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Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0002-6608-0715
2018 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 56, no 1, p. 434-455Article in journal (Refereed) Published
Abstract [en]

We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572–1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics Publications , 2018. Vol. 56, no 1, p. 434-455
Keywords [en]
Crowd aversion, Crowd dynamics, Interacting populations, Mean-field approximation, Mean-field type game, Optimal control
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-224585DOI: 10.1137/17M1119196ISI: 000426744900020Scopus ID: 2-s2.0-85043490666OAI: oai:DiVA.org:kth-224585DiVA, id: diva2:1191710
Funder
Swedish Research Council, 2016-04086
Note

QC 20180320

Available from: 2018-03-20 Created: 2018-03-20 Last updated: 2018-03-26Bibliographically approved

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Aurell, AlexanderDjehiche, Boualem

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Output format
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