Mean Field Mathematical Models for Excursionists Flow
in a
Historic
INDAM-GNAMPA
Research Project, March 2017 - March 2018
This project deals with the problem of managing the excursionists flow in
historic cities.
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.
PARTICIPANTS
Fabio
Bagagiolo (coordinator),
Silvia
Faggian, University Ca' Foscari of
Rosario Maggistro, Polytechnic of
Raffaele Pesenti, University Ca' Foscari of Venice,
Italy.
COLLABORATORS
ACTIVITY
PUBLICATIONS
Contact: fabio.bagagiolo@unitn.it