Dimensionless Numbers Reveal Distinct Regimes in the Structure and Dynamics of Pedestrian Crowds

TL;DR

This paper introduces dimensionless Intrusion and Avoidance numbers to classify pedestrian crowd regimes, revealing distinct structural and dynamic behaviors similar to fluid flow classifications, and develops models specific to these regimes.

Contribution

It proposes novel dimensionless numbers for crowd dynamics classification and demonstrates their effectiveness in identifying distinct behavioral regimes.

Findings

Distinct crowd regimes characterized by structural signatures

Low Avoidance number regimes identified by distance metrics

Low Intrusion number regimes characterized by times-to-collision

Abstract

In fluid mechanics, dimensionless numbers like the Reynolds number help classify flows. We argue that such a classification is also relevant for crowd flows by putting forward the dimensionless Intrusion and Avoidance numbers.Using an extensive dataset, we show that these delineate regimes that are characterized by distinct structural signatures, best probed in terms of distances at low Avoidance number and times-to-collision at low Intrusion number.These findings prompt a perturbative expansion of the agent-based dynamics; the generic models thus obtained perform well in (and only in) the regime in which they were derived.