We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Specific models are presented and their qualitative properties are shown through numerical integrations. In particular, the present model accounts for the possibility of reducing the exit time from a room by carefully positioning obstacles that direct the crowd flow. © 2012 World Scientific Publishing Company.

Colombo, R., Garavello, M., Lécureux Mercier, M. (2012). A class of nonlocal models for pedestrian traffic. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 22(4), 1150023 [10.1142/S0218202511500230].

A class of nonlocal models for pedestrian traffic

GARAVELLO, MAURO;
2012

Abstract

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Specific models are presented and their qualitative properties are shown through numerical integrations. In particular, the present model accounts for the possibility of reducing the exit time from a room by carefully positioning obstacles that direct the crowd flow. © 2012 World Scientific Publishing Company.
Articolo in rivista - Articolo scientifico
nonlocal conservation laws, pedestrian models
English
2012
22
4
1150023
none
Colombo, R., Garavello, M., Lécureux Mercier, M. (2012). A class of nonlocal models for pedestrian traffic. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 22(4), 1150023 [10.1142/S0218202511500230].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/37045
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