| GI/G/1排队系统的几种收敛速度 |
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| 引用本文： | 李晓花,侯振挺.GI/G/1排队系统的几种收敛速度[J].应用数学学报,2011,34(1). |
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| 作者姓名： | 李晓花 侯振挺 |
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| 作者单位： | 1. 北京邮电大学理学院,北京,100876
2. 中南大学数学学院概率统计研究所,长沙,410075 |
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| 基金项目： | 中央高校基本科研业务费资助项目 |
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| 摘 要： | 对随机模型,可以从不同角度研究其稳定性,一种是研究其转移概率函数趋向于平稳分布的速度,即各种遍历性;另一种是研究平稳分布的尾部衰减速度.本文从这两个方面着手,找它们之间的关系,对GI/G/1排队系统,给出等待时间列几何遍历、平稳分布轻尾与服务时间分布轻尾三者等价,l-遍历、平稳分布的尾部(l-1)-阶衰减与服务时间分布的尾部l-阶衰减三者等价,最后证明出等待时间列不是强遍历.
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| 关 键 词： | 排队系统 遍历性 几何遍历性 l-遍历性 轻尾 |
Several Types of Convergence Rates of the GI/G/1 Queueing System |
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| LI XIAOHUA,HOU ZHENTING.Several Types of Convergence Rates of the GI/G/1 Queueing System[J].Acta Mathematicae Applicatae Sinica,2011,34(1). |
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| Authors: | LI XIAOHUA HOU ZHENTING |
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| Institution: | LI XIAOHUA (School of Science,Beijing University of Posts and Telecommunications,Beijing 100876) HOU ZHENTING (School of Mathematics,Central South University,Changsha 410075) |
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| Abstract: | For stochastic models,ergodicity and the decay rate of stationary distribution in tail are two fundamental issues.They are usually studied separately since their concepts are obviously different.In this paper,we study the waiting time process of GI/G/1 queuing system in the two aspects.We shall give that geometric ergodicity,the geometric decay of stationary distribution in tail,and the geometric decay of the service distribution in tail are equivalent.Then we shall prove that l-ergodicity,(l- 1)-th declay ... |
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| Keywords: | queueing system ergodicity geometric ergodicity l-ergodicity light-tailed |
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