A single‐server priority queueing‐location model

This paper considers the problem of locating a single server on a network, relaxing the assumption that the server is always available for service, and explicitly accounting for queueing. The resulting queueing‐location model allows for an arbitrary number of priority classes. Properties of the objective function are developed and algorithms presented for obtaining the optimal location on tree and cyclic networks. Sensitivity analysis with respect to the average arrival rate of calls is investigated. A numerical example is presented to illustrate the results of this paper. The major conclusions of the paper include: (a) the optimal location need not be at a node of the network, (b) the optimal location changes as a function of the arrival rate of calls into the system, (c) the optimal location is usually different from that obtained by grouping all calls into one priority class.