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Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?

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  • Ren-Yong Guo

    (School of Economics and Management, Beihang University, 100191 Beijing, China; Key Laboratory of Complex System Analysis and Management Decision, Ministry of Education, 100191 Beijing, China)

  • Hai Yang

    (Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China)

  • Hai-Jun Huang

    (School of Economics and Management, Beihang University, 100191 Beijing, China; Key Laboratory of Complex System Analysis and Management Decision, Ministry of Education, 100191 Beijing, China)

Abstract

The dynamic traffic equilibrium problem has been a pivotal area of research in transportation for a few decades. The current state-of-the-art research in this area generally considers simultaneous departure time and route choice. In this paper, we theoretically prove that, in the simplest standard bottleneck model with a sufficient number of commuters, a dynamic user equilibrium (DUE) cannot be reached through a day-to-day evolution process of travelers’ departure rate—a central idea behind the iterative dynamic traffic equilibrium algorithms prevalent in the literature. We carry out our exploration with the proportional swap system and then extend our analysis to other typical dynamic equilibrium algorithms such as the network tatonnement process, the simplex gravity flow dynamics, the projected dynamical system, and the evolutionary traffic dynamics. Our investigation indicates that any algorithm analogous to the five categories of systems must be cautious in terms of convergence when it is applied to solve the DUE problem with a departure time choice, and hence puts forward a general question: Are we really solving the DUE problem with a departure time choice?

Suggested Citation

  • Ren-Yong Guo & Hai Yang & Hai-Jun Huang, 2018. "Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?," Transportation Science, INFORMS, vol. 52(3), pages 603-620, June.
    • Handle: RePEc:inm:ortrsc:v:52:y:2018:i:3:p:603-620
    DOI: 10.1287/trsc.2017.0764
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