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

@article{Cabannes2021SolvingND, title={Solving N-player dynamic routing games with congestion: a mean field approach}, author={Theophile Cabannes and Mathieu Lauri{\`e}re and Julien P{\'e}rolat and Rapha{\"e}l Marinier and Sertan Girgin and Sarah Perrin and Olivier Pietquin and Alexandre M. Bayen and {\'E}ric Goubault and Romuald Elie}, journal={ArXiv}, year={2021}, volume={abs/2110.11943} }

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…

## References

SHOWING 1-10 OF 50 REFERENCES

Linearly Solvable Mean-Field Traffic Routing Games

- Mathematics, Computer ScienceIEEE Transactions on Automatic Control
- 2021

It is shown that the mean-field approximation of a dynamic traffic routing game in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers selecting the same route leads to the so-called linearly solvable Markov decision process, implying its mean- field equilibrium (MFE) can be found simply by solving a finite-dimensional linear system backward in time.

The Impact of GPS-Enabled Shortest Path Routing on Mobility: A Game Theoretic Approach

- Computer Science
- 2018

Simulations are run in which the percentage of routing app users is progressively increased to demonstrate the impact of these apps on traffic patterns and, in particular, potential convergence to Nash equilibria solutions of traffic flow problems.

A differential game model of Nash equilibrium on a congested traffic network

- Computer ScienceNetworks
- 1993

This paper considers the problem of the competition among a finite number of players who must transport the fixed volume of traffic on a simple network over a prescribed planning horizon as a N-person nonzero-sum differential game.

Density Flow in Dynamical Networks via Mean-Field Games

- Mathematics, Computer ScienceIEEE Transactions on Automatic Control
- 2017

The density model is rearranged to recast the problem within the framework of mean-field games and conditions for the density to converge to a pre-assigned set are provided, for both the stochastic and the worst-case scenarios.

A mean field route choice game model

- Computer Science2018 IEEE Conference on Decision and Control (CDC)
- 2018

A mean field game based algorithm is developed that generates the drivers' optimal choices and anticipates the evolution of their probability distribution on the network and illustrates via a numerical scheme how the model can also be used to evaluate the performance of different network configurations.

A Game-Theoretic Framework for Autonomous Vehicles Velocity Control: Bridging Microscopic Differential Games and Macroscopic Mean Field Games

- Mathematics, Computer ScienceArXiv
- 2019

This paper proposes an efficient computational framework for longitudinal velocity control of a large number of autonomous vehicles (AVs) and develops a traffic flow theory for AVs and offers a systematic framework to apply MFG to autonomous vehicle velocity control.

A micro-macro traffic model based on Mean-Field Games

- Computer Science, Mathematics2015 American Control Conference (ACC)
- 2015

This paper considers a microscopic model consisting of a large number of rational, utility-maximizing drivers interacting on a single road, and uses the theory of Mean Field Games (MFG) to deduce a macroscopic model of traffic density emerging from these interactions.

Multi-Agent Reinforcement Learning for Dynamic Routing Games: A Unified Paradigm

- Computer ScienceArXiv
- 2020

A multi-agent reinforcement learning (MARL) paradigm is proposed in which each agent learns and updates her own en-route path choice policy while interacting with others on transportation networks and is shown to generalize the classical notion of dynamic user equilibrium (DUE) to model-free and data-driven scenarios.

On a mean ﬁeld game approach modeling congestion and aversion in pedestrian crowds

- Engineering, Mathematics
- 2011

In this paper we present a new class of pedestrian crowd models based on the mean ﬁeld games theory introduced by Lasry and Lions in 2006. This macroscopic approach is based on a microscopic model,…

Energy-Efficient Resource Management in Ultra Dense Small Cell Networks: A Mean-Field Approach

- Computer Science, Mathematics2015 IEEE Global Communications Conference (GLOBECOM)
- 2014

A novel approach for joint power control and user scheduling is proposed for optimizing energy efficiency (EE) in ultra dense small cell networks (UDNs), and it is shown that by weaving notions from Lyapunov optimization and mean field theory, the proposed solution yields an equilibrium control policy which maximizes the network utility while ensuring users' quality- of-service.