  In this paper we introduce a simple Monte Carlo method for simulating the
dynamics of a crowd. Within our model a collection of hard-disk agents is
subjected to a series of two-stage steps, implying (i) the displacement of one
specific agent followed by (ii) a rearrangement of the rest of the group
through a Monte Carlo dynamics. The rules for the combined steps are determined
by the specific setting of the granular flow, so that our scheme should be
easily adapted to describe crowd dynamics issues of many sorts, from stampedes
in panic scenarios to organized flow around obstacles or through bottlenecks.
We validate our scheme by computing the serving times statistics of a group of
agents crowding to be served around a desk. In the case of a size homogeneous
crowd, we recover intuitive results prompted by physical sense. However, as a
further illustration of our theoretical framework, we show that heterogeneous
systems display a less obvious behavior, as smaller agents feature shorter
serving times. Finally, we analyze our results in the light of known properties
of non-equilibrium hard-disk fluids and discuss general implications of our
model.
