Optimal Control of the M/G/1 Queueing System with Removable Server-Linear and Non-Linear Holding Cost Function.

摘要

This report considers the M/G/1 queueing system with removable server. The cases of linear and non-linear customer holding cost functions are both considered. Non-instantaneous start-up times are allowed. The problem is to find an optimal policy for turning the server on and off. The optimality criteria considered are the average cost criterion, the undiscounted cost criterion and the discounted cost criterion. A certain class of simple policies, the hysteretic policies, is considered. Natural hysteretic policies and non-degenerate hysteretic policies are introduced. It is shown that there is a natural hysteretic policy which is average optimal, and that if the start-up times are instantaneous or the holding cost function convex, then there is a natural hysteretic policy which is undiscounted optimal. When discounting is used, the results are not as strong, except for the case where the holding cost function is linear. For the non-linear case we still obtain certain fairly weak sufficient conditions for a natural hysteretic policy to be optimal. (Author)