Capacity constraints in urban transport networks

This paper deals with the equilibrium problem of asymmetric transport networks with elastic demand and capacity constraints. It shows that a homogeneous linear relationship exists between the operator of the variational inequality usually considered in the theory of transport networks and the gradients of the constraints. This linear relationship provides confirmation of a result obtained in a previous paper: a solution of the variational inequality may not be an equilibrium solution, and a transport network may have no equilibrium pattern which satisfies the capacity constraints. However, additional costs can be imposed on some network links, in such a way that a solution of the variational inequality becomes the unique equilibrium solution for the transport network. The paper shows that these additional costs are linear combinations of the coefficients of the gradients of the capacity constraints, and that the way they can be applied to actual transport networks essentially depends on the way the latter are managed. A method of computing both the equilibrium flow pattern and the additional costs is presented, and is applied to the actual networks of three Italian cities, where the additional costs are imposed on drivers as parking taxes at the destination zones of the central areas.