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We present modeling strategies that describe the motion and interaction ofgroups of pedestrians in obscured spaces. We start off with an approach basedon balance equations in terms of measures and then we exploit the descriptivepower of a probabilistic cellular automaton model. Based on a variation of thesimple symmetric random walk on the square lattice, we test the interplaybetween population size and an interpersonal attraction parameter for theevacuation of confined and darkened spaces. We argue that information overloadand coordination costs associated with information processing in small groupsare two key processes that influence the evacuation rate. Our results show thatsubstantial computational resources are necessary to compensate for incompleteinformation -- the more individuals in (information processing) groups thehigher the exit rate for low population size. For simple social systems, it islikely that the individual representations are not redundant and large groupsizes ensure that this non--redundant information is actually available to asubstantial number of individuals. For complex social systems informationredundancy makes information evaluation and transfer inefficient and, as such,group size becomes a drawback rather than a benefit. The effect of group sizeson outgoing fluxes, evacuation times and wall effects are carefully studiedwith a Monte Carlo framework accounting also for the presence of an internalobstacle.

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