Optimal routing of traffic flows with length restrictions in networks with congestion

When traffic flows are routed through a road network it is desirable to minimize the total road usage. Since a route guidance system can only recommend paths to the drivers, special care has to be taken not to route them over paths they perceive as too long. This leads in a simplified model to a nonlinear multicommodity flow problem with constraints on the available paths. In this article an algorithm for this problem is given, which combines the convex combinations algorithm by Frank and Wolfe with column generation and algorithms for the constrained shortest path problem. Computational results stemming from a cooperation with DaimlerChrysler are presented.