Modelling of crowd motion in panic situation.
B. Maury, J. Venel
We propose a microscopic model for crowd motion. We are especially
interested in describing panic situations : people want to leave a
room, building, railway station or a plane, that may contain obstacles.
Our model rests on two principles. On the one hand, we define a
spontaneous velocity, which corresponds to the velocity
each individual would like to have in the absence of other people.
On the other hand, individuals (which are identified to rigid discs)
must obey a non-overlapping constraint. Those two principles lead us to
define the actual velocity field as the projection of the
velocity over the set of admissible velocities (regarding to the
non-overlapping constraints). The model takes the form of a
differential inclusion, for which well-posedness can be established by
means of recent abstract results in convex analysis.
The non-overlapping constraints are handled by means
multipliers that can be interpreted as pressure forces applied on each
individual by its neighbors. We propose a time discretization scheme
based on granular flow principles, which makes it possible to
the evacuation of thousands of highly-packed individuals.
of some typical situations will be presented.
We shall also propose a macroscopic version of this model, and present
the theoretical and modelling issues that it raises.