Mean field games with nonlinear mobilities in pedestrian dynamics

Handle URI:
http://hdl.handle.net/10754/564890
Title:
Mean field games with nonlinear mobilities in pedestrian dynamics
Authors:
Burger, Martin; Di Francesco, Marco; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Wolfram, Marie Therese
Abstract:
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Discrete and Continuous Dynamical Systems - Series B
Issue Date:
Apr-2014
DOI:
10.3934/dcdsb.2014.19.1311
ARXIV:
arXiv:1304.5201
Type:
Article
ISSN:
15313492
Sponsors:
MTW acknowledges financial support of the Austrian Science Foundation FWF via the Hertha Firnberg Project T456-N23. MDF is supported by the FP7-People Marie Curie CIG (Career Integration Grant) Diffusive Partial Differential Equations with Nonlocal Interaction in Biology and Social Sciences (DifNonLoc), by the 'Ramon y Cajal' sub-programme (MICINN-RYC) of the Spanish Ministry of Science and Innovation, Ref. RYC-2010-06412, and by the by the Ministerio de Ciencia e Innovacion, grant MTM2011-27739-C04-02. The authors thank the anonymous referees for useful comments to improve the manuscript.
Additional Links:
http://arxiv.org/abs/arXiv:1304.5201v1
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBurger, Martinen
dc.contributor.authorDi Francesco, Marcoen
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorWolfram, Marie Thereseen
dc.date.accessioned2015-08-04T07:24:15Zen
dc.date.available2015-08-04T07:24:15Zen
dc.date.issued2014-04en
dc.identifier.issn15313492en
dc.identifier.doi10.3934/dcdsb.2014.19.1311en
dc.identifier.urihttp://hdl.handle.net/10754/564890en
dc.description.abstractIn this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.en
dc.description.sponsorshipMTW acknowledges financial support of the Austrian Science Foundation FWF via the Hertha Firnberg Project T456-N23. MDF is supported by the FP7-People Marie Curie CIG (Career Integration Grant) Diffusive Partial Differential Equations with Nonlocal Interaction in Biology and Social Sciences (DifNonLoc), by the 'Ramon y Cajal' sub-programme (MICINN-RYC) of the Spanish Ministry of Science and Innovation, Ref. RYC-2010-06412, and by the by the Ministerio de Ciencia e Innovacion, grant MTM2011-27739-C04-02. The authors thank the anonymous referees for useful comments to improve the manuscript.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.relation.urlhttp://arxiv.org/abs/arXiv:1304.5201v1en
dc.subjectCalculus of variationsen
dc.subjectMean field limiten
dc.subjectNumerical simulationsen
dc.subjectOptimal controlen
dc.subjectPedestrian dynamicsen
dc.titleMean field games with nonlinear mobilities in pedestrian dynamicsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalDiscrete and Continuous Dynamical Systems - Series Ben
dc.contributor.institutionInstitute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, 48149 Münstar, Germanyen
dc.contributor.institutionDepartment of Mathematical Sciences, University of Bath, 4W, 1.14, Claverton Down, Bath, BA2 7AY, United Kingdomen
dc.contributor.institutionDepartment of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austriaen
dc.identifier.arxividarXiv:1304.5201en
kaust.authorMarkowich, Peter A.en
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