A CLASS OF NONLOCAL MODELS FOR PEDESTRIAN TRAFFIC

Rinaldo M. Colombo · Mauro Garavello · Magali Lécureux-Mercier

190 citations0/0 files storedMathematical Models and Methods in Applied Sciences

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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.

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References

2002A continuum theory for the flow of pedestrians 2002Pedestrian and evacuation dynamics 2003Pedestrian route-choice and activity scheduling theory and models 2002Simulation of pedestrian crowds in normal and evacuation situations 2002T HE F LOW OF H UMAN C ROWDS 2009Pedestrian, Crowd and Evacuation Dynamics 2011On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives 2003Simulation of pedestrian flows by optimal control and differential games

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2014Mean field games with nonlinear mobilities in pedestrian dynamics 2012Nonlocal Crowd Dynamics Models for Several Populations

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