Dynamics of commuting decision behaviour under advanced traveller information systems

Transportation Research Part C 7 (1999) 91±107

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Dynamics of commuting decision behaviour under advanced traveller information systems Hani S. Mahmassani a,*, Yu-Hsin Liu b a

b

Department of Civil Engineering and Department of Management Science & Information Systems, The University of Texas, Austin, TX 78712-1076, USA Institute of Management Science and Department of Accounting, I-Shou University, 1, Sec. 1, Hsueh-Cheng Rd., Ta-Hsu Hsiang, Kaohsiung, Taiwan, ROC

Abstract This paper addresses departure time and route switching decisions made by commuters in response to Advanced Traveller Information Systems (ATIS). It is based on the data collected from an experiment using a dynamic interactive travel simulator for laboratory studies of user responses under real-time information. The experiment involves actual commuters who simultaneously interact with each other within a simulated trac corridor that consists of alternative travel facilities with di€ering characteristics. These commuters can determine their departure time and route at the origin and their path en-route at various decision nodes along their trip. A multinomial probit model framework is used to capture the serial correlation arising from repeated decisions made by the same respondent. The resulting behavioural model estimates support the notion that commuters' route switching decisions are predicated on the expectation of an improvement in trip time that exceeds a certain threshold (indi€erence band), which varies systematically with the remaining trip time to the destination, subject to a minimum absolute improvement (about 1 min). Ó 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction The response of drivers to real-time information continues to be an important missing link in our ability to evaluate the e€ectiveness of Advanced Traveller Information Systems (ATIS), and to design bene®cial information supply strategies. Due to limited deployment of ATIS technologies, it is not practical to observe actual behaviour of users under di€erent real-time information strategies on a daily basis together with the various performance measures a€ecting these

*

Corresponding author. Tel.: +1-512-475-6361; fax: +1-512-475-8744. E-mail address: [email protected] (H.S. Mahmassani)

0968-090X/99/$ - see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 8 - 0 9 0 X ( 9 9 ) 0 0 0 1 4 - 5

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responses (Mahmassani and Herman, 1990). Laboratory experiments have been proposed and tested to a limited extent as an e€ective and practical approach to gain insights into tripmakers' decision processes under di€erent types of ATIS-provided information (Adler et al., 1993; Bonsall and Parry, 1991; Chen and Mahmassani, 1993; Koutsopoulos et al., 1994; Vaughn et al., 1993). An interactive multi-user simulator has been developed at the University of Texas at Austin, and used in a set of laboratory experiments to examine the day-to-day commuter behaviour under real-time information and develop the mathematical models presented in this paper. Models of the decision processes that determine pre-trip departure time and route switching as well as enroute path switching as a function of the user's cumulative and recent experience with the system are developed and calibrated under a multinomial probit model framework, so as to take account of travellers' learning from past experience with the system, and to capture the serial correlation arising from repeated decisions made by the same respondent. Section 2 describes the laboratory experiment, followed by the boundedly rational behaviour framework for commuters' day-to-day departure time and route switching models under ATIS. A brief discussion and interpretation of the model speci®cation is presented in Section 4. The estimation results are discussed in Section 5, followed by concluding comments in Section 6. 2. The laboratory experiment The dynamic interactive simulator developed at the University of Texas at Austin adopts the client/server modelling concept used extensively in X Window System applications (Chen and Mahmassani, 1993). At the core is a simulation-assignment model based on the corridor network version of the DYNASMART model (Jayakrishnan et al., 1994) that includes pre-trip route selection and en-route path switching. Another program controls the layout of windows displayed on the screens of a set of Macintosh and Intergraph computers (used by subjects, one computer per subject) interconnected through a local area network. The participants receive the real-time information via the computer monitor and use the keyboard or mouse to input their responses during the experiment. All user responses are input to the simulation-assignment model and thus directly in¯uence prevailing trac conditions to create a dynamic trac environment. This interactive simulator possesses several unique features for investigating tripmaker behaviour under ATIS. First, it o€ers multiple user capabilities, whereby a number of users can have access to di€erent information systems simultaneously. Therefore, data can be collected on several subjects (as many as 100 subjects at the same time) simultaneously, since this allows real-time interaction of the di€erent users with the prevailing trac situation. Second, the simulator is dynamic, as all participantsÕ responses are input to the simulation-assignment model and thus directly in¯uence prevailing trac conditions. There are no predetermined consequences for the subjects' responses, other than those that result from the nonlinear interactions taking place in the trac system. Third, this simulator can be run in real time. It is calibrated in such a way that every simulation time step conforms to the speed of the host computer's clock. Naturally, other desired simulation speeds can also be achieved. Last, it supports experiments intended to be collective but not collaborative in design (Chen and Mahmassani, 1993). All the human/machine interfacing with a given participant takes place via the computer assigned to him/her. Each participant is provided with a view of the basic network con®guration and

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his/her relative vehicle position in the network at all times. Each participant's vehicle is moved according to his/her decisions in real time. Di€erent situational messages are shown to him/her in the space provided on the screen as determined by the trac system's evolution. Participants are alerted by a `beep', produced by the built-in audio device in computers every time a message appears on screen. The simulation-assignment model is based on the corridor network version of the DYNASMART model developed at the University of Texas at Austin. The model is comprised of three main components: the trac performance simulator, the network path processing component, and the user decision-making component. The trac performance simulator is a ®xed time-step mesoscopic trac simulator. Vehicles on a link are moved individually at prevailing local speeds consistent with macroscopic speed±density relations (modi®ed Greenshield's model). Inter-link transfers are subject to capacity constraints. For the given network representation and link characteristics, the simulator uses a time-dependent input function to determine the associated vehicular movements, thereby yielding the resulting link trip times, including estimated delays associated with queuing at nodes. These form the input to the path processing component, which calculates the pertinent path trip times, which are in turn supplied to the participating commuters and the user decisions component. The latter is intended to predict the responses of the simulated commuters in the system to the available information according to a set of behaviour rules. This capability allows us to control the fraction of users in the system that are equipped with ATIS devices. The simulator could consider a variety of information strategies; the primary one used to date had been of the so-called TRAVTEK (or AUTOGUIDE) variety: prevailing trip times on the network links with no attempt by some central controller or coordinating entity to predict future travel times. Another function of the path processing component is to translate the user path selection and switching decisions into time-varying link ¯ow patterns on the network's links. Further detail on the simulation-assignment methodology may be found in the papers by Mahmassani and Jayakrishnan (1991) and Jayakrishnan et al. (1994). In this experiment, the participants interacted with each other within a simulated trac corridor that consists of three parallel facilities, highways 1, 2 and 3 with speed limit 89 km/h (55 mph), 72 km/h (45 mph) and 56 km/h (35 mph), respectively. The cross-over links had a free mean speed of 72 km/h (45 mph). The layout of the information displayed on the monitor screen is shown in Fig. 1. Each of the three highways was 9 miles long, and each was discretized into nine one-mile segments, with cross-over links at the end of the third, fourth, ®fth, and sixth miles to allow commuters to switch from one highway to any of the other two based on the real-time information provided by the system. The commuters could determine their route selection before starting the trip and their path en-route as they approach the nodes of these cross-over links. In addition, they can also change their next dayÕs departure time after completing a given dayÕs commute. Forty ®ve randomly selected subjects were recruited to participate in this experiment for ®ve decision days from full-time faculty and sta€ members at the University of Texas at Austin. The majority were between the ages of 20 and 60 (93.3%). The work starting time was set to 8:00 a.m. for all participants in this experiment. About 31% of the participants reported tolerance to lateness in excess of 5 min at the workplace. The average reported preferred arrival time was 13.7 minutes before work starting time for the participants. The preferred arrival time re¯ects a safety margin to protect against lateness at work and allows some time for preparation at the onset of

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Fig. 1. Layout of information display in dynamic simulator.

the working day. It was found to be an important determinant of commuter behaviour dynamics in previous studies (Mahmassani and Chang, 1985; Mahmassani, 1996). From the post-experiment questionnaire, most of the participants perceived accurate information (95.6%) and about 76% of the participants tended to adopt this information system for future use. The average travel time in the experiment was 31.1, 29.3, 30.2 and 28.2 min on days 2, 3, 4 and 5, respectively. In the analysis, only days 2, 3, 4 and 5 are considered; day 1 was eliminated as a `trial' day, though it provided the basis for de®ning pre-trip departure time and route switches on day 2. 3. Modelling framework The boundedly rational rule is applied to commuters' departure time and route switching behaviour under real-time information and is described in the following. 3.1. Departure time switching Departure time switching in response to real-time information has not been investigated nor suggested by researchers. Departure time changes could take place from day-to-day and

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eventually over the long term. The boundedly rational model formulation of departure time switching in day-to-day commute initially developed by Mahmassani and Chang (1985, 1987), and extended by Mahmassani and Jou (1996) by combining early and late side indi€erence bands of tolerable schedule delay (de®ned as the di€erence between the actual arrival time and the preferred arrival time for a given commuter) is adopted in this study. The boundedly-rational mechanism governing day-to-day departure time switching decisions postulates that commuter i does not switch his/her next dayÕs departure time so long as the corresponding schedule delay SDit on the current day t, which is the di€erence between preferred arrival time PATi and actual arrival time ATit , remains within the user's indi€erence band for departure time switching IBDit (with di€erent components EBDit and LBDit for early and late arrivals, respectively), as follows: SDit ˆ PATi ÿ ATit ˆ ESDit

if SDit P 0;

ˆ LSDit

if SDit < 0;

 dit ˆ

t ˆ 1; 2; . . . ; T ;

ÿ1 if 0 6 ESDit 6 EBDit or ÿ LBDit 6 LSDit 6 0; 1 otherwise:

…1† …2†

ESDit and LSDit denote the early-side and the late-side schedule delay, respectively. The variable dit is a departure time switching decision indicator variable, which equals 1 when user i switches departure time after the commute on day t ÿ 1; dit equals ÿ1 otherwise. EBDit and LBDit are the respective departure time indi€erence bands of tolerable schedule delay corresponding to early and late arrivals (relative to PATi ) for day t. These are latent quantities modelled as random variables with systematic and random components given by: EBDit ˆ fe …Xi ; Zit ; hit † ‡ sit;e ; sit;e  MVN…0; Rse †; LBDit ˆ fl …Xi ; Zit ; hit † ‡ sit;l ; sit;l  MVN…0; Rsl †:

…3†

The subscripts `e' and `l' represent the early-side and the late-side indi€erence bands, respectively, with systematic components fe (
) and fl (
). These depend on the vector of user attributes Xi and the vector of performance characteristics Zit , which capture user i's inherent attributes and experience up to day t; hit is a vector of parameters to be estimated. The random terms sit;e and sit;l are assumed to be normally distributed over days and across commuters with zero means and general error term structure. The departure time indi€erence band with early-side and late-side components can be written in compact form for joint estimation purposes by introducing a binary indicator variable xit , which equals 1 if SDit ˆ ESDit P 0 (early-side), and 0 if SDit ˆ LSDit < 0 (late-side). IBDit ˆ xit EBDit ‡ …1 ÿ xit †LBDit ˆ xit fe …Xi ; Zit ; hit † ‡ …1 ÿ xit †fl …Xi ; Zit ; hit † ‡ xit sit;e ‡ …1 ÿ xit †sit;1 : Letting f …Xi ; Zit ; hit † ˆ xit fe …Xi ; Zit ; hit † ‡ …1 ÿ xit †fl …Xi ; Zit ; hit †; sit ˆ xit sit;e ‡ …1 ÿ xit †sit;1 ;

…4†

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we obtain IBDit ˆ f …Xi ; Zit ; hit † ‡ sit :

…5†

3.2. Route switching The mechanism governing commuters' pre-trip route selection and en-route path switching postulates that commuter i does not switch route or path so long as the corresponding trip time saving TTSijt (at decision node j on day t), which is the trip time di€erence between the current path TTCijt (from decision node j to the destination for user i on day t) and the best path TTBijt (the shortest path from decision node j to the destination on day t), remains within the commuter's route indi€erence band IBRijt , as follows: j ˆ 1; 2; 3; 4; 5; TTSijt ˆ TTCijt ÿ TTBijt P 0;  ÿ1 if 0 6 TTSijt 6 IBRijt ; /ijt ˆ 1 otherwise:

t ˆ 1; 2; . . . ; T ;

…6† …7†

The subscript j represents the decision node location, j ˆ 1 represents pre-trip route selection at the origin and j ˆ 2, 3, 4, 5 represent en-route path switching nodes (Fig. 2). The variable /i1t is the route switching decision indicator variable, which equals 1 when user i switches initial route on day t after the commute on day t ÿ 1, and /i1t equals ÿ1 otherwise; /ijt (j ˆ 2, 3, 4, 5) equals 1 when user i switches his/her path en-route at decision node j, with /ijt equal to ÿ1 otherwise. IBRijt is the indi€erence band for pre-trip route selection and en-route path switching corresponding to user i at decision node j on day t. Following the model proposed by Mahmassani and Jayakrishnan (1991) and implemented in DYNASMART (Jayakrishnan et al., 1994), the following equation has been adopted in the user decision component for both pre-trip route selection and en-route path switching.    ÿ1 if TTCijt ÿ TTBijt 6 max gijt TTCijt ; pijt ; …8† /ijt ˆ 1 otherwise;

Fig. 2. Commuting corridor with three parallel facilities.

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where gijt ˆ gr …Xi ; Zijt ; hijt † ‡ nijt;r ; pijt ˆ gm …Xi ; Zijt ; hijt † ‡ nijt;m ;

nijt;r  MVN…0; Rnr †; nijt;m  MVN…0; Rnm †;

…9†

gijt represents the relative indi€erence band, as a fraction of the TTCijt (trip time along the current path) from decision node j to the destination for user i to switch from the current path on day t; pijt denotes the corresponding minimum trip time saving, from decision node j to the destination, necessary for user i to switch from the current path on day t. Both quantities are latent variables, modelled as random variables, with mean values anticipated to vary systematically with the userÕs characteristics and experience to date. As such, they consist of both systematic and random components. In Eq. (9), the subscripts `r' and `m' represent the relative indi€erence band and the minimum trip time saving, respectively. The systematic components of the relative indi€erence band and the minimum trip time saving are gr (
) and gm (
), respectively. These depend on the user's inherent attributes Xi and vector of performance characteristics Zijt experienced by user i up to decision node j on day t; hijt is a vector of parameters to be estimated. The random terms nijt;r and nijt;m are assumed to be normally distributed, along ®ve decision nodes over days and across commuters, with zero means and general covariance structure. Comparing Eqs. (7) and (8), the expression for the indi€erence band for pre-trip route selection and en-route path switching is obtained as follows: IBRijt ˆ max‰gijt TTCijt ; pijt Š:

…10†

A binary indicator variable Wijt is introduced to represent two di€erent subsets of decisions, depending on which of the corresponding two components of IBRijt is larger, and thereby governs the decision. Wijt equals 0 if IBRijt ˆ pijt (i.e., gijt TTCijt 6 pijt ); Wijt equals 1 if IBRijt ˆ gijt TTCijt (i.e., gijt TTCijt > pijt ). Therefore, Eq. (10) can be rewritten as: IBRijt ˆ Wijt gijt TTCijt ‡ …1 ÿ Wijt †pijt ˆ Wijt TTCijt gr …Xi ; Zijt ; hijt † ‡ …1 ÿ Wijt †gm …Xi ; Zijt ; hijt † ‡ Wijt TTCijt nijt;r ‡ …1 ÿ Wijt †nijt;m :

…11†

Let g…Xi ; Zijt ; hijt † ˆ Wijt TTCijt gr …Xi ; Zijt ; hijt † ‡ …1 ÿ Wijt †gm …Xi ; Zijt ; hijt †;

…12†

nijt ˆ Wijt TTCijt nijt;r ‡ …1 ÿ Wijt †nijt;m ;

…13†

and we obtain IBRijt ˆ g…Xi ; Zijt ; hijt † ‡ nijt :

…14†

A 6T ´ 6T (where T is the number of decision days included in the sample of observations) variance±covariance matrix for joint departure time and route switching decisions under real-time

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information, R (joint), can capture serial correlation due to the persistence of unobservable attributes across the sequence of departure time choice, and pre-trip route selection as well en-route path switching decisions made by the same user. The variance±covariance structure proposed for this study is as follows: E…s2it † ˆ r2D ; E…n2i1t † ˆ r21 ˆ Wi1t2 TTC2i1t r21r ‡ …1 ÿ Wi1t †2 r21m ; E…n2ijt † ˆ r22 ˆ Wijt2 TTC2ijt r22r ‡ …1 ÿ Wijt †2 r22m ; E…sit ; ni1t † ˆ cD1 ˆ Wi1t TTCi1t cD1;r ‡ …1 ÿ Wi1t †cD1;m ; E…sit ; nijt † ˆ cD2 ˆ Wijt TTCijt cD2;r ‡ …1 ÿ Wijt †cD2;m ; …15†

E…sit ; sit0 † ˆ cD ; E…ni1t ; ni1t0 † ˆ c1 ˆ Wi1t Wi1t0 TTCi1t TTCi1t0 c1r ‡ …1 ÿ Wi1t †…1 ÿ Wi1t0 †c1m ‡ c:c:t:; E…ni1t ; nijt † ˆ c2 ˆ Wi1t Wijt TTCi1t TTCijt c2r ‡ …1 ÿ Wi1t †…1 ÿ Wijt †c2 m ‡ c:c:t:; E…nijt nij0 t † ˆ c3 ˆ Wijt Wij0 t TTCijt TTCij0 t c3r ‡ …1 ÿ Wijt †…1 ÿ Wij0 t †c3m ‡ c:c:t:; E…nijt ; nij0 t0 † ˆ c4 ˆ Wijt Wijt0 TTCijt TTCijt0 c4r ‡ …1 ÿ Wijt †…1 ÿ Wijt0 †c4m ‡ c:c:t:; j; j0 ˆ 2; 3; 4; 5; j 6ˆ j0 ;

t; t0 ˆ 1; . . . ; T ; t 6ˆ t0 :

c.c.t.: contemporaneous correlation terms between the relative indi€erence band (g) and the minimum trip time saving (p). In Eq. (15), the variance term for the pre-trip route decision latent variables (j ˆ 1) is di€erent from the ones for en-route switching (e.g., E(n2 i1t ) ˆ r21 and E(n2 ijt ) ˆ r22 , j ˆ 2, 3, 4, 5); the covariance terms between pre-trip route selection and en-route path switching decisions are di€erent from those among en-route decisions (e.g., E(ni1t; nijt ) ˆ c2 , E…nijt ; nij0 t † ˆ c3 , j, j0 ˆ 2, 3, 4, 5, j ¹ j 0 ); the covariance terms between departure time and pre-trip route decisions are di€erent from those between departure time and en-route path decisions (e.g., E(sit; ni1t ) ˆ cD1 , E(sit; nijt ) ˆ cD2 , j ˆ 2, 3, 4, 5). The underlying assumption that the pre-trip decision process is di€erent from that en-route is based on the fact that tripmakers can make their pre-trip decisions with more ample time to evaluate the received information based on their personal past experience with the road conditions and the real-time information system. This kind of in-depth consideration is usually not available once the tripmaker is en-route, especially considering the time constraints under which the tripmakers operate. We also assume that the correlation between two pre-trip decisions on di€erent commuting days are di€erent from those between the same decision nodes en-route between di€erent days (e.g., E…ni1t ; ni1t0 † ˆ c1 , E…nijt ; nij0 t0 † ˆ c4 , j, j 0 ˆ 2, 3, 4, 5, j ˆ j0 , t ¹ t0 ). A summary of the error structure for joint departure time and route (including pre-trip and en-route route selections) switching indi€erence band is shown in Fig. 3. The full variance±covariance structure of the error terms for these two decisions, R(joint), can be rewritten in matrix form and shown in Eq. (16).

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Fig. 3. Summary of error structure for joint departure time and pre-trip route selection as well as en-route path switching indi€erence band (pre-trip route switching decision governed by trip time saving).

Departure Time r2D Pre-Trip …Route† cD1 En-route …Route† cD2 En-route …Route† cD2 En-route …Route† cD2 En-route …Route† cD2

cD1 r21 c2 c2 c2 c2

Departure Time Pre-Trip …Route† En-route …Route† En-route …Route† En-route …Route† En-route …Route†

0 c1 0 0 0 0

cD 0 0 0 0 0

Day 1 cD2 cD2 c2 c2 r22 c3 c3 r22 c3 c3 c3 c3 .. . 0 0 c4 0 0 0

0 0 0 c4 0 0

cD2 c2 c3 c3 r22 c3

cD2 c2 c3 c3 c3 r22

0 0 0 0 c4 0

0 0 0 0 0 c4

... ...

..

.

...

cD 0 0 0 0 0

0 c1 0 0 0 0

r2D cD1 cD2 cD2 cD2 cD2

cD1 r21 c2 c2 c2 c2

Day 0 0 c4 0 0 0 .. . cD2 c2 r22 c3 c3 c3

T 0 0 0 c4 0 0

0 0 0 0 c4 0

0 0 0 0 0 c4

cD2 c2 c3 r22 c3 c3

cD2 c2 c3 c3 r22 c3

cD2 c2 c3 c3 c3 r22 …16†

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Given a speci®cation for f(
) and g(
), the available observations of the departure time and route switching decisions made over T days by N commuters in the sample provide a basis for the maximum likelihood estimation of the model parameters. A general approach to deal with the associated estimation issues was presented by Daganzo and She (1982), who showed that the probability of a sequence of decisions is essentially equivalent to a multinomial probit probability function. This approach was adopted by Mahmassani and coworkers to model the day-to-day switching decisions of departure time and route (Mahmassani, 1990; Mahmassani and Jou, 1996) It is extended here to the model expressed by Eqs. (5), (14) and (16). 4. Model speci®cation The analysis focuses on the day-to-day dynamics of commuter pre-trip departure time and route choices as well as en-route path switching for morning commutes. Based on the preliminary analysis results (Mahmassani and Liu, 1995, 1996, 1997) the speci®cations of the departure time and route switching indi€erence band models consist of the following components: (1) initial band, (2) user characteristics component, (3) information reliability component, (4) myopic component, (5) schedule delay component, incorporating individual preference, and (6) unobserved component. After considerable analysis of the data to identify the appropriate variables to include in the speci®cations, and in light of our behavioural theory, the following speci®cations were derived. The speci®cation of the indi€erence band of tolerable schedule delay for departure time switching decisions can be expressed as shown in Eq. (17). The speci®cations of the relative indi€erence band and the minimum trip time saving for route switching model can be expressed as shown in Eqs. (18) and (19). The de®nitions of the terms included in these expressions are summarized in Table 1. Departure time decision IBDit ˆ xit c1 ‡ …1 ÿ xit †c2 ‡ xit c3 AGEi ‡ …1 ÿ xit †c4 AGEi ‡ xit c5 GENDERi ‡ …1 ÿ xit †c6 GENDERi ‡ xit c7 SERROit ‡ …1 ÿ xit †c8 SERROit ‡ xit c9 SERRUit ‡ …1 ÿ xit †c10 SERRUit ‡ xit c11 kit …DTRit =DDTit † ‡ …1 ÿ xit †c12 kit …DTRit =DDTit † ‡ sit :

Initial band User characteristic component Information reliability component Myopic component Unobserved component

Route decision (Including pre-trip and en-route) j ˆ 1; 2; 3; 4; 5 IBRijt ˆ max‰gijt TTCijt ; pijt Š; gijt ˆ j1 a1 ‡ …1 ÿ j1 †a2 Initial band User characteristics component ‡ a3 GENDERi ‡ a4 ERROijt ‡ a5 ERRUijt Information reliability component Schedule delay component ‡ a6 SDPEijt ‡ a7 SDPLijt ‡ nijt;r ; Unobserved component

(17)

(18)

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Table 1 Variable de®nitions for the indi€erence band in joint departure time and route switching model Element

De®nition

AGEi GENDERi ERROijt

Age of commuter i, 1 if age < 20; 2 if age 2 ‰20; 39Š; 3 if age 2 ‰40; 59Š; 4 if age > 60 Gender of commuter i, ˆ 1 if male; ˆ 0, if female Over-estimation error provided by real-time information; the relative error between actual travel time and travel time reported from the system when actual travel time is shorter than reported travel time  For en-route decision (j ˆ 2, 3, 4, 5) ERROijt ˆ max{(RTTijt ÿ ATTijt )/ATTijt , 0} ATTijt : actual trip time from node (j ÿ 1) to node j RTTijt : reported trip time provided by real-time information for commuter i from node (j ÿ 1) to node j  For pre-trip decision (j ˆ 1) ERROi1t : average error from origin to destination on day (t ÿ 1) ERROi1t ˆ (ERROi2;t ÿ 1 +


+ ERROi5;t ÿ 1 + ERROi6;t ÿ 1 )/5 ERROi6;t ÿ 1 : relative over-estimation error from node 5 to the destination in day (t ÿ 1) Under-estimation error provided by real-time information; the relative error between actual travel time and travel time reported from the system when actual travel time is longer than reported travel time  For en-route decision (j ˆ 2, 3, 4, 5) ERRUijt ˆ max{(ATTijt ÿ RTTijt )/ATTijt , 0}  For pre-trip decision (j ˆ 1) ERRUi1t ˆ (ERRUi2;t ÿ 1 +


+ ERRUi5;t ÿ 1 + ERRUi6;t ÿ 1 )/5 Sum of the values of over-estimation error provided by real-time information including pre-trip and en-route on day t ÿ 1. SERROit ˆ (ERROi2;t ÿ 1 + ERROi3;t ÿ 1 +


+ ERROi6;t ÿ 1 ) ERROi6;t ÿ 1 : relative over-estimation error from node 5 to the destination in day (t ÿ 1) Sum of the values of under-estimation error provided by real-time information including pre-trip and en-route on day t ÿ 1 SERRUit ˆ (ERRUi2;t ÿ 1 + ERRUi3;t ÿ 1 +


+ ERRUi6;tÿ1 ) ERRUi6;t ÿ 1 : relative under-estimation error from node 5 to the destination in day (t ÿ 1) A binary indicator variable, equal to 0 if DTit ˆ DTit ÿ 1 , or equal to 1, otherwise The di€erence between travel times of commuter i on day t and t ÿ 1 (min) The amount of departure time that commuter i has adjusted between day t and t ÿ 1 (min) Early-side schedule delay relative to commuter's preferred arrival time for commuter i at decision node j on day t (min). SDPEijt ˆ max{PATi ÿ RATijt , 0} PATi : preferred arrival time for commuter i RATijt : predicted arrival time for commuter i from node j to destination according to the travel time provided by the real-time information system (RATijt ˆ CLOCKijt + TTCijt ) CLOCKijt : current clock time for commuter i at node j on day t Late-side schedule delay relative to commuter's preferred arrival time for commuter i at decision node j on day t (min). SDPLijt ˆ max{RATijt ÿ PATi , 0} A binary indicator variable, equal to 1 if SDit P 0 (early-side), or equal to 0, if SDit < 0 (late-side) A binary indicator variable, equal to 1 if j ˆ 1 (pre-trip route decision), or equal to 0 if j ˆ 2, 3, 4, 5 (en-route path decision) parameters to be estimated error term of departure time switching indi€erence band for commuter i on day t error term of route switching indi€erence band for commuter i at node j on day t …gijt ; pijt †

ERRUijt

SERROit

SERRUit

kit DTRit DDTit SDPEijt

SDPLijt xit j1 a's, b's, c's, d 's sit nijt ;r , nijt ;m

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pijt ˆ j1 b1 ‡ …1 ÿ j1 †b2 ‡ b3 GENDERi ‡ b4 ERROijt ‡ b5 ERRUijt ‡ b6 SDPEijt ‡ b7 SDPLijt ‡ nijt;m :

Initial band User characteristics component Information reliability component Schedule delay component Unobserved component

(19)

The following assumptions are embedded in the above model speci®cation. First, the initial bands governing pre-trip route switching decisions may be di€erent from those for en-route path switching. Second, the age of commuters may a€ect their departure time switching behaviour. Older commuters may tend to tolerate greater schedule delay than younger ones. Third, commuters' gender may in¯uence their pre-trip departure time and route switching decisions. Female commuters may, on average, have a wider indi€erence band than males. Fourth, the reliability of real-time information may directly in¯uence commuters' travel decisions including departure time and route switching. Fifth, for the departure time switching decision, commuters may tolerate a wider indi€erence band, given that a small adjustment could result in a relatively large di€erence in travel time. This e€ect can be captured by DTRit /DDTit (Mahmassani and Chang, 1986). Sixth, the schedule delay relative to users' preferred arrival time may a€ect their pre-trip route and enroute path switching behaviour under the provision of real-time information. 5. Estimation results The model parameters were estimated using a special purpose maximum likelihood estimation procedure that relies on Monte-Carlo simulation to evaluate the MNP choice probability (Liu and Mahmassani, 1997). Based on the preliminary analysis, the contemporaneous correlation terms (c.c.t., cD2;r , and cD2;m ) and the serial correlation terms for the relative indi€erence band (c1r , c2r , c3r , c4r ) in Eq. (15) are not signi®cant, and assumed to be zero in this study (Mahmassani and Liu, 1996, 1997). The parameter estimation results, for four consecutive days, for the model speci®cation expressed in Eqs. (16)±(19) are presented in Table 2. The initial tolerable schedule delay for the late-side is smaller than that for the early-side in the departure time decision. The respective magnitudes of c1 and c2 for departure time decision are 12.258 and 6.71 minutes, respectively. This reveals that commuters are more prone to switch their departure time with late arrival than with early arrival. It implies that the commuters implicitly increase their anxiety level, as arriving late at work negatively a€ects commuters' daily work schedule, performance evaluation, and morale. This result is the consistent with the earlier ®nding of previous urban commuter behaviour studies (Tong, 1990; Mahmassani and Jou, 1996). The parameters that capture user characteristics e€ects are c3 through c6 for the departure time switching decision. The estimated values have correct signs and reasonable magnitudes. The estimates yield positive signs for c3 and c4 , suggesting that older commuters tend to tolerate greater schedule delay than younger ones for departure time switching decision. The estimates yield negative signs for c5 and c6 , revealing that male commuters have narrower indi€erence band (i.e., are more likely to switch) than females for the departure time switching decision. The parameters that capture the e€ects of real-time information reliability, both over-estimation and under-estimation error of the actual travel time, are c7 through c10 for the departure time

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Table 2 The estimation results for the joint departure time and route switching indi€erence band based on four day commuting data Component/Attribute

Parameter

Initial tolerable schedule delay for DT (e) Initial tolerable schedule delay for DT (l) DT user characteristics 1/AGE (e) DT user characteristics 1/AGE (l) DT user characteristics 2/GENDER (e) DT user characteristics 2/GENDER (l) DT information reliability 1/SERRO (e) DT information reliability 1/SERRO (l) DT information reliability 2/SERRU (e) DT information reliability 2/SERRU (l) DT myopic/kit (DTRit /DDTit ) (e) DT myopic/kit (DTRit /DDTit ) (l) Pre-trip R initial relative indi€erence band En-route R initial relative indi€erence band R user characteristics/GENDER (r) R information reliability 1/ERRO (r) R information reliability 2/ERRU (r) R schedule delay 1/SDPE (r) R schedule delay 2/SDPL (r) Pre-trip R initial minimum trip time saving En-route R initial minimum trip time saving R user characteristics/GENDER (m) R information reliability 1/ERRO (m) R information reliability 2/ERRU (m) R schedule delay 1/SDPE (m) R schedule delay 2/SDPL (m) Standard deviation for DT decision Standard deviation for pre-trip R decision (r) Standard deviation for en-route R decision (r) Covariance for the contemporaneous correlation of DT and pre-trip route decisions (r) Covariance for the serial correlation between DT decisions on days t and t + 1 Standard deviation for pre-trip R decision (m) Standard deviation for en-route R decision (m) Covariance for the contemporaneous correlation of DT and pre-trip route decisions (m) Covariance for the serial correlation between pre-trip and enroute route decisions (m) Covariance for the serial correlation between en-route route decisions (m) Covariance for the serial correlation between pre-trip R decisions on days t and t + 1 (m) Covariance for the serial correlation between en-route route decisions on days t and t + 1 (m) Log-likelihood at convergence

c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 a1 a2 a3 a4 a5 a6 a7 b1 b2 b3 b4 b5 b6 b7 rD r1r r2r cD1;r

Estimates

t

12.2580 6.7100 0.1663 0.1023 ÿ1.7740 ÿ1.5238 0.3899 0.2778 1.3031 1.1659 0.4250 0.1435 0.1934 0.1829 ÿ0.0299 ÿ0.0795 ÿ0.1209 ÿ0.0006 ÿ0.0021 1.1158 1.0871 ÿ0.0961 ÿ0.5189 ÿ0.9629 ÿ0.0165 ÿ0.0292 7.0970 0.0483 0.0347 0.9999

6.12 6.10 7.38 3.47 ÿ7.10 ÿ4.98 4.50 5.50 5.93 6.54 9.44 6.47 4.77 2.76 ÿ3.39 ÿ7.94 ÿ5.99 ÿ1.85 ÿ4.74 7.11 4.40 ÿ9.35 ÿ6.28 ÿ4.96 ÿ6.86 ÿ4.82 4.51 2.81 2.94 4.76

cD

4.2900

4.39

r1m r2m cD1;m

0.5551 0.5103 2.8060

4.64 7.79 6.89

c2m

0.0450

3.58

c3m

0.0373

2.98

c1m

0.0472

3.97

c4m

0.0394

1.87

ÿ399.78

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switching decision. The estimation results yield positive signs for the parameters c7 through c10 , indicating that commuters tend to engage in less departure time switching after experiencing lower reliability of the real-time information. The short term adjustment in response to the most recently experienced travel time change resulting from a departure time change is captured by parameters c11 and c12 , the estimated value of which has correct sign and reasonable magnitude. If commuters have recently experienced a substantial increase in travel time as a result of a small adjustment in departure time, they seem likely to tolerate greater schedule delay in subsequent decisions (i.e., are less likely to switch), as a way of absorbing the possibly large ¯uctuations in trip time associated with small adjustments in departure time. For the route switching indi€erence band, the estimated values of the initial relative indi€erence band reveal that an average of about 19% for pre-trip route decision (parameter a1 in Table 2) and 18% for en-route path decision (parameter a2 in Table 2) trip time saving relative to the travel time along the current path is needed to trigger a route switch under perfect information supply, and no schedule delay. The values of the initial minimum trip time saving for both pre-trip route and en-route path switching decisions (parameter b1 for pre-trip route decision and b2 for en-route path decision in Table 2) indicate that an absolute minimum of 1 minute of trip time saving is required for a route switch to occur, under perfect information supply and no schedule delay. The higher value of parameter a1 compared to that of a2 , and the higher value of b1 than that of b2 further re¯ect that commuters switch their pre-trip route more cautiously than en-route. The parameters that capture user characteristics is a3 for the relative indi€erence band and b3 for the minimum trip time saving. The estimated values have negative signs, indicating that male commuters tend to switch routes more frequently than females both pre-trip and en-route. The parameters that capture the e€ects of real-time information reliability, both over-estimated and under-estimated errors of the actual travel time, are a4 and a5 for the relative indi€erence band and b4 and b5 for the minimum trip time saving. The estimation results yielded negative signs for all four parameters, indicating that travellers tend to more readily switch routes both pre-trip and en-route when the information system has low reliability. The parameters that capture the e€ect of the commuter's `goal' (the preferred arrival time) at each decision node, both early-side and late-side schedule delay, are a6 and a7 for the relative indi€erence band and b6 and b7 for the minimum trip time saving. The estimated values of these parameters have negative signs, indicating that commuters tend to switch their route both pre-trip and en-route in response to higher di€erences between the `predicted' arrival time (based on current time and travel time from current location to the destination as provided by the system) at a given decision node and the preferred arrival time. The lower absolute value of parameter a6 compared to that of a7 , and the lower absolute value of b6 than that of b7 further suggest that commuters are more prone to switch their travel paths when they perceived late arrival following the current path than when they perceived early arrival following the current path. The estimates of r's, cD , cD1;r , and cD1;m are signi®cant at reasonable con®dence level, suggesting that serial correlation of departure time decision and the contemporaneous correlation between departure time and pre-trip route decisions should be considered. The estimates of c1m , c2m , c3m and c4m are all signi®cant at reasonable con®dence level, which con®rms the need to explicitly incorporate serial correlation in the error speci®cation of the minimum trip time saving term. The covariance terms (c's) are generally much smaller than the variance terms. Moreover, the esti-

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105

mates of covariance terms for the departure time and route switching model indicate positive correlation between the unobserved disturbances. 6. Conclusions This paper presented both a model framework and an empirical analysis of tripmakers' indi€erence band for departure time and route switching behaviour in response to real-time information, based on data collected using a laboratory interactive dynamic simulator. The analysis focused on the day-to-day dynamics of commuters' departure time and route decision process in response to the supplied information. The multinomial probit (MNP) model provides a very ¯exible framework to model and calibrate the tripmaker joint departure time and route switching behaviour. Several substantive conclusions have been obtained in this study as summarized hereafter. 1. In the pre-trip departure time switching decision model, older commuters tend to tolerate greater schedule delay than younger ones. Also, female commuters exhibit a wider mean indi€erence band than male commuters for pre-trip departure time and route decisions as well as en-route path switching decision. 2. The reliability of the real-time information is a signi®cant variable that in¯uences commuters' pre-trip departure time and route switching decisions as well as en-route path switching decision. The commuters tend to keep their routine departure time, but change their routes both pre-trip and en-route in response to low reliability of the real-time information system perceived by the commuters. Moreover, tripmakers become more prone to switch routes when the system provides under-estimated trip time information than when the system provides over-estimated trip times. Compared to the ®ndings obtained from previous studies of commuter behaviour without real-time information, the experimental results suggest that real-time information availability tends to induce greater frequency of route switching, both pre-trip and en-route. 3. Commuters are inclined to tolerate greater schedule delay (associated with a particular departure time decision) if they have recently experienced a substantial increase in travel time resulting from a small adjustment in departure time. 4. Commuters tend to switch their route both pre-trip and en-route in response to higher di€erences between the `predicted' arrival time at a given decision node and their own preferred arrival time. Furthermore, travellers become more prone to switch routes when they perceive late arrival by following the current path than when they perceive early arrival by following the current path. 5. The estimates of all variances terms and covariance terms for the minimum trip time saving component are statistically signi®cant in the route switching models, which con®rms the need to incorporate serial correlation in the speci®cation. Moreover, the serial correlation e€ects between pre-trip and en-route decisions are di€erent from those across en-route decisions. 6. The estimates of all variances terms and covariance terms for departure time and pre-trip route decisions are statistically signi®cant in the joint departure time and route switching models. The obtained result con®rms the need to incorporate contemporaneous correlation between departure time and pre-trip route decisions.

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