Uniqueness of equilibrium in steady state and dynamic traffic networks.

This study considers the issue of uniqueness of equilibrium in traffic networks, which are considered to be directed graphs in which traffic flows along acyclic paths, which are called routes, connecting origin destination (OD) pairs. The demand for travel between each OD pair is assumed to be rigid. It is shown that in the steady state model, provided that each linkcost function is a non-decreasing function of link flow, costs at equilibrium are unique. The paper then goes on to consider dynamic user equilibrium in dynamic traffic models, with special attention given to the bottleneck model. In the dynamic bottleneck queueing model, the route cost vector is not a monotone function of the route flow vector; an example network isgiven to illustrate this. An alternative definition of what constitutes an increasing function is given: and the cost function is shown to satisfythis condition in the bottleneck model. A number of additional propertiesarethen put forward that must be satisfied in order for the equilibrium flowpattern to be essentially unique in the single OD pair case; the bottleneck model is shown to satisfy these properties. For the covering abstract see ITRD E144727. Reprinted with permission of Elsevier.