Convergence of a Packet Routing Model to Flows over Time
成果类型：
Article
署名作者：
Sering, Leon; Koch, Laura Vargas; Ziemke, Theresa
署名单位：
Swiss Federal Institutes of Technology Domain; ETH Zurich; Technical University of Berlin; Technical University of Berlin
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2022.1318
发表日期：
2023
页码：
1741-1766
关键词：
摘要：
Mathematical approaches for modeling dynamic traffic can be roughly divided into two categories: discrete packet routing models and continuous flow over time models. Despite very vital research activities on models in both categories, their connection was poorly understood so far. We build this connection by specifying a (competitive) packet routing model, which is discrete in terms of flow and time, and proving its convergence to the intensively studied model of flows over time with deterministic queuing. More precisely, we prove that the limit of the convergence process when decreasing the packet size and time step length in the packet routing model constitutes a flow over time with multiple commodities. In addition, we show that the convergence result implies the existence of approximate equilibria in the competitive version of the packet routing model. This is of significant interest as exact pure Nash equilibria cannot be guaranteed in the multicommodity setting.
来源URL：