An algorithm of elastic incremental network loading respecting capacity constraints

Most of the assignment models used in the current practice do not take explicitly into account link capacity constraints. In fact under the within-day stationarity hypotheses commonly adopted by these models, the existence of the equilibrium solution may not be assured if explicit link capacity constraints are introduced, or continuity of link cost functions is not assured also for values of flow exceeding capacity; in order to overcome this condition, in current practice, cost functions presenting a vertical asymptote as link flow value match the capacity, are approximated by using a tangent (linear) curve. Under these hypotheses the equilibrium solution exists and it allows the exceeding of link capacity. This paper presents a heuristic procedure of network loading for finding equilibrium flow patterns avoiding to exceed link capacities. It consists of an incremental assignment, where loading rate is sequentially evaluated for each origin-destination pair by scanning the maximum demand rate which can be assigned respecting capacity constraints defined by using the assignment matrix. This procedure allows also the evaluation of the maximum demand that can be assigned respecting capacity constraints. Performances of the proposed procedure are evaluated through an application on a real network.