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On a mean field game approach modeling congestion and aversion in pedestrian crowds

Wolfram, Marie-Thérèse; Lachapelle, Aimé (2011), On a mean field game approach modeling congestion and aversion in pedestrian crowds, Transportation Research Part B: Methodological, 45, 10, p. 1572–1589. http://dx.doi.org/10.1016/j.trb.2011.07.011

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Type
Article accepté pour publication ou publié
Date
2011
Journal name
Transportation Research Part B: Methodological
Volume
45
Number
10
Publisher
Elsevier
Pages
1572–1589
Publication identifier
http://dx.doi.org/10.1016/j.trb.2011.07.011
Metadata
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Author(s)
Wolfram, Marie-Thérèse
Lachapelle, Aimé
Abstract (EN)
In this paper we present a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006. This macroscopic approach is based on a microscopic model, that considers smart pedestrians who rationally interact and anticipate the future. This leads to a forward-backward structure in time. We focus on two-population interactions and validate the modeling with simple examples such as self-organization behavior as for instance lane formation. Two complementary classes of problems are addressed, namely the case of crowd aversion and the one of congestion. In both cases we describe the model, build a numerical solver (respectively based on optimization formulation and partial differential equations), and finally provide some numerical tests involving complex group behaviors such as symmetry breaking and lane formation.
Subjects / Keywords
lane formation; numerical approximation; flow of pedestrians; rational expectations; Nash equilibrium; interacting populations; Mean field games
JEL
C61 - Optimization Techniques; Programming Models; Dynamic Analysis
C02 - Mathematical Methods

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