Routing in Road Networks: the toll booth problem

Due to population growth and the massive production of automotive vehicles, traffic congestion problems have become larger and more common. This is a reality that governments are facing everywhere, even in medium sized cities that were not used to this scenario. However, despite the growth of the number of vehicles, traffic congestion can be lessened using different strategies. One possibility, that is explored in this research, is assigning tolls to roads, inducing users to take alternative paths, and thus better distributing the traffic across the road network. This problem is called the toll booth problem and is NP-hard. We propose mathematical formulations for variations of the toll booth problem, using two piecewise linear functions to approximate the congestion cost. We test these models on a set of real-world instances, and apply a previously proposed genetic algorithm to all instances. The experimental results show that the proposed piecewise linear functions approximates the original convex function quite well, and the genetic algorithm produces high quality solutions.