Optimization of the T policy M/G/1 queue with server breakdowns and general startup times

Abstract

This paper investigates the T policy M/G/1 queue with server breakdowns, and startup times. Customers arrive at the system according to a Poisson process. Service times, repair times, and startup times are assumed to be generally distributed. The server is turned on after a fixed length of time T repeatedly until at least one customer is present in the waiting line. The server needs a startup time before starting the service. We analyze various system performance measures and develop the total expected cost function per unit time in which T is a decision variable. We determine the optimum threshold T* and derive analytical results for sensitivity investigations. The sensitivity analysis is particularly valuable to the system analyst when evaluating future conditions. We also present extensive numerical computation for illustration purpose. (c) 2008 Elsevier B.V. All rights reserved.