A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation
A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation
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DOI：
10.1080/02331934.2011.579966
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发表时间：
2013-02
期刊：
影响因子：
2.2
通讯作者：
J. Ke;Chia-Huang Wu;W. Pearn
中科院分区：
文献类型：
--
作者：
J. Ke;Chia-Huang Wu;W. Pearn
本文研究了单重休假策略下具有Bernoulli休假的M/M/c重试排队系统。当一个到达的客户找到一个免费的服务器，客户立即接受服务;否则，客户将进入一个轨道。在服务器完成服务之后，服务器可能会休假或变得空闲（等待下一个到达的重试客户）。再审制度被分析为一个准生与死的过程。得到了系统平衡的充要条件。导出了计算速率矩阵和平稳概率的公式。给出了系统性能指标的显式封闭形式。建立了一个成本模型，以确定服务器数量、服务率和休假率的最优值，使单位时间的总期望成本最小。数值例子来证明这种优化方法。研究了代价模型中各参数对系统性能的影响。
In this study, we consider an M/M/c retrial queue with Bernoulli vacation under a single vacation policy. When an arrived customer finds a free server, the customer receives the service immediately; otherwise the customer would enter into an orbit. After the server completes the service, the server may go on a vacation or become idle (waiting for the next arriving, retrying customer). The retrial system is analysed as a quasi-birth-and-death process. The sufficient and necessary condition of system equilibrium is obtained. The formulae for computing the rate matrix and stationary probabilities are derived. The explicit close forms for system performance measures are developed. A cost model is constructed to determine the optimal values of the number of servers, service rate, and vacation rate for minimizing the total expected cost per unit time. Numerical examples are given to demonstrate this optimization approach. The effects of various parameters in the cost model on system performance are investigated.