Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 873025, 14 pages
doi:10.1155/2010/873025
Dynamic traffic network equilibrium system
Yun-Peng He1
, Jiu-Ping Xu2
, Nan-Jing Huang1
and Meng Wu2
1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2College of Business and Administration, Sichuan University, Chengdu, Sichuan 610064, China
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.