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The first part of this paper contains a brief introduction to conservation law models of traffic flow on a network of roads. Globally optimal solutions and Nash equilibrium solutions are reviewed, with several groups of drivers sharing different cost functions. In the second part we consider a globally optimal set of departure rates, for different groups of drivers but on a single road. Necessary conditions are proved, which lead to a practical algorithm for computing the optimal solution.

Globally optimal departure rates for several groups of drivers