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).

　　Publication: 

　　Mathematics of Operations Research, 17 February 2022,  

　　doi.org/10.1287/moor.2021.1242 

　　Author: 

　　Zhigang Cao 

　　School of Economics and Management, Beijing Jiaotong University, Beijing, China 

　　Email: zgcao@bjtu.edu.cn  

　　Bo Chen 

　　Warwick Business School, University of Warwick, Coventry, United Kingdom 

　　Email: b.chen@warwick.ac.uk  

　　Xujin Chen 

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China 

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China 

　　Email: xchen@amss.ac.cn  

　　Changjun Wang* 

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China 

　　Email: wcj@amss.ac.cn