On the optimality of a switch-over policy for controlling the queue size in an M/G/1 queue with variable service rate

Abstract

This paper considers an M/G/1 queue in which a finite number of service types are available for controlling the queue size. There is a linear holding cost, a service cost rate, and a fixed reward for each customer served. The nurpose of this paper is to show that under the assumption of stochastically ordered service times there is an average cost optimal stationary policy having the property that the service type used is a non-decreasing function of the queue size.