Origin-to-destination network flow with path preferences and velocity controls: a mean field game-like approach

TL;DR

This paper develops a mean field game model for network flow that incorporates path preferences and velocity controls, accounting for global congestion information and agent decision dynamics.

Contribution

It introduces a novel mean field framework with path preference dynamics based on noisy best response, extending standard models to include global congestion awareness.

Findings

Existence of a mean field equilibrium as a fixed point in the network.

Inclusion of bounded control sets depending on local mass-distribution.

Generalization of noisy best response dynamics for path selection.

Abstract

In this paper we consider a mean field approach to modeling the agents flow over a transportation network. In particular, beside a standard framework of mean field games, with controlled dynamics by the agents and costs mass-distribution dependent, we also consider a path preferences dynamics obtained as a generalization of the so-called noisy best response dynamics. Such a preferences dynamics says the agents choose their path having access to global information about the network congestion state and based on the observation of the decision of the agents that have preceded. We prove the existence of a mean field equilibrium obtained as a fixed point of a map over a suitable set of time-varying mass-distributions, defined edge by edge in the network. We also address the case where the admissible set of controls is suitably bounded depending on the mass-distribution on the edge itself.