Stationary analysis for the bulk input Geom([X])/Geom/1 queue with working vacation

被引：2
|
作者：
Xu, Xiuli [1 ]
Liu, Chunping [1 ]
Lu, Guoyun [1 ]
Zhao, Xiaohua [1 ]
机构：
[1] Yanshan Univ, Coll Sci, Qinhuangdao 066004, Peoples R China
来源：
INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE AND ENGINEERING MANAGEMENT | 2009年 / 4卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Geom([X])/ Geom/1 queue; bulk input; single working vacation; stochastic decomposition; the moment generating function order;
D O I：
10.1080/17509653.2009.10671067
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
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
引用
收藏
页码：118 / 128
页数：11
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