The Queueing Maximal Availability Location Problem: A model for the siting of emergency vehicles

The Maximal Availability Location Problem (MALP) has been recently formulated as a probabilistic version of the maximal covering location problem. The added feature in MALP is that randomness into the availability of servers is considered. In MALP, though, it is assumed that the probabilities of different servers being busy are independent. In this paper, we utilize results from queuing theory to relax this assumption, obtaining a more realistic model for emergency systems: the Queueing MALP. We also consider in this model that travel times or distances along arcs of the network are random variables. We show here how to site limited numbers of emergency vehicles, such as ambulances, in such a way as to maximize the calls for service which have an ambulance available within a time or distance standard with reliability α – using a queueing theory model for server availability. We also propose some extensions to the basic model. Formulations are presented and computational experience is offered.