Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach
Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach
复制标题
单向网络中动态用户均衡的随机稳定性：弱非循环博弈方法
DOI：
10.1016/j.trb.2019.05.015
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Iryo Takamasa
中科院分区：
文献类型：
--
作者：
Satsukawa Koki;Wada Kentaro;Iryo Takamasa
本文研究单向网络中具有固定出发时间的动态用户平衡点的稳定性。具体而言，随机稳定的平衡，这是一个稳定的概念，在日常的动态随机效应，在这里被认为是。为了实现这一点，一种新的方法是通过合成三个概念：分解技术的DUE分配，弱非循环游戏，和渐近分析的平稳分布的动态。具体来说，我们首先制定的DUE分配作为一个战略游戏（DUE游戏），处理原子用户。然后，我们证明了存在一个适当的顺序分配用户一个接一个的网络，以确保平衡。利用这个性质，我们证明了DUE对策是弱无圈对策，它是势对策的推广。基于弱非循环对策理论，建立了DUE对策的收敛性和随机稳定性。最后，数值实验验证了这些理论结果。
The aim of this study is to analyze the stability of the dynamic user equilibrium (DUE) with fixed departure times in unidirectional networks. Specifically, the stochastic stability of the equilibrium, which is the concept of stability in a day-to-day 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 the dynamics. Specifically, we first formulate the DUE assignment as a strategic game (DUE game), which deals with atomic users. We then prove that there exists an appropriate order of assigning users one by one to the network for ensuring an equilibrium. With this property, we prove that the DUE game is a weakly acyclic game, which is a generalization of potential games. The convergence and stochastic stability of the DUE game are then established based on the theory of weakly acyclic games. Finally, numerical experiments are conducted to validate these theoretical results.