Stationary Analysis for the Bulk Input Geom[X]/Geom/1 Queue with Working Vacation
International journal of management science and engineering management(2009)
摘要
Abstract In this paper, we analyze a bulk input Geom[X]/Geom/1 queue with single working vacation. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived, from which we got the stochastic decomposition result for the PGF of the stationary queue size. It is important that we find the biparameter addition theorems of the conditional negative binomial distribution, with which we find the upper bound and the lower bound of the stationary waiting time in the moment generating function order. Furthermore, we gain the mean queue size and the upper bound and the lower bound of the mean waiting time. Finally, several numerical examples are presented.
更多查看译文
关键词
Geom([X])/ Geom/1 queue,bulk input,single working vacation,stochastic decomposition,the moment generating function order
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要