tailieunhanh - The optimal control in batch arrival queue with server vacations, startup and breakdowns

This paper studies the N policy M[x]/G/1 queue with server vacations, startup and breakdowns, where arrivals form a compound Poisson process and service times are generally distributed. The server is turned off and takes a vacation whenever the system is empty. | Yugoslav Journal of Operations Research 14 (2004), Number 1, 41-55 THE OPTIMAL CONTROL IN BATCH ARRIVAL QUEUE WITH SERVER VACATIONS, STARTUP AND BREAKDOWNS Jau-CHUAN KE* National Taichung Institute of Technology Taichung 404, Taiwan, . Received: January 2003 / Accepted: January 2004 Abstract: This paper studies the N policy M[x]/G/1 queue with server vacations; startup and breakdowns, where arrivals form a compound Poisson process and service times are generally distributed. The server is turned off and takes a vacation whenever the system is empty. If the number of customers waiting in the system at the instant of a vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N customers in the system, he is immediately turned on and requires a startup time before providing the service until the system is empty again. It is assumed that the server breaks down according to a Poisson process whose repair time has a general distribution. The system characteristics of such a model are analyzed and the total expected cost function per unit time is developed to determine the optimal threshold of N at a minimum cost. Keywords: Breakdowns, cost model, queue, startup, vacation. 1. INTRODUCTION We consider an M[x]/G/1 queuing system in which the server operates N policy and is typically a subject to unpredictable breakdowns. The server leaves for a vacation of random length whenever the system becomes empty. At the end of a vacation, the server inspects the system and decides whether to take a vacation, or to take a general startup time. The server immediately starts serving the waiting customers whenever he completes his startup. * Jau-Chuan Ke. Email: jauchuan@. Postal address: Department of Statistics, National Taichung Institute of Technology, No. 129, Sec. 3, Sanmin Rd., Taichung 404, Taiwan, . 42 . Ke / The Optimal Control in Batch Arrival Queue Queuing systems with