基于单重工作休假的离散时间排队稳态分析

doi:10.12341/jssms09434

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (12): 1613-1621.DOI: 10.12341/jssms09434

基于单重工作休假的离散时间排队稳态分析

徐秀丽, 卢国云, 李沛, 曹学云

燕山大学理学院, 秦皇岛 066004

收稿日期:2010-01-12 修回日期:2010-10-10 出版日期:2010-12-25 发布日期:2010-12-25

PDF ( 557 ) 引用被引次数 ( 13 )

徐秀丽;卢国云;李沛;曹学云. 基于单重工作休假的离散时间排队稳态分析[J]. 系统科学与数学, 2010, 30(12): 1613-1621.

XU Xiuli;LU Guoyun;LI Pei;CAO Xueyun. Stationary Analysis of the Discrete Time Queue Based on the Single Working Vacation[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(12): 1613-1621.

Stationary Analysis of the Discrete Time Queue Based on the Single Working Vacation

XU Xiuli, LU Guoyun, LI Pei, CAO Xueyun

College of Science, Yanshan University, Qinhuangdao 066004

Received:2010-01-12 Revised:2010-10-10 Online:2010-12-25 Published:2010-12-25

详细地分析了一个单重工作休假的离散时间Geom/G/1排队系统.首先,构造二维嵌入马尔可夫链,得到其M/G/1型转移概率矩阵.其次,利用矩阵分析的方法,导出了稳态队长的概率分布,进一步得到稳态队长的随机分解结果和平均队长公式. 最后, 给出稳态等待时间的随机分解结构及其平均等待时间公式.

关键词： Geom/G/1排队, 单重工作休假, 概率母函数(PGF), 随机分解.

This paper is concerned with a discrete time Geom/G/1 queue with single
working vacation. Firstly, a two-dimensional embedded Markov chain is stablished and its transition probability matrix is obtained. By using the matrix analysis method, the probability distribution of the stationary queue size is derived. Furthermore, the stochastic decomposition structure of the stationary queue size and the expression of mean queue size are given. Finally, the PGF of the stationary waiting time and mean waiting time are obtained.

Key words: Geom/G/1 queue, single working vacation, probability generating function(PGF), stochastic decomposition.

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