Journal of Applied Mathematics
Volume 2012 (2012), Article ID 612142, 12 pages
http://dx.doi.org/10.1155/2012/612142
Research Article

Traffic Network Equilibrium Problems with Capacity Constraints of Arcs and Linear Scalarization Methods

X. Q. Tian1 and Y. D. Xu2

1Chongqing University of Science and Technology, Chongqing 401331, China
2College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received 13 September 2012; Accepted 15 November 2012

Academic Editor: Nan-Jing Huang

Copyright © 2012 X. Q. Tian and Y. D. Xu. 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

Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak) vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin (2010), and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak) vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.