Mean field games with nonlinear mobilities in pedestrian dynamics

Burger M, Di Francesco M, Markowich PA, Wolfram MT (2014)

Publication Language: English

Publication Type: Journal article

Publication year: 2014

Journal

Discrete and Continuous Dynamical Systems-Series B American Institute of Mathematical Sciences (AIMS)

Book Volume: 19

Pages Range: 1311-1333

Issue: 5

DOI: 10.3934/dcdsb.2014.19.1311

Abstract

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.

Authors with CRIS profile

Martin Burger

Involved external institutions

University of Bath GB United Kingdom (GB) Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) King Abdullah University of Science and Technology (KAUST) / جامعة الملك عبد الله للعلوم و التقنية SA Saudi Arabia (SA) Medizinische Universität Wien AT Austria (AT)

How to cite

APA:

Burger, M., Di Francesco, M., Markowich, P.A., & Wolfram, M.-T. (2014). Mean field games with nonlinear mobilities in pedestrian dynamics. Discrete and Continuous Dynamical Systems-Series B, 19, 1311-1333. https://dx.doi.org/10.3934/dcdsb.2014.19.1311

MLA:

Burger, Martin, et al. "Mean field games with nonlinear mobilities in pedestrian dynamics." Discrete and Continuous Dynamical Systems-Series B 19 (2014): 1311-1333.

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