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A Single-server Discrete-time Retrial G-queue with Server Breakdowns and Repairs 被引量：1

A Single-server Discrete-time Retrial G-queue with Server Breakdowns and Repairs
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摘要 This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system. This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system.
作者 Jin-ting Wang Peng Zhang
机构地区 Department of Mathematics Qingdao Branch
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2009年第4期675-684,共10页 应用数学学报（英文版）
基金 Supported by the National Natural Science Foundation of China(No.10871020)
关键词 Discrete-time retrial queue G-queue Markov chain unreliable server Discrete-time retrial queue G-queue Markov chain unreliable server
分类号 TP271.8 [自动化与计算机技术—检测技术与自动化装置] TP368.5 [自动化与计算机技术—计算机系统结构]
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参考文献31

  • 1Alfa, A.S. Discrete-time analysis of the GI/G/1 system with Bernoulli retrials: An algorithmic approach. Annals of Operations Research, 141:51-66 (2006).
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  • 10Atencia, I., Moreno, P. A discrete-time Geo/G/1 retrial queue with general retrial time. Queueing Systems, 48:5-21 (2004).

引证文献1

Acta Mathematicae Applicatae Sinica
2009年 第4期

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