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Analysis of the finite source MAP/PH/N retrial G-queue operating in a random environment

机译:随机环境中运行的有限源MAP / PH / N重试G队列分析

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Finite source retrial G-queues are good mathematical models of communication systems and networks, so their investigation is important for theory and applications. In this paper, we analyze the MAP/PH/N retrial queue with finite number of sources and MAP arrivals of negative customers operating in a finite state Markovian random environment. The arrival of a negative customer with equal probability goes to any busy server to remove the customer being in service. The multi-dimensional Markov chain describing the behavior of the system is investigated. The algorithms for calculating the stationary state probabilities are elaborated. Main performance measures are obtained. Illustrative numerical examples are presented.
机译:有限源重试G队列是通信系统和网络的良好数学模型,因此对其进行研究对于理论和应用很重要。在本文中,我们分析了在有限状态马尔可夫随机环境中运行的,具有有限数量的来源和负面客户的MAP到达的MAP / PH / N重试队列。否定客户到达的可能性相同,它将去往任何繁忙的服务器,以除去正在使用的客户。研究了描述系统行为的多维马尔可夫链。阐述了计算稳态概率的算法。获得了主要的性能指标。给出了说明性的数值示例。

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