Dynamic system optimal traffic assignment with atomic users: Convergence and stability

Koki Satsukawa, Kentarou Wada, David Watling

Research output: Contribution to journalArticlepeer-review

Abstract

In this study, we analyse the convergence and stability of dynamic system optimal (DSO) traffic assignment with fixed departure times. We first formulate the DSO traffic assignment problem as a strategic game wherein atomic users select routes that minimise their marginal social costs, called a ‘DSO game’. By utilising the fact that the DSO game is a potential game, we prove that a globally optimal state is a stochastically stable state under the logit response dynamics, and the better/best response dynamics converges to a locally optimal state. Furthermore, as an application of DSO assignment, we examine characteristics of the evolutionary implementation scheme of marginal cost pricing. Through theoretical comparison with a fixed pricing scheme, we found the following properties of the evolutionary implementation scheme: (i) the total travel time decreases smoother to an efficient traffic state as congestion externalities are perfectly internalised; (ii) a traffic state would reach a more efficient state as the globally optimal state is stabilised. Numerical experiments also suggest that these properties make the evolutionary scheme robust in the sense that they prevent a traffic state from going to worse traffic states with high total travel times.

Original languageEnglish
Pages (from-to)188-209
Number of pages22
JournalTransportation Research Part B: Methodological
Volume155
DOIs
Publication statusPublished - 2022 Jan

Keywords

  • Convergence
  • Dynamic traffic assignment
  • Nash equilibrium
  • Potential game
  • Stochastic stability
  • System optimal
  • Weakly acyclic game

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation

Fingerprint

Dive into the research topics of 'Dynamic system optimal traffic assignment with atomic users: Convergence and stability'. Together they form a unique fingerprint.

Cite this