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| In the classical model of Hughes for crowd motion pedestrians seek to minimize their travel time to a-priori known destinations/exits, but try to avoid regions of high density. One of the basic assumptions is that the overall density of the crowd is known to every agent at every time.
We present results on a modification that includes localizing effects such as limited vision to a Hughes-type equation. The basic mechanism permits agents to perceive information on the current crowd density only in a local neighborhood, while taking assumptions on the density outside that region. We discuss the modelling aspects and consider both a microscopic and macroscopic perspective. As the suggested model leads to the problem of solving varying Hamilton-Jacobi equations depending on the agent's location, efficient numerical solvers that reduce computational costs are developed.
Our main object of study is the reduction of the overall performance of the crowd. We quantify and illustrate with numerical experiments, how the ability of the crowd to evacuate effectively is reduced by limiting the information available to every agent. |
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