Solving N-player dynamic routing games with congestion: a mean field approach - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

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

Theophile Cabannes
  • Fonction : Auteur
Mathieu Lauriere
  • Fonction : Auteur
Julien Perolat
  • Fonction : Auteur
Raphael Marinier
  • Fonction : Auteur
Sertan Girgin
  • Fonction : Auteur
Sarah Perrin
  • Fonction : Auteur
Olivier Pietquin
  • Fonction : Auteur
Alexandre M. Bayen
  • Fonction : Auteur
Eric Goubault
Romuald Elie
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-03416248 , version 1 (05-11-2021)

Identifiants

Citer

Theophile Cabannes, Mathieu Lauriere, Julien Perolat, Raphael Marinier, Sertan Girgin, et al.. Solving N-player dynamic routing games with congestion: a mean field approach. 2021. ⟨hal-03416248⟩
29 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More