2. Microscopic model of fractional order for evacuation of crowds

In modeling of crowds of pedestrians using calculus of integer order, the distribution of time between interchanging opinions is assumed to satisfy a Gaussian distribution, while this assumption is not always satisfied in reality. Burst phenomenon which is commonly observed in decision-making process of human is also hard to be described using calculus of integer order. In the previous research, the dynamic decision-making process has been seldom considered. Modeling of the twoalternative decision-making process for evacuation of crowds of pedestrians from a bounded room has been firstly considered in this chapter using the framework of fractional calculus. Dynamic decision-making models of fractional order have been presented for symmetric interactions and asymmetric interactions, respectively. A stability analysis for asymmetric interactions has been studied using the technique of linearization. Finally, a collective decision-making process for asymmetric interactions is proved to depend on the initial distribution, while this is not the case for symmetric interactions. Future work based on the results of this chapter is also discussed.