# Meeting Details

Title: Optima and Equilibria for a model of traffic flow Computational and Applied Mathematics Colloquium Alberto Bressan, Penn State U. After reviewing the Lighthill-Whitham model of traffic flow, a cost functional will be considered, depending on the departure time and on the arrival time of each driver. Under natural assumptions, there exists a unique globally optimal solution, minimizing the total cost to all drivers. In a realistic situation, however, the actual traffic is better described by the Nash equilibrium solution, where no driver can lower his individual cost by changing his own departure time. A characterization of the Nash solution can be provided, establishing its existence and uniqueness. The costs of the optimal and the equilibrium solution can be compared on some specific examples. This leads to an optimal pricing problem: how to design a time-dependent toll, charged at the entrance of the highway, so that the Nash equilibrium solution is best possible". Various extensions an open problems will be discussed.