On optimal exhaustive policies for the M/G/1-queue

Given an M=G=1 queue controlled by an exhaustive policy P, we consider a (P+ )-policy consisting of turning the server on at a random time later than P. The objective is to obtain necessary and su cient conditions such that the (P+ )-policy are better than the P-policy. Under the in nite-horizon average-cost criterion, policies are compared when the costs assumed are linear. When the holding cost is the waiting time cost per unit time per customer, the optimality of the N -policy over, both the (N + )-policy and the D-policy is showed. We will also discuss on the di erent types of T -policies, single and multiple, establishing a relation between them, which is independent of the optimization criterion. c © 2000 Elsevier Science B.V. All rights reserved.