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The recent emergence of navigational tools has changed traffic patterns andhas now enabled new types of congestion-aware routing control like dynamic roadpricing. Using the fundamental diagram of traffic flows - applied inmacroscopic and mesoscopic traffic modeling - the article introduces a newN-player dynamic routing game with explicit congestion dynamics. The model iswell-posed and can reproduce heterogeneous departure times and congestion spillback phenomena. However, as Nash equilibrium computations are PPAD-complete,solving the game becomes intractable for large but realistic numbers ofvehicles N. Therefore, the corresponding mean field game is also introduced.Experiments were performed on several classical benchmark networks of thetraffic community: the Pigou, Braess, and Sioux Falls networks withheterogeneous origin, destination and departure time tuples. The Pigou and theBraess examples reveal that the mean field approximation is generally veryaccurate and computationally efficient as soon as the number of vehiclesexceeds a few dozen. On the Sioux Falls network (76 links, 100 time steps),this approach enables learning traffic dynamics with more than 14,000 vehicles.

Solving N-player dynamic routing games with congestion: a mean field approach