Origin of the correlations between exit times in pedestrian flows through a bottleneck

TL;DR

This paper investigates the statistical features of pedestrian flow through bottlenecks, revealing that correlations and burst patterns arise from simple mechanisms rather than complex interleaving, with implications for various particulate flows.

Contribution

The study introduces simple models that explain the origin of correlations and burst statistics in pedestrian flows, challenging previous assumptions about their causes.

Findings

Anticorrelations result from pedestrians crossing within short intervals, not zipper-like intercalation.

Burst size distributions are exponential unless the bottleneck is nearly congested, where power-law behavior emerges.

Mechanisms are general and applicable to other particulate flow systems.

Abstract

Robust statistical features have emerged from the microscopic analysis of dense pedestrian flows through a bottleneck, notably with respect to the time gaps between successive passages. We pinpoint the mechanisms at the origin of these features thanks to simple models that we develop and analyse quantitatively. We disprove the idea that anticorrelations between successive time gaps (i.e., an alternation between shorter ones and longer ones) are a hallmark of a zipper-like intercalation of pedestrian lines and show that they simply result from the possibility that pedestrians from distinct 'lines' or directions cross the bottleneck within a short time interval. A second feature concerns the bursts of escapes, i.e., egresses that come in fast succession. Despite the ubiquity of exponential distributions of burst sizes, entailed by a Poisson process, we argue that anomalous (power-law) statistics arise if the bottleneck is nearly congested, albeit only in a tiny portion of parameter space. The generality of the proposed mechanisms implies that similar statistical features should also be observed for other types of particulate flows.