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

Koki Satsukawa, Kentaro Wada, Takamasa Iryo
2019 Transportation Research Part B: Methodological  
資源タイプ Resource Type Journal Article / 学術雑誌論文 版区分 Resource Version publisher 権利 Rights a b s t r a c t 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
more » ... 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.
doi:10.1016/j.trb.2019.05.015 fatcat:xmil5opno5batenwk667qumkfu