A Variational Inequality Model for Traffic Assignment

The traditional traffic equilibrium problems is to find a set of path flow to meet certain demand constraints. In order to prove the existence, uniqueness and convergence of solutions, the problem can be transformed as a nonlinear program problem, a non-linear problem, a variational inequality problem, or the fixed point problem. In this paper, we discusses the problem of traffic equilibrium, which the cost of path is not the simple sum of the cost of links. A variational inequality model is established to characterize the solutions of traffic equilibrium problems, and then the solution of traffic assignment problem can be got by so solving the variational inequality.