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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 162128, 10 pages
Research Article

Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System

MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China

Received 29 January 2013; Accepted 23 April 2013

Academic Editor: Leonid Shaikhet

Copyright © 2013 Wenyi Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study proposes a nonlinear min-cost-pursued swapping dynamic (NMSD) system to model the evolution of selfish routing games on traffic network where travelers only swap from previous costly routes to the least costly ones. NMSD is a rational behavior adjustment process with stationary link flow pattern being the Wardrop user equilibrium. NMSD is able to prevent two behavioral deficiencies suffered by the existing min-cost-oriented models and keep solution invariance. NMSD relaxes the homogeneous user assumption, and the continuous-time NMSD (CNMSD) and discrete-time NMSD (DNMSD) share the same revision protocol. Moreover, CNMSD is Lyapunov-stable. Two numerical examples are conducted. The first one is designed to characterize the NMSD-conducted network traffic evolution and test the stability of day-to-day NMSD. The second one aims to explore the impacts of network scale on the stability of route-swaps conducted by pairwise and min-cost-pursed swapping behaviors.