A trade-off between average and maximum arc congestion minimization in traffic assignment with user constraints

In system optimal traffic assignment of traffic flows with user constraints the total travel time is minimized on a set of paths with bounded length ensuring a certain level of fairness for users. Minimizing the total travel time may lead to experience large travel times on some arcs. On the other hand, when minimizing the maximum arc travel time, the total travel time cannot be controlled. The increase of arc travel time with respect to arc free-flow travel time is related to the arc congestion that is one of the main issues in road networks. In this paper we propose a new model that is a compromise between minimizing the average arc congestion and the worst arc congestion on the road network. The model is a linear program that minimizes the average arc congestion over a given percentage of the most congested arcs. A heuristic algorithm aimed at reducing the number of paths that are considered for the model is also proposed. A computational study is performed that shows the flexibility of the model and the quality of the heuristic.