The semi-markovian queue: theory and applications
The semi-markovian queue: theory and applications
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半马尔可夫队列：理论与应用
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
B. Sengupta
中科院分区：
文献类型：
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作者：
B. Sengupta
本文研究了一个先来先服务的单服务台半马尔可夫排队系统，其中到达和服务机制都是半马尔可夫过程。到达间隔时间和服务时间可能相互依赖，服务时间的边际分布被假定为相位型。对于这种排队，我们证明了等待时间、在系统中的时间和虚拟等待时间的分布都是矩阵指数分布。此外，这些矩阵指数分布具有相位型表示。对于到达间隔时间与服务时间无关的特殊情形，证明了队长分布是矩阵几何分布。对于这种特殊情况，我们证明了队长分布问题是等待时间分布问题的对偶，即，找到一个问题的解决方案，就能立即找到另一个问题的解决方案。我们表明，我们的方法是计算上可行的，并报告我们的数值经验。我们给出这样的队列出现自然的例子…
In this paper, we study a first-come-first-served single server semi-Markovian queue in which both the arrival and service mechanisms are semi-Markov processes. The interarrival time and service times may depend on one another and the marginal distribution of the service times is assumed to be phase-type. For this queue, we show that the distributions of waiting time, time in system and virtual waiting time are matrix-exponential. Further, these matrix-exponential distributions have phase-type representations. For the special case when the interarrival times are independent of the service times, we show that the queue length distribution is matrix-geometric. For this special case, we prove that the queue length distribution problem is the dual of the waiting time distribution problem, i.e., finding the solution of one problem immediately gives the solution of the other. We show that our methods are computationally feasible and report our numerical experience. We give Examples where such queues arise natur...