The stationary tail asymptotics in the GI/G/1-type queue with countably many background states
The stationary tail asymptotics in the GI/G/1-type queue with countably many background states
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DOI：
10.1239/aap/1103662965
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发表时间：
2004-12
影响因子：
1.2
通讯作者：
M. Miyazawa;Yiqiang Q. Zhao
中科院分区：
文献类型：
--
作者：
M. Miyazawa;Yiqiang Q. Zhao
研究了具有可数背景状态空间的离散时间GI/G/1型排队系统平稳尾概率的渐近行为。这些概率以矩阵形式相对于背景状态空间，并示出为马尔可夫更新方程的解决方案。利用这个事实，我们考虑它们的衰变率。应用马尔可夫更新定理，它表明，某些合理的条件导致的几何衰减的尾概率的水平走向无穷大。我们使用一个离散时间的优先级队列与一个单一的服务器和两种类型的客户来验证这个结果。
We consider the asymptotic behaviour of the stationary tail probabilities in the discrete-time GI/G/1-type queue with countable background state space. These probabilities are presented in matrix form with respect to the background state space, and shown to be the solution of a Markov renewal equation. Using this fact, we consider their decay rates. Applying the Markov renewal theorem, it is shown that certain reasonable conditions lead to the geometric decay of the tail probabilities as the level goes to infinity. We exemplify this result using a discrete-time priority queue with a single server and two types of customer.