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

Abstract

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: (i) a Becker-Döring-type dynamics and (ii) a probabilistic cellular automaton model. In both models the group formation is a¿ected 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 ¿nd the exit of the corridor. Although being of mathematically di¿erent 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 e¿ect numerically by solving both model systems. Finally we list some of our main open questions and conjectures