On a switch-over policy for controlling the workload in a queueing system with two constant service rates and fixed switch-over costs

Abstract

This paper considers a single-server system where jobs arrive in accordance with a Poisson process. Each job involves an amount of work which is known upon arrival and is sampled from an exponential distribution. The server has available two constant service rates 1 and 2 where rate 2 is faster than rate 1. The total work remaining to be processed in the system (= workload) is controlled by a switch-over policy which switches from rate 1 to rate 2 only when the workload exceeds the levely1 and switches from rate 2 to rate 1 only when the workload falls to the levely2 where 0⩽y2⩽y1. The costs of this system consist of a linear holding cost, a service-cost rate and fixed switch-over costs. The purpose of this paper is to derive an explicit expression for the average cost of this policy.