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

TL;DR

This paper introduces a new N-player dynamic routing game with congestion dynamics and proposes a mean field game approximation, enabling efficient analysis of large traffic networks with heterogeneous behaviors.

Contribution

It develops a well-posed congestion-aware routing game model and demonstrates that the mean field approximation is accurate and scalable for large traffic networks.

Findings

Mean field approximation is accurate for networks with more than a few dozen vehicles.

The approach efficiently models traffic dynamics with over 14,000 vehicles.

The model reproduces phenomena like heterogeneous departure times and congestion spill back.

Abstract

The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and mesoscopic traffic modeling - the article introduces a new N-player dynamic routing game with explicit congestion dynamics. The model is well-posed and can reproduce heterogeneous departure times and congestion spill back phenomena. However, as Nash equilibrium computations are PPAD-complete, solving the game becomes intractable for large but realistic numbers of vehicles N. Therefore, the corresponding mean field game is also introduced. Experiments were performed on several classical benchmark networks of the traffic community: the Pigou, Braess, and Sioux Falls networks with heterogeneous origin, destination and departure time tuples. The Pigou and the Braess examples reveal that the mean field approximation is generally very accurate and computationally efficient as soon as the number of vehicles exceeds 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.