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

Koki Satsukawa, Kentaro Wada, David Watling

Research output: Contribution to journalArticlepeer-review


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
Publication statusPublished - 2022 Jan


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

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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