On the Optimal Control of Two Queues with Server Setup Times and its Analysis

AblJract Two queues are fed by independent, time-homogeneous Poisson arrival processes. One server is available to handle both. All service-durations, in both queues, are 'drawn independently from the sarpe distril?uUon. A ~etup time is. incurred whenever the server moves (switches) from one queue to the other. We prove that in order to minimize the sum of discounted setup charges and holding costs, assumed linear in queue length and having the same rate at the two queues, the service ~t each queue should be exhaustive. A "threshold policy" is defined as a policy'under which the server switches (from an empty queue) only when the the other reaches a critical size. It is shown to be a likely candidate for the optimal policy, both for the discounted version and for the long-time average crit~rion. " The steady-state performance bf this polic~ (undeT somewhat more general distributional assumptions) and the optimal thr~sliolds are determined for a humber of cases.