The effect of different arrival rates on the N-policy of M/G/1 with serversetup

It is very important in many real-life systems to decide when the server sh ould start his service because frequent setups inevitably make the operatin g cost too high. Furthermore, today's systems are too intelligent for the i nput to be assumed as a simple homogenous Poisson process. In this paper, a n M/G/1 queue with general server setup time under a control policy is stud ied. We consider the case when the arrival rate varies according to the ser ver's status: idle, setup and busy states. We derive the distribution funct ion of the steady-state queue length, as well as the Laplace-Stieltjes tran sform of waiting time. For this model, the optimal N-value from which the s erver starts his setup is found by minimizing the total operation cost of t he system. We finally investigate the behavior of system operation cost and the optimal N for various arrival rates by a numerical study. (C) 1999 Els evier Science Inc. All rights reserved.