Mean field games with nonlinear mobilities in pedestrian dynamics

Martin Burger, Marco Di Francesco, Peter A. Markowich, Marie-Therese Wolfram

Research output: Contribution to journalArticlepeer-review

85 Citations (SciVal)


In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Original languageEnglish
Pages (from-to)1311-1333
Number of pages23
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number5
Publication statusPublished - 1 Jul 2014


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