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Behavior near walls...
Behavior near walls in the mean-field approach to crowd dynamics
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- Aurell, Alexander (author)
- KTH,Matematisk statistik
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- Djehiche, Boualem, 1962- (author)
- KTH,Matematisk statistik
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(creator_code:org_t)
- Society for Industrial & Applied Mathematics (SIAM), 2020
- 2020
- English.
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In: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 80:3, s. 1153-1174
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- This paper introduces a system of SDEs of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at and move along walls by means of sticky boundaries and boundary diffusion. As an alternative to Neumann-type boundary conditions, sticky boundaries and boundary diffusion have a "smoothing" effect on pedestrian motion. When these effects are active, the pedestrian paths are semimartingales with the first-variation part absolutely continuous with respect to the Lebesgue measure dt rather than an increasing process (which in general induces a measure singular with respect to dt) as is the case under Neumann boundary conditions. We show that the proposed mean-field model for pedestrian motion admits a unique weak solution and that it is possible to control the system in the weak sense, using a Pontryagin-type maximum principle. We also relate the mean-field type control problem to the social cost minimization in an interacting particle system. We study the novel model features numerically, and we confirm empirical findings on pedestrian crowd motion in congested corridors.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- pedestrian crowd modeling
- mean-field type control
- sticky boundary conditions
- boundary diffusion
Publication and Content Type
- ref (subject category)
- art (subject category)
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