On traffic equilibrium models with a nonlinear time/money relation

We consider a traffic equilibrium problem in which each route has two attributes, time delay and monetary outlay, which are combined into a generalized time through a nonlinear relation. It is shown that this problem can be stated as a convex optimization model. Two simplicial decomposition type methods are proposed for its solution. The subproblem of these methods, which is a two-attribute shortest route problem, can be efficiently solved by the multi-labelling technique which has previously been applied to resource-constrained shortest path problems. Our numerical experiments show that both methods are feasible approaches to the equilibrium problem.