A simple Monte Carlo model for crowd dynamics

TL;DR

This paper presents a simple Monte Carlo simulation model for crowd dynamics using hard-disk agents, adaptable to various scenarios, validated through serving time statistics, and revealing differences between homogeneous and heterogeneous crowds.

Contribution

The paper introduces a flexible Monte Carlo approach for crowd simulation that can be tailored to different scenarios and provides insights into crowd behavior with homogeneous and heterogeneous agents.

Findings

Homogeneous crowds have predictable serving times.

Heterogeneous crowds show shorter serving times for smaller agents.

Model aligns with properties of non-equilibrium hard-disk fluids.

Abstract

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.