Abstract

The crowd motion modeling and the study of flow dynamics have become in the last decades two of the main targets of several research communities. In the transportation area, for example, the interest towards such topics is due to the continuous growth of traffic flow as well as the spread of information technologies which are changing the transportation system dynamics and affecting the users’ decision making and behaviors. In this talk we introduce a mean field approach to modeling the agents flow over a transportation network. In particular, beside the usual framing of mean field games, we also consider the path preferences dynamics. Such a 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. Our outcomes are two-fold. First we prove the existence of a mean field equilibrium obtained as a fixed point of a map over a suitable set of time-varying distributions. Then, a bi-level optimization problem is formulated for an external controller who aims to induce a suitable mean field equilibrium.

Joint work with Fabio Bagagiolo and Raffaele Pesenti.