Mean field games with nonlinear mobilities in pedestrian dynamics

Journal article


Publication Details

Author(s): Burger M, Di Francesco M, Markowich PA, Wolfram MT
Journal: Discrete and Continuous Dynamical Systems-Series B
Publication year: 2014
Volume: 19
Pages range: 1311-1333
ISSN: 1531-3492
Language: English


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.


External institutions with authors

King Abdullah University of Science and Technology (KAUST) / جامعة الملك عبد الله للعلوم و التقنية
Medizinische Universität Wien
University of Bath
Westfälische Wilhelms-Universität (WWU) Münster


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.

BibTeX: 

Last updated on 2018-03-12 at 16:08