A Micro-simulation Model of Updating Expected Travel Time in Provision of Travel Information: A Bayesian Belief Approach Implemented in a Multi-state Supernetwork

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Procedia Computer Science 32 ( 2014 ) 796 – 801

doi: 10.1016/j.procs.2014.05.493

ScienceDirect

The 3rd International Workshop on Agent-based Mobility, Traffic and Transportation Models,

Methodologies and Applications (ABMTRANS)

A Micro-Simulation Model of Updating Expected Travel Time in

Provision of Travel Information: A Bayesian Belief Approach

Implemented in a Multi-State Supernetwork

Zahra Parvaneh

a

, Feixiong Liao

a

, Theo Arentze

a

, Harry Timmermans

a,

*

a_{Urban Planning Group, Eindhoven University of Technology, Eindhoven,5612 AZ, The Netherlands}

Abstract

This study introduces a model of individual belief updating of subjective travel times as a function of the provision of different types of travel information. Travel information includes real-time prescriptive or descriptive, and public or personal information. The model is embedded in a start-of-the art multi-state supernetwork representation of individual daily activity-travel scheduling behavior. The belief updating process of subjective travel times under information provision is based on Bayes’ Theorem. The multi-state supernetwork predicts daily activity travel choices based on the minimization of generalized costs related to the full activity-travel pattern. These generalized costs are based on expected travel times across the network. Thus, the simulation model will capture changes in activity-travel scheduling decisions that are made by individuals after updated their beliefs about expected travel times when receiving new travel information.

Selection and peer-review under responsibility of Elhadi M. Shakshuki.

Keywords: : micro-simulation; Bayes’ Theorem; multi-state supernetwork; travel information; route choice;

1. Introduction

Individuals make decisions based on their beliefs of reality, their knowledge of the environment and their past experiences1_{. Individuals are not always aware of all available alternatives and thus choose from a limited set of}

known alternatives. How individuals choose between routes, modes, departure times, etc. has always been an

*Corresponding author. Tel.: +31- 040-247-3044. E-mail address: [email protected]

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important research question in transportation planning and management2,3_{. Providing travel information to}

individuals may change their beliefs, increase their knowledge of the environment and introduce them to new alternatives. In addition, it has been argued that travel information may decrease uncertainty about the state of the transportation network4, 5_.

The present study addresses the question how an individual with certain beliefs and preferences adapts his schedule when receiving travel information. We assume that individuals hold particular beliefs about travel times in the network, based on their past experiences. When receiving information, they need to consider updating (at least momentarily) their beliefs of expected travel times. This updating will depend on the kind of information they received. Based on their updated expected travel times of alternative routes, they then may reschedule the remaining activities and travel in their schedule. A multi-state supernetwork6, 7_{is employed to represent individuals’ complex}

multi-modal, multi-activity activity-travel decisions under space-time constraints. A multi-state supernetwork represents in an integral manner individual activity-travel choices. Individuals are supposed to schedule their activity-travel behavior such as to minimize their generalized costs of conducting the activity programs. These costs are based on individuals’ beliefs of travel times and the state of the environment.

The remainder of the paper is structured as follows. Section 2 briefly describes the problem and the conceptualization. Section 3 discusses the proposed Bayesian Belief model, while Section 4 introduces the larger simulation framework. Section 5 draws major conclusions and discusses future works.

2. Definition of the problem

Consider an individual with an activity-travel schedule involving different locations to conduct different activities during a day. In addition, assume that the individual receives different types of travel information during a day. Travel Information can be either public, received from a public information service provider like a radio station, or personal, received from a more advanced information service provider via for example a navigation device with capabilities of considering individual’s preferences. It can also be either descriptive (e.g. indication of travel time of a route), or prescriptive (a recommendation to take a certain route because it is the shortest one without giving any more information). Consequently, they may change their beliefs about the travel time along certain routes and possibly adapt their planned activity-travel schedule. These processes may differ for different types of information. In case of public information, all travellers will receive the same information. Updating expected travel times should thus consider the fact that individuals may strategically choose the route that maximizes their expected utility, taking into account possible strategic behavior of other individuals8_{. In presence of personal information, the effect of}

strategic choices is not taken into account and individuals’ beliefs, preferences and past experiences may be more highlighted. Moreover, in case of descriptive information, individuals may have to update their beliefs about attributes of existing alternatives. However, in presence of prescriptive information, they may have to compare all possible alternatives. The provision of prescriptive travel information implies choosing between their initial schedule and the recommended one without knowing the exact attributes of each alternative. The reason is that prescriptive information just involves the recommendation of choosing a particular route alternative, without specifying the attributes of that alternative.

3. Bayesian Belief Framework

Following Arentze and Timmermans9_{, we propose a Bayesian Belief model to represent the updating of beliefs of}

travel times under travel information provision. That is to say, we use Bayesian Belief Network (BBN) principles to update the conditional probability representing individual’s beliefs of travel times under the provision of travel information. Considering that travel information may be either prescriptive or descriptive, we propose networks shown in Fig.1.

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(a) (b)

Fig. 1. The belief updating process in the provision of the travel information; (a) Prescriptive information network; (b) Descriptive information network

We argue that individuals’ belief about objective of given travel information impacts the updating process. In these networks, node ܱܾ݆݁ܿݐ݅ݒ݁ represents whether the objective of the existing policy is to optimize transportation network performance or to maximize individuals’ utility. Two states are defined for this node: system-optimization and personal-optimization. These different policy objectives dictate what recommendation will be provided to an individual traveler. System optimization may imply that the recommended route does not necessarily reflect utility-maximization at the individual level.

Node ݐݕ݌݁ represents the information type, which has two states: personal or public. Type of information would be specified considering the services available on the route and whether the individual uses a personal navigation system. We assume that for each individual just one type of information is provided. As a result, the probability of each state can either be equal to Ͳ or ͳ.

ܶܶ௧௥ represents the subjective travel time of route ݎ at moment ݐ before receiving travel information. It is

assumed that the subjective travel time of a route has a normal distribution ܶܶ௧௥̱ܰሺߤǡ ߪଶሻ that is given for each

individual, where ߤ ൌ ܽݒ݃ܶܶ௧௥ and ߪ specifies the standard deviation of route ݎ travel time. Five different states of

travel time are defined for this node: very-short, short, normal, long, very-long. To specify the probability of these different states, we discretize the distribution into 5 equal intervals. These categories are a representation of length of travel in minutes. An initial value will be set for each category for simulation.

Moreover, node ܴ represents the given recommendation, which is either route 1 or route 2. This recommendation is a result of comparing real travel times of different routes, and it does not include the value of travel time. To specify the conditional probability table (CPT) of this node, a logit model is used. Considering the state of the parent node, ݋ܾ݆݁ܿݐ݅ݒ݁, and credibility of the recommendation, different situations may occur. We assume that if the state of ݋ܾ݆݁ܿݐ݅ݒ݁ is equal to Personal-optimization the probability that the recommended route brings the highest utility for the individual will be higher in comparison with the situation where the state of the ݋ܾ݆݁ܿݐ݅ݒ݁is equal to system-optimization. We skip demonstration of the model for this paper.

ܴܶ௧௥ is the received information about the travel time of route ݎ given by the information source. It is assumed

that this node also has five different states (very-short, short, normal, long, very long), which represents the state of real travel time of the route.

Node ܱݐ݄݁ݎݏ݄ܿ݋݅ܿ݁ represents individual beliefs about other individuals’ behavior after receiving the travel information. This node has 5 states: everyone would choose route 1, most of the people would choose route 1, equal share would choose route 1 or 2, everyone would choose route 2, most of the people would choose route 2. Depending on type and objective of information, individual has different beliefs about other individuals’ choices. For instance, if the information is public then individual gives a higher probability that other individual would receive the same information and follow that. We proposed a multinomial logit model to identify the probabilities of the CPT. Since details of the BBN is not scope of this paper we leave further details.

Finally, ܶܶ_௧ାଵ௥ _{represents the expected subjective travel time of route ݎ at ݐ ൅ ͳ after receiving travel}

information. Similar to node ܶܶ௧௥, this node also has five different states: very-short, short, normal, long, very-long.

A complete explanation of the network specifications can be found in Parvaneh et al.10 R Objective Others choice Type Others choice Type 0 r t TT ri t TT 1 i r t TT 0 1 r t TT 0 r RT RTri 0 r t TT ri t TT 1 i r t TT 0 1 r t TT

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4. Simulation framework 4.1. Basic concept

To represent individuals’ belief updating of subjective travel times in presence of advanced travel information, we propose a Bayesian Belief micro-simulation framework. Each individual is modeled as an agent that has certain beliefs and preferences about different attributes of the environment. Individuals decide where and when to conduct the activities, which transport mode to take and which route to follow. Each individual is identified by an id, socio-economic information, and preferences for different roads, activities and location types.

It is assumed that at the start of a day an activity-travel schedule is generated for each individual. An activity schedule specifies type, start time, location and duration of each activity in individual’s daily agenda and a travel plan including routes and transport mode. Individuals implement their schedule in a multi-state supernetwok. Subsequently, for each individual, a personalized multi-state supernetwork is constructed. This network represents the individual’s choice space of conducting the activity program. In this multi-state supernetwork, nodes denote real locations in space and any link is either a transport link, which always causes a change of location, or a transition link, which never causes any change of location but of mode or activity state. Any link represents an individual’s specific action such as walking, cycling, driving, parking or picking-up a car, boarding or alighting a bus or train, conducting a specific activity, etc. Time-dependent and personalized link costs can be readily defined. By considering the start and end points of multi-state supernetworks as virtual O-D pairs, any path (Fig. 2) represents a feasible activity-travel pattern expressing the choice of mode, route, parking and activity location, and sequence of activities7_.

In the proposed multi-state supernetworks organically activity programs from the demand side and integrated land-use transport network from the supply side are linked. Therefore, by aggregating the route choices made by the individuals, real-time travel times can be derived. We adopt the BPR* function and calculate real-time travel times by counting the number of vehicles on the road.

Fig. 2 Multi-state supernetwork representation.

During the implementation, at each node of the network (a decision point) an individual receives real time travel information about the two best alternative routes to the next node. It is assumed that the individual has initial beliefs about the travel time along these routes. After receiving the travel information, individuals update their beliefs about

*_{BPR function is volume-delay function defined by Bureau of Public Roads as: ݐሺݔ}

௔ሻ ൌ ݐ଴ሺͳ ൅ ͲǤͳͷ ቀ௫_஼ೌ

ೌቁ

ସ

ሻ where ݐ଴ is the free flow, ݔ௔ is

the link ܽ traffic volume, ܥ௔ is the capacity of link ܽ, and ݐሺݔ௔ሻ is travel time of link ܽ.

PVN Bike PTN PTN PTN PTN PTN PTN PVN Car PTN PTN PVN Car PTN PTN PVN Car PTN PTN PVN Car PTN PTN PVN Bike PTN PTN PVN Bike PTN PTN PVN Bike PTN PTN H H’ H 00 s1s2 10 01 11 P0 P1 P2 P5 P3 P4 PVN Car P1 P2 H P3 P4 H_PVN Bike PTN H A1& P3 A2 P2 P4 P1 Vehicle state

Fig. 1 Multi-state supernetwork representation. H and H’ denote the O-D pair, which is the same location, i.e. home in reality. The path denoted by the bold links shows that the individual leaves home by car to conduct the fixed activity at A1with parking at P2, then returns home and switches to bike to conduct the flexible activity at A2with parking at P4, and finally returns home. PVNs and PTNs are personalized private vehicle networks and public transport networks respectively.

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expected travel time of the routes. This is done by executing the Bayesian Belief updating framework. Subsequently, rescheduling may take place using these updated travel times. That is to say, the multi-state supernetwork employs these updated expected travel time to update individuals’ activity-travel program. This process is iterated until the activity programs have been conducted.

4.2. Simulation algorithm and implementation

The simulation algorithm involves the following steps: Step 0, Input individuals’ daily activity travel programs, the land use and transportation system, choice heuristics and personalized preferences. Step 1, Construct a multi-state supernetwork and find the optimal activity-travel path. Step 2, Select the first and second optimal routes to the next activity location. Calculate the related travel time for each route using a BPR function. Step 3, Construct the Bayesian Belief Network and update the expected travel time of the selected routes based on the received travel information. Step 4, Reschedule the activity-travel pattern if the generalized costs based on the updated expected travel times of a new schedule are lower than the generalized costs of the schedule that is being executed. Step 5, Repeat step 2-5 until the schedule is implemented.

This algorithm is implemented using the C programming language. A Netica API for C is used to implement and execute the proposed BBN model. An important part of BBN generation is related to sub-programs that define conditional probability tables (CPT) of each node of the BBN. It should be mentioned that the size of each BBN depends on the number of possible routes between origin and destination and will increase with an increasing number of possible routes. In this study, we just consider the two shortest paths between an origin and destination. As a result, the BBN has 8 nodes. More information can be found in Parvaneh et al.10

4.3. Illustration

In this section, we discuss results of the numerical simulations to illustrate the proposed Bayesian Belief model. In light of page limitations, we will just explain the results of a single case for one agent. This agent wants to travel between two nodes and he has initial subjective beliefs about the travel times of two alternative routes. These initial believed for route 1 and 2 are as following: ܶܶ௧ଵ̱ܰሺʹͳǡ͵Ǥ͵ͷሻ, ܶܶ௧ଶ̱ܰሺʹͺǡͳͲǤͷ͸ሻ. It is assumed that the given

travel information is in the form of a recommendation. In BBN, the values of very-short, short, normal, long and very-long travel time are set to: ሼͷǤͲǡ ͳͷǤͲǡ ʹͷǤͲͲǡ ͵ͷǤͲͲǡ ͶͷǤͲͲሽ minutes.

Table 1 represents the updated expected travel times for three different scenarios for this case; For Scenario one, ܴ ൌ “Route 1”, ݋ܾ݆݁ܿݐ݅ݒ݁ ൌ “System optimization” and ܶݕ݌݁ ൌ “Personal”; For Scenario two, ܴ ൌ “Route 1”, ݋ܾ݆݁ܿݐ݅ݒ݁ ൌ “System optimization” and ܶݕ݌݁ ൌ “Public”; For scenario three, ܴ ൌ “Route 1”, ݋ܾ݆݁ܿݐ݅ݒ݁ ൌ “Personal optimization” and ܶݕ݌݁ ൌ “Personal”.

The last two columns of the table show the updated expected travel time, ܧሺܶܶ௧ାଵ୰ ሻȘǡ of the two routes. It is

shown that in all three scenarios, the increase in expected travel time of route 2 is higher than route 1. Column “ܱݐ݄݁ݎݏᇱ_{݄ܿ݋̶݅ܿ݁ shows that in scenario one individual has a definite belief that most of the people choose route 1,}

not all of them. In case of scenario two, individual believes the probability that all other individuals choose route 1 is equal to 37.4 and the probability that most other individuals would choose route 1 is equal to 62.6. In comparison with scenario one, in this case more individuals will follow the recommendation. Consequently, the expected travel time will have a higher increase. As for third scenario individual believes that everyone will take route 1. Since the objective is “Personal optimization” and the type is “Personal”. The combination of “Personal optimization” and “Public” information is not valid, since the public information is given to all the individuals, which cannot aim to maximize everyone’s utility.

† _ܧሺܶܶ

௧ାଵ୰ ሻ ൌ σ௦௧௔௧௘௦ܲݎ௦௧௔௧௘Ǥ ܶܶ௦௧௔௧௘ǡ where ܲݎ௦௧௔௧௘ is probability of the state, ܶܶ௦௧௔௧௘ is the travel time set to each state, ݏݐܽݐ݁ݏ ൌ

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Table 1, Results of updating beliefs about expected travel time of two alternatives Scen ar io ܶܶ௧௥భ ܶܶ௧௥మ ܱܾ݆݁ܿݐ݅ݒ݁ ܶݕ݌݁ ܴ ܱݐ݄݁ݎݏǯ݄ܿ݋݅ܿ݁ ܶܶ௧ାଵ௥భ ܶܶ௧ାଵ௥మ ܧሺܶܶ௧ାଵ௥భሻ ܧሺܶܶ௧ାଵ௥మ) V er y shor t Shor t

Normal Long Very long Ver

y shor t Shor t Normal Long Ver y long Sys te m Optimiza tion Per sonal Optimiza tion Per sonal

Public Route 1 Route 2 All

R oute 1 Mo st ly R oute 1 E qual s har e Mo st ly R oute 2 All R oute 2 Ve ry s hor t shor t nor mal long Very long Very s hor t Shor t

Normal Long Very long

1 _0.0 3. 81 96. 1 0. 0 0. 0 0. 0 0. 0 65. 7 34. 3 0. 0 100 0.0 100 0.0 100 0.0 0.0 100 0.0 0.0 0 0. 0.0 0.0 100 0.0 0.0 0.0 0.0 1.62 97. 9 0. 46 25.00 34.877 2 _0.0 3. 81 96. 1 0. 0 0. 0 0. 0 0. 0 65. 7 34. 3 0. 0 100 0.0 0.0 100 100 0.0 37. 4 62. 6 0. 0 0. 0 0. 0 0. 0 0. 0 88. 3 11. 7 0. 0 0. 0 0. 0 1. 02 78. 5 18. 5 _26.17 _36.855 3 _0.0 3. 69 96. 3 0. 0 0. 0 0. 0 0. 005 _68.2 _31.8 _0.0 _0.0 ₁₀₀ ₁₀₀ _0.0 ₁₀₀ _0.0 ₁₀₀ _0.0 _0.0 _0.0 _0.0 _0.0 _0.0 _68.7 _31.3 _0.0 _0.0 _0.0 0. 004 _48.7 _51.3 28.13 40.131 5. Conclusion

Previous research on the impact of travel time information has primarily been concerned with the impact of descriptive real time information on route and departure time choices. This paper sets out the framework and simulation approach for a more comprehensive approach that simulates effects of different types of travel information, issued with different underlying policies in mind, on multi-faceted activity-travel rescheduling decisions during the implementation of a planned schedule. The rescheduling involves duration, route choice, destination, and cancellation/insertion/resequencing of activities. The rescheduling takes place in a multi-state supernetwork that finds the optimal least generalized costs path in the supernetwork. These costs are largely dictated by subjectively expected travel times. A Bayesian belief network simulates the effects of different types of travel information and underlying policy objectives on changes in anticipated travel times on specific links of the network. The numerical simulation illustrated the expected travel time updating process, and supports the face validity of the suggested approach.

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