Abstract: Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are $N$ groups of drivers. The $i$-th group consists of $κ_i$ drivers, sharing the same departure and arrival costs $φ_i(t)$, $ψ_i(t)$. For any given population sizes $κ_1,…, κ_n$, we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure time. The possible nonuniqueness, and a characterization of this Nash equilibrium solution, are also discussed.