A CLASS OF NONLOCAL MODELS FOR PEDESTRIAN TRAFFIC
By Rinaldo M. Colombo, Mauro Garavello, Magali L'ecureux-Mercier. 2011
222 citations recorded by the source corpus.
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.
Subfields: Control and Systems Engineering, Ocean Engineering, Transportation
View Paper: https://www.semanticscholar.org/paper/0a0b330498283ab23a67f6f03c81675034ec094d
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In Control and Systems Engineering
In Ocean Engineering
In Transportation
Citations in the corpus
- Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel (2018, background): “Unlike similar non-local equations [2, 3, 6–8, 12, 20], these models are characterized by the presence of an anisotropic discontinuous kernel, which makes general theoretical results [1–3] inapplicable as such.”