A mean field approach to model flows of agents with path preferences over a network
Abstract
In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined with a path preferences dynamics. The path preferences are influenced by the congestion status on the whole network as well as the possible hassle of being forced to run during the tour. We prove the existence of a mean field equilibrium as a fixed point, over a suitable set of time-varying distributions, of a map obtained as a limit of a sequence of approximating functions. Then, a bi-level optimization problem is formulated for an external controller who aims to induce a specific mean field equilibrium.
Keywords
Cite
@article{arxiv.1903.00561,
title = {A mean field approach to model flows of agents with path preferences over a network},
author = {Fabio Bagagiolo and Rosario Maggistro and Raffaele Pesenti},
journal= {arXiv preprint arXiv:1903.00561},
year = {2019}
}
Comments
6 pages, Accepted in 58th IEEE Conference on Decision and Control 2019