The negative dependence of evacuation time on group size under a binding mechanism

This paper initiates the analysis of the relation between evacuation time and group size by applying an extended floor field cellular automaton model. Agents with various speeds, a group structure containing leaders and followers, and a dynamic field dependent on local population density are implemented all together in the model. Most importantly, a complete binding mechanism which includes leaders waiting for followers is brought up for the first time. A counterintuitive negative relation between evacuation time and group size is discovered in simulations. An entropy like quantity, namely the mixing index, is constructed to analyze the cause of that relation. It is found that under the binding mechanism, the higher degree of group mixing, the longer the evacuation time will be. Moreover, through a constant scale transformation, it is shown that the mixing index can be a key indicator that contains useful information about the evacuation system.