OPTIMAL MULTISERVER STOCHASTIC SCHEDULING OF 2 INTERCONNECTED PRIORITY-QUEUES

A number of jobs on two interconnected queues are to be processed by m identical servers. The servers operate in parallel, so that every server can process any job. Jobs in queue i, i = 1, 2, incur an instantaneous holding cost C(i) during the time they remain in the system. The service time for jobs in queue i, denoted by X(i), is a random variable with a general distribution. The interconnection process is independent of the service process. We establish sufficient conditions on the service times, the holding costs and the interconnection process under which the non-preemptive scheduling strategy that gives priority to queue 1 minimizes the total expected alpha-discounted cost. We call this strategy Pl. We present counterexamples showing that if any of the sufficient conditions is not satisfied PI may not be optimal, and that the optimal policy for the single-server problem is not necessarily optimal for the multiserver problem.