• 论文 •

### 基于单重工作休假的离散时间排队稳态分析

1. 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

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

1. College of Science, Yanshan University, Qinhuangdao 066004
• Received:2010-01-12 Revised:2010-10-10 Online:2010-12-25 Published:2010-12-25

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.

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