Single Server Queueing-Location Models with Rejection

Abstract

This paper considers the problem of locating a single server on a network while explicitly accounting for queueing of calls for service. Calls from a node can either all be accepted or all be rejected by the service system. Two models are considered. In the first model a call can be rejected independent of the state of the system when the call arrives. In the second model, an arriving call can be rejected only if it finds the server busy. The queueing systems are analyzed for both models. A greedy heuristic is developed which, parametrically in the arrival rate of calls, determines the location of the server and the rejection strategies at nodes. Extreme case analysis with respect to the arrival rate is investigated. A numerical example illustrates our results. Our major observation is that the rejection strategies for calls are dependent on the arrival rate, and the choice of model.

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