Assigning a single server to inhomogeneous queues with switching costs

Abstract

In this paper we study the preemptive assignment of a single server to two queues. Customers arrive at both queues according to Poisson processes, and all service times are exponential, but with rates depending on the queues. The costs to be minimized consist of both holding costs and switching costs. The limiting behavior of the switching curve is studied, resulting in a good threshold policy. Numerical results are included to illustrate the complexity of the optimal policy and to compare the optimal policy with the threshold policy.