Statistical fluctuations in pedestrian evacuation times and the effect of social contagion

TL;DR

This paper investigates the relationship between microscopic evacuation time statistics and overall distribution, introducing a cellular automaton model that incorporates social contagion effects, revealing significant correlations affecting safety assessments.

Contribution

It proposes a simple relation between microscopic and global evacuation time distributions and introduces a novel cellular automaton model with social contagion to test this relation.

Findings

The relation holds in the absence of correlations.

Social contagion can cause the relation to fail at high contagion levels.

Correlations significantly impact evacuation time statistics.

Abstract

Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models are now available, their calibration and test against empirical data are generally restricted to global, averaged quantities, the statistics compiled from the time series of individual escapes (" microscopic " statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the " microscopic " statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with novel features that afford a semi-quantitative reproduction of the experimental " microscopic " statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may dramatically fail at high contagion strengths, the latter being responsible for the emergence of strong correlations in the system. We conclude with comments on the potential practical relevance for safety science of calculations based on " microscopic " statistics.