On modelling the influence of group formations in a crowd

Abstract

Inspired by doubts from social scientists on the validity of computer models that see a crowd as a pure aggregation of individuals, we develop a mathematical model for group formation within crowds. It is based on a few simple characteristics. Most importantly, small groups stick together as they thread their way through a crowd. Additionally, groups have a tendency to walk abreast to ease communication. Through simulation, we establish that the occurrence of groups significantly impacts crowd movement, namely evacuation times. Further, we complement and validate the simulations by a small experiment: a classroom egress. The simulation results match the measurements qualitatively. We get a good quantitative match after calibrating the supposed desire to communicate while walking—and hence to walk abreast. We conclude that it is one of the crucial parameters to calibrate the group model against reality. While working on a mathematically complete model, a new gap between the mathematical modelling and the social sciences emerged: some model assumptions are based on the modeller's intuition rather than on sociological or psychological insight validated by the scientific community. We hope the findings—and resulting suggestions—will in return inspire new cooperation between the disciplines.

Acknowledgement

This work was partially funded by the German Federal Ministry of Education and Research through the priority programme Schutz und Rettung von Menschen within the project REPKA—Regional Evacuation: Planning, Control and Adaptation.

Notes

For a more detailed description, see Davidich & Köster (2010), Hartmann (2010), Köster et al. (2010) and Kneidl et al. (2010).

Free-flow velocity is the technical term used to describe the speed at which a person likes to walk when their path is free. It is the desired speed of an individual.

There is a small-order effect. We introduce round number as an additional explanatory variable in the regression model, β ₂ = 0.19, t(4) = 3.18, p = 0.03.

Again the order effect is small. With round number as an additional explanatory variable, β ₂ = 0.27, t(3) = –7.42, p = 0.005.