Free to move or trapped in your group: Mathematical modeling of information overload and coordination in crowded populations

TL;DR

This paper models pedestrian movement and evacuation in obscured spaces, highlighting how group size and information overload affect evacuation efficiency through probabilistic and computational methods.

Contribution

It introduces a novel combination of measure-based balance equations and probabilistic cellular automata to analyze crowd evacuation dynamics.

Findings

Larger groups improve evacuation rates in small populations.

Information redundancy in large groups can hinder evacuation in complex systems.

Computational resources are crucial for modeling incomplete information effects.

Abstract

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information -- the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non--redundant information is actually available to a substantial number of individuals. For complex social systems information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects are carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.