Reprint of “Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach”

Koki Satsukawa, Kentaro Wada, Takamasa Iryo

Research output: Contribution to journalArticlepeer-review


The aim of this study is to analyze the stability of dynamic user equilibrium (DUE) with fixed departure times in unidirectional networks. Specifically, stochastic stability, which is the concept of stability in evolutionary dynamics subjected to stochastic effects, is herein considered. To achieve this, a new approach is developed by synthesizing the three concepts: the decomposition technique of DUE assignments, the weakly acyclic game, and the asymptotic analysis of the stationary distribution of perturbed dynamics. Specifically, we first formulate a DUE assignment as a strategic game (DUE game) that deals with atomic users. We then prove that there exists an appropriate order of assigning users for ensuring equilibrium in a unidirectional network. With this property, we establish the relationship between DUE games in unidirectional networks and weakly acyclic games. The convergence and stochastic stability of better response dynamics in the DUE games are then proved based on the theory of weakly acyclic games. Finally, we observe the properties of the convergence and stability from numerical experiments. The results show that the strict improvement of users’ travel times by the applied evolutionary dynamics is important for ensuring the existence of a stochastically stable equilibrium in DUE games.

Original languageEnglish
Pages (from-to)117-135
Number of pages19
JournalTransportation Research Part B: Methodological
Publication statusPublished - 2020 Feb


  • Convergence
  • Dynamic user equilibrium
  • Nash equilibrium
  • Stochastic stability
  • Unidirectional network
  • Weakly acyclic games


Dive into the research topics of 'Reprint of “Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach”'. Together they form a unique fingerprint.

Cite this