Pedestrians moving in dark: Balancing measures and playing games on lattices

TL;DR

This paper introduces two novel models for pedestrian movement in dark corridors, highlighting how group size impacts individual success in finding exits, with numerical illustrations and open questions.

Contribution

It presents two new modeling approaches—becker-Döring-type dynamics and probabilistic cellular automata—for pedestrian motion in obscured environments.

Findings

Larger groups may hinder individual exit success

Both models show limited knowledge affects group formation

Numerical solutions illustrate the models' behaviors

Abstract

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-D\"{o}ring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures.