標題: The performance measures and randomized optimization for an unreliable server M-[x]/G/1 vacation system
作者: Ke, Jau-Chuan
Huang, Kai-Bin
Pearn, Wen Lea
工業工程與管理學系
Department of Industrial Engineering and Management
關鍵字: Batch arrival queue;Randomized control;Server breakdown;Supplementary variable technique;Vacations;Reliability
公開日期: 1-Jul-2011
摘要: This paper examines an M-[x]/G/1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the Jth vacation, the server becomes idle in the system. Whenever one or more customers arrive at server idle state, the server immediately starts providing service for the arrivals. Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair time has a general distribution. For such a system, we derive the distributions of important system characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, the distributions of idle period, busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p*,J*) at a minimum cost, and some numerical examples are presented for illustrative purpose. (C) 2011 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.amc.2011.03.008
http://hdl.handle.net/11536/150307
ISSN: 0096-3003
DOI: 10.1016/j.amc.2011.03.008
期刊: APPLIED MATHEMATICS AND COMPUTATION
Volume: 217
起始頁: 8277
結束頁: 8290
Appears in Collections:Articles