A continuous-time linear complementarity system for dynamic user equilibria in single bottleneck traffic flows

• 成果类型: Article
• 署名作者: Pang, Jong-Shi; Han, Lanshan; Ramadurai, Gitakrishnan; Ukkusuri, Satish
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; Purdue University System; Purdue University; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Madras
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-010-0433-z
• 发表日期: 2012
• 页码: 437-460
• 关键词: congestion; uniqueness; EXISTENCE; ARRIVALS; MODEL

摘要

This paper formally introduces a linear complementarity system (LCS) formulation for a continuous-time, multi-user class, dynamic user equilibrium (DUE) model for the determination of trip timing decisions in a simplified single bottleneck model. Existence of a Lipschitz solution trajectory to the model is established by a constructive time-stepping method whose convergence is rigorously analyzed. The solvability of the time-discretized subproblems by Lemke's algorithm is also proved. Combining linear complementarity with ordinary differential equations and being a new entry to the mathematical programming field, the LCS provides a computational tractable framework for the rigorous treatment of the DUE problem in continuous time; this paper makes a positive contribution in this promising research venue pertaining to the application of differential variational theory to dynamic traffic problems.