A mathematical model of the evacuation of a crowd from bounded domains is derived by a hybrid approach with kinetic and macro-features. Interactions at the micro-scale, which modify the velocity direction, are modeled by using tools of game theory and are transferred to the dynamics of collective behaviors. The velocity modulus is assumed to depend on the local density. The modeling approach considers dynamics caused by interactions of pedestrians not only with all the other pedestrians, but also with the geometry of the domain, such as walls and exits. Interactions with the boundary of the domain are non-local and described by games. Numerical simulations are developed to study evacuation time depending on the size of the exit zone, on the initial distribution of the crowd and on a parameter which weighs the unconscious attraction of the stream and the search for less crowded walking directions.

A kinetic theory approach to the dynamics of crowd evacuation from bounded domains / Agnelli, J.P.; Colasuonno, F.; Knopoff, D.. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 25:1(2015), pp. 109-129. [10.1142/S0218202515500049]

A kinetic theory approach to the dynamics of crowd evacuation from bounded domains

COLASUONNO, FRANCESCA;
2015

Abstract

A mathematical model of the evacuation of a crowd from bounded domains is derived by a hybrid approach with kinetic and macro-features. Interactions at the micro-scale, which modify the velocity direction, are modeled by using tools of game theory and are transferred to the dynamics of collective behaviors. The velocity modulus is assumed to depend on the local density. The modeling approach considers dynamics caused by interactions of pedestrians not only with all the other pedestrians, but also with the geometry of the domain, such as walls and exits. Interactions with the boundary of the domain are non-local and described by games. Numerical simulations are developed to study evacuation time depending on the size of the exit zone, on the initial distribution of the crowd and on a parameter which weighs the unconscious attraction of the stream and the search for less crowded walking directions.
2015
A kinetic theory approach to the dynamics of crowd evacuation from bounded domains / Agnelli, J.P.; Colasuonno, F.; Knopoff, D.. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 25:1(2015), pp. 109-129. [10.1142/S0218202515500049]
Agnelli, J.P.; Colasuonno, F.; Knopoff, D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/581765
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