Approximate Analysis of Optimal Operating Policies for a GI/G/1 Queueing System

Abstract

In this paper, applying a method of diffusion approximation, we consider optimal operating policies for a GI/G/1 queueing system with a removable server. The following costs are incurred in the system : a cost per unit time of keeping the server running, fixed costs for turning the server on or off, and a holding cost per customer in the system per unit time. The average cost rate is used as a criterion for optimality. By using a couple of diffusion processes that approximate the number of customers in the system, an explicit form of the average cost rate is derived. Furthermore, some sufficient conditions under which the optimal operating policy falls into specific forms are obtained. It is examined numerically how the boundary condition at the origin of the diffusion process effects the optimal operating policy and its cost.