標題: ANALYSIS OF AN UNRELIABLE SERVER M-[x]/G/1 SYSTEM WITH A RANDOMIZED VACATION POLICY AND DELAYED REPAIR
作者: Ke, Jau-Chuan
Huang, Kai-Bin
工業工程與管理學系
Department of Industrial Engineering and Management
關鍵字: Batch-arrival vacation queue;Delayed repair;Randomized control;Reliability;Supplementary variable technique
公開日期: 1-一月-2010
摘要: This article examines an M-[x]/G/1 queueing system with a randomized vacation policy and at most J consecutive vacations. Whenever the system is empty, the server immediately takes a vacation. Upon returning from a vacation, the server will be immediately activated for service if there is at least one customer waiting in the queue. 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 at the end of the J th vacation, the server becomes idle in the system until at least one customer arrives at the queue. Assume that the server may suffer an unpredictable breakdown and the repair may be delayed. For such a system, we derive the distributions of some important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the initiation epoch of a busy period, the distributions of idle and busy periods, and reliability indices. Finally, a cost model is developed to determine the joint parameters (p, J) that correspond to minimum cost, and some numerical examples are presented for illustrative purpose.
URI: http://dx.doi.org/10.1080/15326341003756262
http://hdl.handle.net/11536/149995
ISSN: 1532-6349
DOI: 10.1080/15326341003756262
期刊: STOCHASTIC MODELS
Volume: 26
起始頁: 212
結束頁: 241
顯示於類別:期刊論文