Traffic Network Design Research Articles

A descent approach to solving the complementary programming problem

In recent years, much attention has focused on mathematical programming problems with equilibrium constraints. In this article we consider the case where the constraints are complementarity constraints. Problems of this type arise, for instance, in the design of traffic networks. We develop here a descent algorithm for this problem that will converge to a local optimum in a finite number of iterations. The method involves solving a sequence of subproblems that are linear programs. Computational tests comparing our algorithm with the branch-and-bound algorithm in [7] bear out the efficacy of our method. When solving large problems, there is a definite advantage to coupling both methods. A local optimum incumbent provided by our algorithm can significantly reduce the computational effort required by the branch-and-bound algorithm.

An Equilibrium Model for the Environmental Orientated Design of Traffic Networks

One essential objective of an environmental orientated transportation planning is the reduction of car traffic. Therefore a traffic model is required, that considers restraint measures like restrictions of carparks and road capacities. Especially difficult is the consideration of congestion, because the forming of queues is a time dependent process and the usual traffic assignment models presume continuous flows. This paper shows, that congestion may be described by stationary queues, which may be included in traffic assignment models without an essential increase of computing time. The formation of stationary queues presumes, that traffic demand is reduced by growing journey times. The model therefore considers, that the traffic demand and the modal choice depend on journey times. It is shown, that equilibrium models have to be used, to prevent large errors in the calculation of lengths of queue. Moreover a simultaneous calculation of traffic assignment and modal split is necessary to assure convergence.