Wardrop Equilibrium in Discrete-Time Selfish Routing With Time-Varying Bounded Delays

• 成果类型: Article
• 署名作者: Giuseppi, Alessandro; Pietrabissa, Antonio
• 署名单位: Sapienza University Rome
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2981906
• 发表日期: 2021
• 页码: 526-537
• 关键词: LaSalle's invariance principle; selfish routing; time-delay systems; Wardrop equilibrium

摘要

This article presents a multicommodity, discrete-time, distributed, and noncooperative routing algorithm, which is proved to converge to an equilibrium in the presence of heterogeneous, unknown, time-varying but bounded delays. Under mild assumptions on the latency functions, which describe the cost associated with the network paths, two algorithms are proposed: The former assumes that each commodity relies only on measurements of the latencies associated with its own paths; the latter assumes that each commodity has (at least indirectly) access to the measures of the latencies of all the network paths. Both algorithms are proven to drive the system state to an invariant set that approximates and contains the Wardrop equilibrium, defined as a network state in which no traffic flow over the network paths can improve its routing unilaterally, with the latter achieving a better reconstruction of the Wardrop equilibrium. Numerical simulations show the effectiveness of the proposed approach.