Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 873025, 14 pages
doi:10.1155/2010/873025
Research Article

Dynamic Traffic Network Equilibrium System

Yun-Peng He,1 Jiu-Ping Xu,2 Nan-Jing Huang,1,2 and Meng Wu2,3

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2College of Business and Administration, Sichuan University, Chengdu, Sichuan 610064, China
3College of General Studies, Konkuk University, Seoul 143-701, South Korea

Received 20 November 2009; Accepted 1 March 2010

Academic Editor: Lai Jiu Lin

Copyright © 2010 Yun-Peng He 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.

Abstract

We discuss the dynamic traffic network equilibrium system problem. We introduce the equilibrium definition based on Wardrop's principles when there are some internal relationships between different kinds of goods which transported through the same traffic network. Moreover, we also prove that the equilibrium conditions of this problem can be equivalently expressed as a system of evolutionary variational inequalities. By using the fixed point theory and projected dynamic system theory, we get the existence and uniqueness of the solution for this equilibrium problem. Finally, a numerical example is given to illustrate our results.