Computation of a near-optimal service policy for a single-server queue with homogeneous jobs

We present an algorithm for computing a near-optimal service policy for a single-server queueing system when the service cost is a convex function of the service time. The policy has state-dependent service times, and it includes the options to remove jobs from the system and to let the server be off. The system's semi-Markov decision model has infinite action sets for the positive states. We design a new tailor-made policy-iteration algorithm for computing a policy for which the long-run average cost is at most a positive tolerance above the minimum average cost. For any positive tolerance our algorithm computes the desired policy in a finite (and small) number of iterations. The number is five for the numerical example used in the paper to illustrate results obtained by the algorithm.