TY - JOUR
T1 - Mean field games with nonlinear mobilities in pedestrian dynamics
AU - Burger, Martin
AU - Di Francesco, Marco
AU - Markowich, Peter A.
AU - Wolfram, Marie-Therese
PY - 2014/7/1
Y1 - 2014/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84902192859&partnerID=8YFLogxK
UR - http://dx.doi.org/10.3934/dcdsb.2014.19.1311
U2 - 10.3934/dcdsb.2014.19.1311
DO - 10.3934/dcdsb.2014.19.1311
M3 - Article
AN - SCOPUS:84902192859
SN - 1531-3492
VL - 19
SP - 1311
EP - 1333
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 5
ER -