Journal
TRANSPORTATION SCIENCE
Volume 52, Issue 3, Pages 603-620Publisher
INFORMS
DOI: 10.1287/trsc.2017.0764
Keywords
dynamical system; dynamic user equilibrium (DUE); bottleneck model; algorithm; convergence
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Funding
- Research Grants Council of the Hong Kong Special Administrative Region of China [HKUST16211114]
- National Basic Research Program of China [2012CB725401]
- National Natural Science Foundation of China [71622005]
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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?
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