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 practice, 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 examples.

Various extensions and open problems will be discussed.