Equilibrium in Transport Networks with Capacity Constraints

Abstract

This paper considers the problem of multimodal transport networks with elastic demand and capacity constraints. It is shown that, when capacity constraints are active, there is not equilibrium in these networks. However an equilibrium solution can be assured in any case if additional costs are imposed on network links. The paper presents a model of multimodal networks where capacity constraints, and both demand and cost functions, are symmetric: in this case the additional costs are the Lagrange multipliers of capacity constraints. A method to calculate these additional costs is proposed and is used in a simple numerical example.