Optimal multi-server stochastic scheduling of two interconnected priority queues

Summary form only given, as follows. 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 nonpreemptive scheduling strategy that gives priority to queue 1 minimizes the total expected α-discounted cost. We call this strategy P_i. We present counterexamples showing that if any of the sufficient conditions is not satisfied P₁ may not be optimal, and that the optimal policy for the single-server problem is not necessarily optimal for the multiserver problem