Pergamon Computers ind. Engng Vol. 35, Nos 1-2, pp. 335-338, 1998 © 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain PIh S0360.8352(98)00088-6 0360-8352198 $19.00 + 0.00 A STEADY-STATE ANALYSIS OF OPTIMAL THRESHOLD POLICY WITH HETEROGENEOUS ARRIVALS TO THE M/G/1 QUEUE SUN HUR and SEUNG-JIN PAIK Department of Industrial Engineering, Hanyang University Ansan, 425-791, KOREA ABSTRACT An M/G/1 queue with general server setup time under a control policy is studied. We consider the case when the arrival rate varies according to the server's status: idle, setup and busy states. For this model, the optimal N-value from which the server starts his setup is found by minimizing the total operation cost of the system. © 1998ElsevierScienceLtd.All rights reserved. KEYWORDS N-policy; setup cost; nonhomogeneous Poisson; supplementary variables; arrival rates INTRODUCTION When operating a system it often needs a setup before the server starts his service. However, since a frequent server setup inevitably incurs cost, some kind of server operating policy is necessary. Among many control policies the N-policy is the most general. By N-policy we mean that the server does not start his service until there are N customers waiting in the queue. This policy is often used to avoid frequent setups. Minh (1988) studied an M/G/1 system with exponential server setup time to find the optimal N-policy. Medhi and Templeton (1992) extended Minh's result to the general setup time. Park et al. (1996)% model is unique in the sense that they considered the early setup : the server starts his setup when m < N customers are waiting. If there still are less than N customers when he finishes his setup, he waits until N customers are in the system. Almost all researches regarding M/G/1 N-policies including those mentioned above have studied under the assumption that the arrival rate of the customer into the system is fixed. In reality, however, the arrival rate may depend on the time, system state, or server's status. In this paper we find the optimal N-policy to minimize the system cost in the M/G/1 queueing system when the customers' arrival rate varies according to the server's status: idle, setup, or busy period. The customer's attitude to join the queue can be different according to whether the server is immediately available or not. For example, the arrival rate when the server is busy may be higher than when the server is idle since the customer expects he would be served very soon. This study generalizes the M/G/1 N-policy which is adequate for the case when the behavior of arriving customers depends on the server's states. 335