Mean Field Mathematical Models for Excursionists Flow
INDAM-GNAMPA Research Project, March 2017 - March 2018
This project deals with the problem of managing the excursionists flow in
We introduce a mean field model to study the possibility of directing the excursionists through different routes to avoid congestion. We cast the problem in two different approaches: the Mean Field Games (MFG) and the Dynamic Traffic Assignment (DTA).
Both approaches consider an optimal control problem with costs depending on the satisfaction of visiting the sites and on the congestions (the mean field) of the chosen path inside the city. Our goal is to study the possible dynamic equilibria.
The excursionists have more than one target to reach. This leads to the fact that a memory effect must be taken into account: different excursionists may occupy the same place at the same instant, but they may have different purposes, depending on which sites they have already visited.
Keywords: Optimal Control, Viscosity Solutions of Hamilton-Jacobi Equations, Transport Equations, Mean Field Games, Hysteresis and Memory Effects, Partial Differential Equations, Dynamic Traffic Assignment, Mathematical Programming, Dynamics on Networks, Pedestrian Flows, Jumping Processes, Hybrid Systems.
Faggian, University Ca' Foscari of
Rosario Maggistro, Polytechnic of
Raffaele Pesenti, University Ca' Foscari of Venice, Italy.