Narrow Results

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 is carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.

Particle diffusion is modified by the presence of barriers. In cells macro-molecules, behaving as obstacles, slow down the dynamics so that the mean-square displacement of molecules grows with time as a power law with exponent smaller than one. In different situations, such as grain and pedestrian dynamics, it can happen that an obstacle can accelerate the dynamics. In the framework of very basic models, we study the time needed by particles to cross a strip for different bulk dynamics and discuss the effect of obstacles. We find that in some regimes such a residence time is not monotonic with respect to the size and the position of the obstacles. We can then conclude that, even in very elementary systems where no interaction among particles is considered, obstacles can either slow down or accelerate the particle dynamics depending on their geometry and position.