Optimal location problem for urban emergency vehicles with continuous-time Markov chain

In this paper, we consider the optimal location problem for urban emergency vehicles. Examples of urban emergency vehicles are ambulances, police cars, etc. Emergency vehicles stand by the base until a service demand occurs. And if a service demand occurs, they move to give a service from its base to the demanded site. There are at least two important factors for performing effective services, i.e., 1) the location of bases for emergency vehicles until a service demand occurs, and 2) the number of the emergency vehicles stored there. We apply a continuous-time Markov chain to this problem, and propose a model for determining location of bases for emergency vehicles, and the number of the emergency vehicles deployed there. This model handles appropriately the mutual cooperation among emergency vehicles on congested situation, the assignment of the optimal emergency vehicles in each system state, and various service times. We apply this model to the emergency system of Seto city, Aichi, and evaluate its practicality.