A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule
A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule
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DOI：
10.1016/j.cie.2012.08.015
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Jinbiao Wu;Z. Lian
中科院分区：
文献类型：
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作者：
Jinbiao Wu;Z. Lian
研究了具有负顾客和优先权的M/G/1重试排队系统，系统服从Bernoulli休假调度，服务台故障和修理。正顾客和负顾客的到达是两个独立的泊松过程。如果服务器在他们到达时处于空闲状态，积极的客户将立即获得服务。否则，它们可能以概率p加入优先队列，或者以互补概率p ′进入重试轨道。在忙碌的服务器上的故障由负客户的到达表示，负客户的到达导致正在服务的客户丢失。服务器在服务或维修完成后进行伯努利休假。假设服务器具有任意的修理时间和休假时间分布。利用李雅普诺夫函数得到了嵌入马尔可夫链遍历性的充分必要条件。应用补充变量法，我们得到了系统的稳定状态解，同时给出了系统的可靠度量。此外，我们还研究了随机分解律。此外，还讨论了一些特殊的情况。最后，数值分析了各种参数对系统性能的影响。
We consider an M/G/1 retrial queue with negative customers and priority under Bernoulli vacation schedule subject to the server breakdowns and repairs. Arrivals of both positive customers and negative customers are two independent Poisson processes. Positive customers receive service immediately if the server is idle upon their arrivals. Otherwise, they may either with probability p join the priority queue or with complementary probability p¯ enter a retrial orbit. A breakdown at the busy server is represented by the arrival of a negative customer which causes the the customer being in service to be lost. The server takes Bernoulli vacation after a service or a repair completion. It is assumed that the server has arbitrary repair time and vacation time distributions. With the help of Lyapunov functions we have obtained the necessary and sufficient condition for ergodicity of embedded Markov chain. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law. Besides, some special cases of interest are discussed. Finally, the effects of various parameters on the system performance are analyzed numerically.