A Characterization of Waiting Time Performance Realizable by Single-Server Queues

In this paper we study the problem of designing scheduling strategies when the demand on the system is known and waiting time requirements are pre-specified. This important synthesis problem has received little attention in the literature, and contrasts with the common analytical approach to the study of service systems. This latter approach contributes only indirectly to the problem of finding satisfactory scheduling rules when the desired (or required) response-time performance is known in advance. Briefly, the model studied assumes a Markov queueing system with M (priority) classes of jobs. For each class, a desired mean waiting time is given in advance. Making use of a well known conservation law, we prove a necessary and sufficient condition for the existence of a scheduling strategy that achieves the desired performance. We also give a constructive procedure for checking the condition and, if a solution exists, a procedure for finding one such strategy. Our assumptions are discussed and the possibility of relaxing them is explored.