     (Vc/  V j/ )  jt 2 j   exp   1  exp     1 j          t  2 tc     1   jt       j  

Based on the above formulation, the likelihood function, Li, of an individual observation, i, can be written as:

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2 1     (Vci/  V ji/ )     (Vci/  V ji/ )   1   ci  1  ji  1  exp    exp   t       t   n  ci         ji Li      J ( )   J ( / )]  j 1   1 ji jt 2 ji       2    1   jt     D ji is a binary indicator variable for the chosen activity type

D ji

(14)

Here Dji is a binary indicator variable for the chosen alternative activity. Now if we consider the sequence of activity selection and corresponding time expenditure, i.e., the activity scheduling process for 24-hour time period, the joint likelihood function of the complete schedule of an individual, i,, becomes: 2 D ji    / / / /          1    ( V  V )  ( V  V ) 1   ci  1     ji ci ji ci ji      exp 1  exp            t tci     S A           ji LTi        J ( )   J ( / )]  Z 1   1 ji jt 2 ji  j 1          2 1   jt       Z

(15)

Here, S is the total number of activities performed in the 24-hour time period. The likelihood function (LTi) specified in equation (15) refers to a generalized likelihood function of complete scheduling of any individual respondent, i. In case of the RP scheduling data, the likelihood function (LTi) for a full RP schedule of the individual, i, can be referred as (LRP-Ti). For the kth complete SP schedule of the same individual respondent, i, can then be referred as (Lk-Ti). If the individual, i, has a total of K number of SP responses, then the joint likelihood (Li) of RP and all SP responses become: K

Li  LRP Ti   Lk TI

(16)

k 1

Such joint likelihood function allows differentiating scale parameters (μ) between RP and SP datasets. It is possible to estimate separate scale parameters for each SP schedules considering the RP schedule as the reference schedule. Now, If we have a sample of observation with sample size, N, the joint likelihood function for the sample, L, becomes: N

L   Li

(17)

i 1

This expression is a sample likelihood function of a dynamic RUM discrete-continuous model. It is of a closed form and can be estimated using classical Maximum Likelihood Estimation (MLE) algorithms. In this paper, the parameter estimates are obtained by maximizing the log-likelihood function using code written in GAUSS which applies the BFGS optimization algorithm (Aptech, 2010).

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In the joint probability distribution, as per the formulations, a positive value of the correlation coefficient refers to a negative correlation between unobserved factors affecting activity type choice and the choice of spending no time on it, and vice versa. However, it should be clear that the value indicates a correlation between unobserved and random elements influencing both activity type and time expenditure choice models. A higher value of this correlation coefficient is an indication of poorly defined deterministic specifications of the utility functions of both model components. However, statistical insignificance of the correlation coefficient will nullify the argument of the joint estimation of the mode and departure time models.

Travel-Activity Scheduling Survey and Data: The survey used to collect data for this study was conducted in Zurich, Switzerland in 2010. The survey includes an RP travel diary and four SP scenarios corresponding to four alternative travel time changes. A sample of respondents was recruited for participation in a five-day travel diary, from which one day was selected for further analysis. The surrounding conditions of that day’s travel were changed using pre-defined heuristics based on the household characteristics and the activities reported by the respondents, in order to attain significant changes in the generalized costs of the reported schedule and thus provide an impulse for changing behaviour. The households were faced with these changes in face-to-face interviews, where all household members were asked to state the likely effects that the implied changes would have on their activity scheduling on the specified day. The scenarios assigned to the respondents in the household interviews did not aim at determining the effects of specific policies. They were formulated as generally as possible, in the following form: “Imagine your reported trip to [Activity] would take [y] minutes instead of [x]. This may result from the location where the activity was conducted relocating or closing, and you needing to choose a different location.” Travel times for the selected trips (and the return trips, if applicable) were progressively increased by 50, 100 and 200 percent, then decreased by 50 percent, thus creating four scenarios per household. The aim was for the household members to state their likely reactions to such a scenario, including the following possibilities:  Choice of a different departure time for certain trips;  Choice of a different travel mode for certain trips;  Changing the order and/or duration of certain activities;  Cancelling certain activities, or adding additional ones;  Switching certain activities between household members;  Combinations of the above. The day for which the household interview was conducted was chosen by the researchers. Ideally, the household members should have conducted a sufficiently large number of activities, so that changes to the schedule become visible and are substantial enough for the household to change its behaviour on one of the abovementioned levels. Thus, the day with the largest number of conducted activities was used for the interviews. The assignment of scenarios to the household was carried out using heuristics determining which trip is modified. The following rules were followed:

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 If at least one household member is employed (or a student), check for commute trips (that is, trips that have either work or education as a purpose). If such trips are present, change their properties;  Else, if there are children in the household, check whether accompanying trips to or from the children’s school(s) are present; if so, vary those trips;  Else, check whether shopping trips are present, and modify one of them accordingly;  Else, modify the longest leisure trip. This procedure ensures that priority is given to mandatory (that is, commute and to a certain extent shopping) trips, which are carried out routinely and for which changing travel conditions represent a larger modification to the scheduling constraints than for leisure trips. Thus the scenarios created provided the base for interactive interviews, where the household members progressively adapted their stated behaviour to reach convergence to a schedule that seemed satisfying to them. The effects that the scenarios and the stated adaptations had on the respondents’ schedules were directly visible to them. Household addresses in the canton of Zurich, Switzerland, were acquired from an address retailer. Announcement letters with a brief description of the study were sent to the households. A few days after these introductory letters were dispatched, interviewers called the potential respondents to establish the households’ willingness to participate in the study and provide them with detailed information on the survey process. 1344 persons were reached by phone. Members of 340 households agreed to participate in the survey, which corresponds to a recruitment rate of 25.3 percent. 200 of the recruited households requested a paper questionnaire, while 140 preferred filling out an internet survey. 101 paper questionnaires were been sent back, and 57 of the invitations to participate in the online survey yielded useable data. Weiss et al (2010) reports (Table 2 and 3 of Weiss et al. 2010) the sample characteristics of the survey data in terms of national population as well as values and dispersions of the variables in the sample dataset. In this study, we focus on a 24 hour activity scheduling process and hence separate the day of the week during which stated adaptation scenarios are created for each individual. After removing the records with missing values and ambiguous information, a dataset of 184 individuals is selected for modelling. All of these 184 individuals provided 24-hour RP scheduling data together with stated adaptation survey data corresponding to the scenarios. Scenarios are created by changing travel times. Of the 184 individuals, 184 responded to scenario 1, 183 responded to scenario 2, 174 to scenario 3 and 125 to scenario 4. We developed individual models for the reference schedule (using RP scheduling data) and for each scenario. Scenario 1, 2 and 3 are created by increasing travel time for the selected trips by 50, 100 and 200 percent respectively. Scenario 4 is created by decreasing travel time for the selected trips by 50 percent. For modelling the RUM based dynamic scheduling model we classified the activities into 8 broad categories. These are: a. Work b. Education c. Shopping for daily needs d. Shopping for long-term needs e. Errands f. Business 11

g. Others In terms of variables in the model, we considered activity specific variables as well as market segmentation variables. Activity specific variables include activity start time, travel time to reach the activity location, activity duration, number of participants, involvement of family members and friends, etc. Market segmentation variables include age, gender, occupation, income, household car ownership, car availability, etc. The variables used in the models provide a means of investigating the effects of transportation system performance on activity-travel behaviour.

Empirical Model: A total of five models are developed and presented in Table 1. The reference schedule model is developed using the RP scheduling data and models corresponding to the scenarios are developed by using the corresponding stated adaptation responses. The joint models are developed by pooling the RP and SP datasets together. In each case, the RUM based scheduling model starts with an activity type choice at the beginning of the day, and the corresponding time expenditure decision. At the end of the first activity, the process of activity type and time expenditure choice repeats until the end of the day. At every scheduling step in the continuous time expenditure model component, there is a trade-off between time expenditure for the specific chosen activity type, and the time left over for the composite activity. To ensure theoretical consistency in the econometric specification of the utility maximizing time expenditure model, the following specifications are considered for the satiation parameter: α =1exp(-τy). Here, τ is the parameter vector corresponding to a set of variables. In the case of individual RP and SP models, we could only consider activity specific constants, with the composite activity as the reference. However, in the case of the joint RP-SP model, separate constants are introduced for each SP scenario, considering the reference schedule as the reference. Such parameterization in the joint RP-SP model allows us to investigate time valuation subject to various time pressures created by the SP scenarios. Similarly, in the case of variance of the time expenditure utility function, unit variance is assumed for all individual SP and RP data based models without any loss of generality. However, in the case of joint the RP-SP model, separate constants are introduced for each SP scenario, considering the reference schedule as the reference. Such parameterization in the joint RP-SP model allows us to investigate the variation or randomness in time expenditures subject to various time pressures created by SP scenarios. All available variables are considered for parameterization of all components of the RUM-based scheduling model. These include socio-economic, residential location, transportation system performance, and activity specific attributes. Considering that the data set is rather small in relation to the large number of parameters to be estimated, the estimated coefficients are considered statistically significant if the corresponding two-tailed ‘t’ statistics satisfy the 90% confidence interval, (t = 1.64). Some variables with statistically insignificant parameters are also retained in the models because they provide considerable insight into the behavioural process. Retention of some of the insignificant variables is also due to the expectation that, if a larger data set were available, these parameters might show statistical significance. In case of joint model, two models are presented in the table. One includes only statistically significant variables and the other includes some additional variables that are not very significant. Comparison of these two 12

models clarifies that the dropping of apparently insignificant variables does not change sign of any existing parameter. This justifies retaining the parameters with apparently lower t-statistics, but with behavioral implications. A series of specifications were tested and, after removing highly insignificant parameters in different combinations of variable specifications, the final specifications are presented in Table 1. A similar specification was maintained for the reference schedule and the four SP scenarios as well as the joint RP-SP model. In terms of variables, similar variables entered into the systematic part of the activity type choice utility function and the baseline utility function of the continuous time expenditure model. In addition, an unrestricted correlation between unobserved factors influencing activity type choice and time expenditure is accommodated. The goodness-of-fit of the estimated model is calculated using the Rho-squared value: Rho - Squared  1 

Log likelihood of Full Model Log likelihood of the Constant - Only Model

(17)

The Rho-squared value is the highest for scenario 4, which represents a 50 percent decrease in travel time. However, the values of other models do not vary by a wide margin. Interestingly, the lowest rho-square value is found for the joint RP-SP model. However, the joint model is not directly comparable with other individual models because it uses pooled datasets and it has a higher number of parameters than the individual model. Overall, the Rho-square values vary from 0.12 to 0.15, which reflect a reasonably good fit for such complex models. The correlation coefficients between activity type choice and time expenditure are positive for all models. This suggests that the unobserved factors that influence activity type choices also influence a tendency toward longer time expenditures. This means that people prefer to spend more time on the activities which they schedule. However, the presence of time pressure created by the time budget constraints forces them to do a trade-off between time expenditures to the specific activity and saving time for the composite activity. The correlation coefficients of the joint RP-SP model, reference schedule model and the model for scenario 1 could be parameterized as functions of the time of the day. This allows to capture the dynamic relationship between the unobserved factors influencing activity type choice and time expenditure. This suggests that unobserved factors influencing activity type choice and the time expenditure decision become more strongly correlated later in the day. Stronger correlations refer to greater influences of the unobserved factor, and thereby imply more random behaviour. Interestingly, the correlation coefficient is the lowest for the joint RP-SP model, which is 40 percent lower than that of the RP reference schedule model. This highlights the robustness of the joint modelling approach for activity scheduling. Pooling RP and SP data collected from the same group of people increases the capacity of the pooled dataset in representing a wide variety of transportation demand-supply situations. Joint modelling by using such a rich dataset with explicit recognition of variances and valuation in time expenditure increases the robustness of systematic components of the model in capturing behavioural responses of scheduling process. However, in the cases of scenario 2, 3, and 4, we found constant correlation coefficients across the day and identified that the value is the highest for scenario 4 (representing a 50 percent decrease in travel time). Constant correlation decreases with increasing travel time. A possible 13

explanation for not having the dynamic correlation coefficient for SP scenarios represent more than a 50 percent increase in travel time would be the increased complexity in choosing a SA response. Increasing the travel time by more than 50 percent seems to create situations where people may change their valuation of time. Similarly, an asymmetric response is visible in the case of reduced travel time because this scenario increases the time available for activities. Activity Type Choice Model Component In terms of the activity type choice component of the dynamic scheduling model, a series of variables are used. Types of variables considered are alternative specific constants, activity specific variables and market segmentation variables. For individual RP and SP models, the scale parameter (μ) is not identifiable, however, for the joint RP-SP model, the scale parameter of SP choices is estimated with respect to that of the RP choices. We found a lower scale for SP choices, which means higher variations. Compared to the unit scale of RP schedule data, the SP data has the scale of 0.93 (exponential of -0.07), which cannot be captured in the individual SP scenario specific models. In the systematic utility component, the Alternative Specific Constants (ASC) of activity type choices are negative for all activity types except for work activities. ASC captures the baseline utility of activity type choice. The work activity is fundamentally different from other activity types because people earn money at work but spend it in other activities. Therefore, the positive sign of the work activity choice ASC reflects the basic microeconomic nature of activity scheduling processes. Interestingly, the value of the work activity ASC increases with increasing travel time. This indicates that the priority of scheduling work activities increases in case of increasing time pressures resulting from increasing travel time (scenario 1, 2 and 3). However, it is also clear that the value increases even in the event of decreasing travel time (scenario 4). This refers to the asymmetric response towards transportation system performance. In the case of the joint RP-SP model, this constant is positive, but lower than in any other models. Among other activity types, the leisure activity type has the most negative alternative specific constant. This ASC increases when travel times increases above 50 percent, however it further decreases with increasing travel time more than 50 percent and decreasing travel time by 50 percent. This refers to a nonlinear preference change to leisure activities (which is the most flexible activity type) with changes in transportation system performance. Nonlinear responses in baseline preferences in terms of changes in ASCs are also true for business, education, errands and shopping activities. The joint RP-SP model has the lowest ASCs for all activity type choices. Lower values of ASC refer to a better model and suggest that the variables used in the systematic utility function better capture the systematic responses. So, it is clear that pooling multiple SP and RP datasets with explicit representation of scale/variance differences improves the activity type choice model component of the activity scheduling process. In all models, activity start time is represented as a continuous variable and expressed as a fraction of the 24 hour day. The coefficient for start time is negative for work and daily shopping activities only. This coefficient is the lowest (most negative) for work activities meaning that work activities are often scheduled early in the day. Daily shopping activities demonstrate the second lowest start time coefficient value, suggesting that people also prefer to conduct shopping trips earlier in the day. It is clear that increases in travel time influence early starts of the work 14

activities. However, the response is not the same for travel time reductions. It seems that a reduction in travel time also influences an early start for the work activity. In the case of shopping for long term needs, the highest positive coefficients are shown for the reference state. This coefficient decreases with changes in transportation system performances and shows an asymmetric response for travel time loss and gain. The same is true for business and leisure activities. The joint model reflects that people tend to schedule work activities earlier in the day and that the sequence of preference for other activity types is: shopping for daily needs, shopping for long-term needs, business and leisure. The sequence of scheduling preference captured by the joint model reflects the differential planning horizons for the corresponding activity types. For example, work is the regular activity and shopping for daily needs stems from daily activity planning. However, shopping for long-term needs, business and leisure may stem from activity planning over time frames longer than one day. However, the priority in scheduling captured in the joint model reflects the temporal flexibility in start time, which may be influenced by other factors also, e.g. activity location choice. In order to capture the direct impact of travel time on activity scheduling choices, we consider travel ratio as a variable in the models. The concept of travel ratio has been successfully used in activity-based travel demand modelling in the past (Habib and Miller 2009). Travel ratio is calculated as the ratio of travel time and the summation of activity duration and the travel time. It represents the price of activity time in terms of travel time. By definition, it is less than 1. The longer the travel times to the place of an activity, the greater the values. This variable allows trip information to be represented inside the model in a normalized way instead of using simple travel times. However, it was difficult to accommodate this variable in the utility function of all activity types. One possible reason is that the scenarios were already defined based on changes in travel time and that the datasets already contain the effects of travel time changes indirectly in the scheduling process information. The travel ratio was found to be significant for leisure activities only. This negative sign of travel ratio for leisure activity type choice suggests that an increase in travel time reduces the utility of scheduling leisure activities. This suggests that increasing travel time affects quality of life. However, the travel ratio has a positive sign for decreasing travel time. This means that in the case of improvement in transportation system performance, people tend to schedule recreational activities with a higher travel ratio earlier in the day. No linear changes in this coefficient are visible across the scenarios. Similarly, an asymmetric response between time loss and gain of time for transportation system performance change was found. Market segmentation variables, such as age, gender, income, household auto ownership and car availability are used in the model; it was difficult to accommodate these variables in all models with statistical significant coefficients. A possible reason for the low significance of these segmentation variables in the models is the small size of the data sets causing potentially insufficient variations of these variables. It should be mentioned that these variables are constant across the data sets as the same group of people are surveyed for both RP reference schedules as well as for the corresponding scenarios. Some patterns have been found for the relationship between socioeconomic characteristics and activity scheduling behavior. People between 35 and 45 years of age are found to have different activity scheduling choices than people in younger or older groups. It seems that people in this age group are averse to shopping for long term needs. Female respondents are more likely to 15

conduct errands than males. The number of cars in a household has significant effects on certain activity type choices and it is consistent across the models. A higher level of household auto ownership increases the utility of scheduling work activities and errands, but reduces the utility of business activities. People with an income of less than 6000 Swiss Francs demonstrate a higher utility in scheduling shopping for daily needs compared to the higher income groups. People with an income of less than 4000 Swiss Francs show a higher utility of scheduling leisure activities compared to the higher income groups. A probable explanation of income effects is that income affects lifestyle preferences which in turn affect activity scheduling. Higher car availability increases the utility of scheduling work and leisure activities, but reduces the utility of scheduling shopping for longer term needs. Baseline Utility Function of Activity Duration Choice The baseline utility of activity duration choice explains the baseline preference of time expenditure for the activity types. As per the formulation of the time expenditure model component, the baseline utility function multiplies the utility of time expenditure (which is a power function of time expenditure itself). In addition, the baseline utility function accommodates a systematic and random component of time expenditure utility. The systematic baseline utility function is expressed as a linear-in-parameter function of activity specific and market segmentation variables. Activity-specific dummy variables (the alternative specific constants) capture the baseline time expenditure preferences to the activity types. They capture the systematic utility components that are not explained by available activity specific and market segmentation variables. It is clear that the highest unexplained baseline utility is shown for education activities, and this is consistent across all scenario schedules and the reference case. It is understandable that educational activities have higher baseline utility and that the duration of such activities is often controlled by external factors. However, with increasing travel time this value changes non-linearly. For example, it increases up to 50 percent increase in travel time and then starts reducing. Contrary to this, the value decreases for 50 decreases in travel time. It is shown that there are nonlinear responses for increasing travel time and asymmetric responses for time gains versus time losses. In the case of work activities, the constant grows with increases in travel times up to 100 and then reduces. However, it reduces subject to reductions in travel time. In the case of shopping for daily needs, the constant decreases with increasing travel times. It also reduces for the reduction in travel time. Similar nonlinear changes with respect to increasing travel time and asymmetric response between gains and losses are true for all other activity types. Consistent with the individual models, the joint model reveals that the highest constant value is for education and then for work, shopping for daily needs, shopping for long-term needs, other, leisure, errands and business consecutively. Such sequences of values reflect the relative unexplained systematic utility of time expenditure choices. This also reflects the relative controls of other factors or the relative fixities defined by factors not in control of the decision makers in the case of activity duration choices. Activity start time has a significant impact on time expenditures for all activity types. Start time is specified as a continuous variable expressed as a fraction of 24 hours. It is shown that activities with longer durations are scheduled later in the day. The coefficient also shows nonlinear change 16

with respect to increases in travel time as well as asymmetric response in time gain versus time loss. This suggests that when subject to large deviations in travel times, the influence of start time on activity duration becomes critical and people tend to schedule longer activities later in the day. The direct influence of travel time on RUM based activity utility is accommodated through the incorporation of travel ratio in the baseline utility function. This variable has an expected negative sign indicating that longer travel time reduces activity duration. However, this value did not enter into the model for scenario 3 representing a 200 percent increase travel time. This means that, with very large increases in travel time, it is difficult for the respondents to perceive the effects on time expenditure. However, intuitively, a decrease in travel ratio increases flexibilities in time expenditure decisions by reducing the impact of travel ratio. In terms of market segmentation variables, only household auto ownership, income, driving license and car availability could be considered in the time expenditure utility functions. Higher auto ownership reduces the duration of shopping for daily needs, leisure and other activities, perhaps due to increased ease and frequency of such activities. Higher levels of auto ownership at the household level may reduce the competition of sharing cars among the household members and allow the members to conduct longer duration business activities. Consistently, similar effects are visible for the auto availability variable, which expresses the interaction between driving license possession and car availability. In case of all market segmentation variables, it is clear that effects change nonlinearly with increasing travel time. Also, the asymmetric change for gains due to reduction in travel time and loss due to increase is visible. Satiation Function of RUM Activity Duration Choice The satiation function is parameterized as α =1-exp(-τ). Here, τ refers to a set of activity specific constants, which explains the satiation effects while executing the corresponding activity types. With relatively lower values of the satiation parameter, there is a relatively lower satiation effect and thereby tendency of having shorter activity duration. These values are to be evaluated relatively with respect to the time saving for rest of the day (composite activity) at the time of scheduling the specific activity. For all individual models, the parameter for the composite activity is the reference and set to 0. However, for the joint model, 0 is set for RP scheduling information with respect to the fact that separate parameters are estimated for each SP information set. It is clear that the highest values are seen for leisure activities indicating that the most satisfaction is gained in doing leisure activities. Contrary to this, the lowest value of the satiation parameter is seen for education activities. Anecdotal explanations would state that people enjoy longer recreational activities the most and longer educational activities the least. In addition to the activity type specific constant, the satiation factor of composite activity of the joint RP-SP model is parameterized to recognize the different data generation process in the RP reference schedule as well as in the SP scenarios. The coefficients are plotted in Figure 1. It is clear that the relative satiation (thereby valuation of time expenditure) across the activity types remains the same for all models. However, variation in magnitude of valuation changes widely. The most variation is visible in the educational activity and the least variation is visible in the leisure and errands activities. This indicates that the valuation of time expenditure for leisure activities is least affected by changes in transportation system performances; however, significant variation is possible in the education, shopping and work activity. 17

Figure 2 presents the distribution of composite activity satiation parameters in the joint model. Composite activity captures the time pressure effects while scheduling a specific activity. Time pressure is created while making trade-offs in allocating time to the activity to be scheduled and the saving time for rest of the day’s activities. The value is set to 0 for the RP reference schedule. Increasing values of composite activity satiation parameters suggests more careful scheduling by saving more time for rest of the day’s activities. A high value of this parameter suggests that people become more conservative in allocating time to the specific activities and a low value states that people become more relaxed in spending time. It is clear that travel time changes have a nonlinear relationship with time pressure created by changes in travel time. Interestingly, the relationship can be better explained by a quadratic function. A quadratic function clearly explains that people’ capacity for accommodating time pressure increases with an increase in travel time, but only up to certain limit. After the limit, the situation becomes too complex to cope with and people become more likely to satisfice than to maximize utility. This finding is also verified by the changes in variances of the time expenditure utility function presented in Figure 3, which shows a similar quadratic relationship. Such behavioural response toward complexities of the context of decision making is also shown by other works (Swait and Adamowicz 2011, Habib and Swait 2011). The results of this investigation underline the importance of considering the complexities and context in the activity-travel scheduling process. It also highlights the limitation of using only RP data for developing travel demand models and applying them to wide ranges of transportation system performance. It also shows an innovative method of joint RP-SP modelling for the activity scheduling process, where RP data can be further enriched by pooling it with stated adaptation responses for targeted transportation performance ranges.

Conclusions and Further Research: This paper uses RUM based activity-travel scheduling models to investigate the relationship between transportation system performance and daily activity-travel scheduling processes. The objectives of this study include improving the understanding of activity-travel scheduling decision making by using a RUM based approach, investigating the limitations of using only RP data in capturing responses to wide ranges of variations in transportation system performances, and demonstrating the means of enriching RP data by adding stated adaptation responses to responses for targeted transportation performance ranges. An innovative activity-travel survey was used to collect data on RP scheduling information from a population sample in Zurich as well as stated adaptation responses to up to 200 percent increases and 50 percent decreases in travel time performances. The data are used to develop a series of individual RP and SP models together with a joint RP-SP activity-travel scheduling model. The RUM based scheduling model clearly captured the time pressure effects because of time budget limitations. Thus, it clearly identifies differential effects of changes in transportation system performances reflected through changes in travel time on activity type choice, time of the day choice and activity duration jointly. Results of empirical models show that our activity-travel scheduling processes are sensitive to transportation system performance. However, such sensitivity may not be constant over different ranges of changes in transportation system performances. It becomes clear that people change their valuation of time while scheduling activities when travel time changes by great margins. A nonlinear relationship between the changes in time 18

pressure effects (thereby time valuation) and corresponding transportation system performance is shown. Also, asymmetric responses to reductions and increases in travel time are demonstrated. It becomes clear that a quadratic relationship exists between time pressure effects and the corresponding changes in transportation system performance. A possible explanation is that people spend more mental energy in making activity scheduling decisions subject to hypothetical increases in travel time due to increased complexity of the scheduling context. Up to a limited level of complexity, people can apply increased effort to make optimal decisions, but beyond that point, the context becomes too complex to make optimum decisions. Hence, people operate more as satisficers than as utility maximizers in making activity-travel scheduling decisions. Such complex behavioural responses may not always be captured in RP data of activity-travel decisions. However, SP data corresponding to a wide range of transportation system performances can be used to enrich RP data. Joint RP-SP data can be used to develop joint models to enhance the capacities of our activity-travel scheduling model in accommodating a wide range of policy scenarios. However, data limitations in terms of the small size of the sample limit the possibility of more robust investigations including jointly modelling activity location and mode choice within the scheduling model. A more detailed SP survey with smaller increments and decrements of travel time would produce more extensive and robust data for further investigation. These are considered for the next steps of this research.

Acknowledgements: This research was partially funded by a Natural Science Engineering Research Council of Canada Discovery grant. The data collection was funded by the SVI project SVI 2004/012 Aktivitätenorientierte Analyse des Neuverkehrs (Activity-oriented Analysis of Induced Demand). We are grateful for the input and advice of the project committee chaired by M. Simon. Christoph Dobler invested a great amount of time and programming skill into the implementation of the survey software, for which he deserves our gratitude.

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Table 1: RUM Based Activity Scheduling Model

Reference Schedule Scenerio 1 Scenerio 2 Model Model Model Number of individuals

Scenerio 3 Model

Scenerio 4 Joint RP-SP Joint RP-SP Model Model-Full Model-Refined

186

184

183

174

125

852

852

Loglikelihood of Full Model

-1254

-1193

-1002

-1133

-865

-5536

-5539

Rho-Square Value

0.14

0.13

0.14

0.12

0.15

0.12

0.12

Activity Type Choice Model Variable Activity Type Param t-Stat Param Alternative Specific Constant Work 1.20 1.48 1.67 Education -1.76 -2.29 -1.37 Shop (Daily Needs) -0.70 -0.72 -0.68 Shop (Long-Term Needs) -1.91 -1.62 -1.41 Errands -2.68 -2.17 -1.31 Business -3.82 -1.68 -1.91 Leisure -3.15 -3.05 -3.71 Starting Hour as a Fraction of 24 hours Work -5.05 -3.69 -5.64 Shop (Daily Needs) -0.65 -0.35 -0.92 Shop (Long-Term Needs) 2.82 1.42 2.47 Business 4.20 1.20 2.49 Leisure 5.12 3.34 6.25 Travel Ratio: Travel Time Divided by Total Activity Duration Errands 2.42 2.48 0.01 Leisure -0.56 -0.65 -2.02 Dummy Variable (1) for the Age between 35 and 45 Work 0.44 0.98 0.52 Shop (Long-Term Needs) -0.91 -1.10 -1.17 Dummy Variable (1) for Male Errands -0.29 -0.43 -0.56

t-Stat Param t-Stat Param t-Stat Param t-Stat Param t-Stat

Param

t-Stat

1.99 -1.77 -0.73 -1.26 -1.16 -1.04 -3.37

2.52 -1.58 0.61 0.67 -1.46 -2.98 -2.44

3.32 -2.23 0.70 0.54 -1.35 -1.47 -2.74

2.59 -1.80 -0.06 -1.09 -1.21 -3.75 -2.88

3.03 -2.67 -0.05 -0.93 -1.16 -1.51 -2.97

1.76 -3.07 -0.10 -0.79 -2.23 -4.50 -1.86

2.15 -2.60 -0.12 -0.68 -1.65 -2.03 -2.12

0.70 -0.82 -0.13 -0.48 -0.44 -0.85 -1.00

4.52 -5.30 -0.81 -2.28 -2.19 -2.44 -5.36

0.66 -0.78 -0.11 -0.45 -0.42 -0.79 -0.91

4.76 -5.78 -0.76 -2.31 -2.27 -2.45 -5.84

-4.09 -0.54 1.36 0.87 3.65

-6.19 -2.64 -2.12 3.63 4.35

-4.40 -1.56 -0.93 1.14 3.32

-6.54 -0.81 1.41 3.70 5.49

-4.27 -0.35 0.72 1.05 3.86

-5.22 -3.75 -1.70 -1.07 1.61 0.75 7.36 2.01 1.94 1.51

-2.13 -0.44 0.61 0.75 1.68

-7.20 -1.46 1.73 1.38 5.70

-2.02 -0.43 0.56 0.67 1.56

-8.47 -1.52 1.74 1.33 6.30

0.07 -2.14

1.76 -0.51

1.78 -0.74

1.74 -1.22

1.65 -1.24

0.57 0.94

0.00 -0.35

0.08 -2.34

---0.31

---2.27

1.17 -1.46

0.32 -0.49

0.73 -0.53

0.64 -0.97

1.40 -0.91

-0.14 -0.35 -1.49 -1.79

0.19 -0.38

2.27 -2.33

0.18 -0.36

2.34 -2.35

-0.84

-0.54

-0.89

-0.45

-0.81

-0.22

-1.86

-0.21

-1.92

0.58 0.55

0.12

0.19

22

Table 1: (Continued) RUM Based Activity Scheduling Model Number of Household Cars Work 0.60 2.52 0.38 Errands 0.58 1.48 0.47 Business -0.77 -1.00 -1.32 Dummy Variable (1) for the Income less than 4000 units Shop (Daily Needs) 0.66 0.96 0.81 Shop (Long-Term Needs) -0.84 -0.73 -1.39 Leisure 0.62 0.96 0.90 Dummy Variable (1) for the Income between 4000 to 6000 units Work -0.11 -0.23 -0.08 Shop (Long-Term Needs) -1.27 -1.22 -1.54 Errands -0.08 -0.09 -0.14 Leisure -0.40 -0.65 -0.32 Car Availability Work 0.37 1.87 0.31 Education -0.71 -0.99 -1.98 Shop (Long-Term Needs) -0.38 -1.11 -0.47 Business -0.16 -0.37 -0.38 Leisure 0.06 0.17 0.15

1.51 1.22 -1.80

0.29 0.61 -0.85

1.34 1.92 -1.09

0.25 0.28 -0.39

1.17 0.88 -0.48

0.24 1.33 0.12 0.39 -0.93 -1.55

0.14 0.18 -0.30

3.13 2.71 -2.43

0.13 0.17 -0.29

3.28 2.89 -2.47

1.27 -1.18 1.37

0.13 -1.24 0.88

0.20 -1.01 1.68

-0.17 -1.27 0.70

-0.21 -0.91 1.08

-0.14 -0.24 -2.12 -1.92 -0.88 -1.65

0.19 -0.33 0.11

1.53 -1.66 0.89

0.15 -0.34 ---

1.37 -1.83 ---

-0.16 -0.78 -1.51 -12.22 -0.16 -1.76 -0.50 -0.52

-1.63 -0.05 -1.61 -0.92

-0.31 -0.03 0.37 -0.55

-0.56 -0.59 -1.20 -0.04 -12.23 -0.05 0.53 0.63 0.79 -0.93 -0.54 -0.96

-0.07 -0.55 -0.02 -0.17

-0.69 -2.61 -0.13 -1.50

-0.06 -0.52 ---0.17

-0.67 -2.67 ---1.68

1.56 -1.64 -1.32 -1.03 0.80

1.60 -0.85 -0.97 -0.81 0.59

0.08 -0.11 -0.42 -0.32 0.05

0.39 -0.27 -1.27 -0.60 0.25

0.10 -0.10 -0.13 -0.10 0.04

2.78 -1.01 -2.04 -1.40 1.16

0.10 -0.10 -0.12 -0.10 0.03

2.87 -1.00 -2.05 -1.40 1.05

Param t-Stat Param t-Stat Param t-Stat Param t-Stat Param t-Stat

Param

t-Stat

0.32 -0.55 -0.45 -0.43 0.11

0.31 1.35 0.08 0.14 -0.48 -1.11 -0.74 -1.47 0.18 0.77

Activity Duration Choice Model: Baseline Utility Function Variable Activity Type Param t-Stat Alternative Specific Constant Work 8.00 4.14 Education 19.41 1.91 Shop (Daily Needs) 10.35 3.15 Shop (Long-Term Needs) 5.53 2.11 Errands 3.04 1.29 Business 0.37 0.02 Leisure 3.99 1.33 Other 5.33 2.79 Starting Hour as a Fraction of 24 hours All Acttivity Types 2.34 2.11

7.82 22.81 8.46 3.77 1.03 1.06 1.87 3.27

3.73 1.49 2.60 1.48 0.46 0.29 1.05 1.85

8.88 20.75 3.95 9.80 3.36 4.34 4.30 2.68

3.97 2.18 2.10 2.57 1.71 1.24 2.50 1.64

7.96 10.10 0.89 6.35 -0.22 1.13 1.19 2.26

3.53 1.71 0.56 2.14 -0.15 0.01 0.83 1.41

5.00 10.84 6.96 6.78 1.33 4.41 4.14 2.42

2.10 1.13 2.16 2.32 0.76 1.32 1.80 1.39

9.15 16.25 6.48 6.38 1.76 1.47 3.97 4.60

6.46 3.47 4.17 3.93 1.52 0.84 3.58 4.18

8.76 15.61 5.91 6.15 1.51 --3.45 4.23

7.79 3.54 4.69 4.19 1.47 --3.85 4.74

2.73

2.75

0.50

0.59

2.16

2.62

1.65

2.15

2.14

4.23

2.13

4.40

23

Table 1: (Continued) RUM Based Activity Scheduling Model Number of Household Cars Shop (Daily Needs) -0.90 -1.72 -1.35 Business 1.01 0.06 1.72 Leisure -0.53 -1.04 -0.39 Others -0.98 -2.27 -1.09 Dummy Variable (1) for the Income less than 6000 units All Acttivity Types -0.40 -1.13 -0.30 Driving License x Car Availability Work -0.08 -0.41 -0.29 Shop (Daily Needs) -0.33 -0.78 -0.54 Business 2.21 0.26 2.84 Leisure 0.00 0.00 -0.04 Others -0.55 -1.69 -0.67 Travel Ratio: Travel Time Divided by Total Activity Duration All Acttivity Types -3.77 -4.18 -0.35

-2.51 1.00 -1.17 -2.27

-0.51 1.16 -0.31 -0.13

-1.04 0.01 -1.13 -0.28

-0.30 1.98 -0.44 -0.49

-0.68 0.00 -1.42 -1.21

-0.67 -1.62 2.85 1.21 -0.24 -0.78 -0.40 -1.29

-0.70 -0.36 -0.41 -0.83

-2.83 -0.40 -2.49 -3.66

0.00 -0.67 ---0.34 -0.78

0.00 -2.91 ---2.33 -3.68

-0.84

-0.01

-0.03

-0.05

-0.15

-0.19 -0.66

-0.12

-0.64

---

---

-1.53 -1.23 2.24 -0.16 -2.03

-0.31 0.34 2.28 -0.21 -0.19

-1.69 0.85 0.02 -0.93 -0.61

0.06 0.49 3.01 -0.28 -0.58

0.26 0.93 0.01 -0.97 -1.89

-0.10 -0.20 0.66 -0.51 -0.25

-0.47 -0.53 0.78 -1.73 -0.81

-0.12 -0.11 1.74 -0.12 -0.57

-1.29 -0.48 3.02 -0.91 -3.33

-0.14 --1.60 ---0.53

-1.48 --3.15 ---3.35

-4.30

-2.68

-4.00

0.00

---

-2.50 -4.04

-2.87

-7.70

-2.75

-8.22

Param t-Stat Param t-Stat Param t-Stat Param t-Stat Param t-Stat

Param

t-Stat

-1.01 -1.41 -1.18 -1.03 -0.71 -0.73 -0.70 -0.81

-14.68 -7.23 -12.64 -9.29 -5.73 -7.45 -8.42 -12.69

0 0.02 --0.03 ---

--0.94 --1.06 ---

Activity Duration Choice Model: Satiation Parameter(Exponential Function) Variable Activity Type Param t-Stat Activity Type Specific Constant Work -0.98 -7.97 Education -1.56 -4.01 Shop (Daily Needs) -1.38 -7.42 Shop (Long-Term Needs) -0.93 -4.29 Errands -0.81 -3.02 Business -0.83 -1.66 Leisure -0.67 -4.02 Other -0.82 -6.27 Composite Activity Reference schedule 0 --Scenario 1: 50% increase in travel time Scenario 2: 100% increase in travel time Scenario 3: 200% increase in travel time Scenario 4: 50% decrease in travel time

-0.95 -1.67 -1.28 -0.85 -0.77 -1.09 -0.56 -0.72

-7.06 -3.28 -6.51 -3.76 -2.90 -2.60 -2.96 -5.48

-0.88 -1.46 -0.71 -1.14 -0.57 -0.93 -0.49 -0.46

-5.70 -3.73 -3.40 -4.21 -2.18 -2.08 -2.41 -2.77

-0.90 -1.01 -0.69 -0.93 -0.31 -0.99 -0.24 -0.55

-5.79 -2.64 -3.73 -3.90 -1.23 -2.11 -1.26 -3.57

-0.56 -0.94 -1.04 -0.89 -0.15 -1.04 -0.46 -0.45

-2.46 -1.36 -3.88 -3.57 -0.45 -2.74 -1.70 -2.31

0

---

0

---

0

---

0

---

-1.04 -12.15 -1.44 -7.17 -1.21 -11.53 -1.05 -8.76 -0.74 -5.53 -0.89 -4.29 -0.73 -7.59 -0.83 -10.51 0 0.04 0.02 0.04 0.01

--1.15 0.79 1.24 0.24

24

Table 1: (Continued) RUM Based Activity Scheduling Model

Correlation Coefficient Starting hr as a fraction of 24 hr0.62 3.10 0.67 4.12 Constant for whole day Scale Parameter of Activity Type Choice Model (Exponential Function) Reference schedule dummy 0 --Stated adaptatin scenarios dummy 0 --Variance of RUM Duration Choice Model: Exponential Function Reference schedule dummy 0 --Scenario 1: 50% increase in travel time dummy 0 --Scenario 2: 100% increase in travel time dummy Scenario 3: 200% increase in travel time dummy Scenario 4: 50% decrease in travel time dummy

0.79

9.20

0.71

8.75

0

---

0

---

0

0.37

4.30

0.37

4.47

---

0.00 -0.07

---0.68

0.00 0.00

-----

---

0.00 0.19 0.08 0.15 -0.01

--2.11 0.88 1.75 -0.14

0.00 0.16 --0.13 ---

--2.05 --1.69 ---

0.92 14.64

0

--0

--0

25

Joint RP-SP Model SP Scenario 4 SP Scenario 3 SP Scenario 2 SP Scenario 1 RP Reference Schedule

Satiation Parameter for Composite Activity

Figure 1: Satiation Parameters of Time Expenditure Model Components

Parameter = 0.0003(% increase)-6E-07(% increase)2 + 0.0108 R² = 0.7608

0.05

0.04 0.03 0.02

0.01 0.00 -200

-150

-100

-50

-0.01

0

50

100

150

200

250

300

350

-0.02 -0.03 -0.04

-0.05 Percentage Incerase in Travel Time

Figure 2: Satiation Parameters of Composite Activity Time Allocation

26

Variance = 0.0013(% increase) -4E-06(% increase)2 + 1.0529 R² = 0.5742

Varaince of Random Utility of Time Expenditure

1.25 1.2 1.15

1.1 1.05 1 0.95 0.9

-200

-150

-100

-50

0

50

100

150

200

250

300

350

Percentage Incerase in Travel Time

Figure 3: Variance of Time Expenditure in Joint Model

27