Bounding Residence Times for Atomic Dynamic Routings

• 成果类型: Article; Early Access
• 署名作者: Cao, Zhigang; Chen, Bo; Chen, Xujin; Wang, Changjun
• 署名单位: Beijing Jiaotong University; University of Warwick; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1242
• 发表日期: 2022
• 关键词: flows; algorithms; equilibria

摘要

In this paper, we are concerned with bounding agents' residence times in the network for a broad class of atomic dynamic routings. We explore novel token techniques to circumvent direct analysis on complicated chain effects of dynamic routing choices. Even though agents may enter the network over time for an infinite number of periods, we prove that under a mild condition, the residence time of every agent is upper bounded (by a network-dependent constant plus the total number of agents inside the network at the entry time of the agent). Applying this result to three game models of atomic dynamic routing in the recent literature, we establish that the residence times of selfish agents in a series-parallel network with a single origin-destination pair are upper bounded at equilibrium, provided the number of incoming agents at each time point does not exceed the network capacity (i.e., the smallest total capacity of edges in the network whose removal separates the origin from the destination).