Locating an n-server facility in a stochastic environment
We consider a demand-responsive service system in which n mobile units (servers) are garaged at one facility. Service demands arrive in time as a homogeneous Poisson process, but are located over the service region according to an arbitrary probability law. Given a random service demand, either (1) a mobile unit is dispatched to the demand's location to provide on-scene service or (2) the demand is lost (i.e. it is handled by some back-up system). The resultant queueing system is an M/G/n loss system operating in steady state. The objective is to locate the garage facility so that the average cost of response is minimized, where the cost of response is a weighted sum of mean travel time to a random serviced demand and the cost of a lost demand, the weights being the respective probabilities of occurrence. We show that the optimum facility location reduces to Hakimi's well-known minisum location.
scientific article; zbMATH DE number 3984931