The discrete time Geom/Geom/1 queue with multiple working vacations

被引：29
|
作者：
Tian, Naishuo [1 ]
Ma, Zhanyou [1 ]
Liu, Mingxin [2 ]
机构：
[1] Yanshan Univ, Coll Sci, Qinhuangdao 066004, Hebei, Peoples R China
[2] Yanshan Univ, Coll Informat Sci & Engn, Qinhuangdao 066004, Hebei, Peoples R China
来源：
APPLIED MATHEMATICAL MODELLING | 2008年 / 32卷 / 12期
基金：
中国国家自然科学基金;
关键词：
discrete time queue; working vacation; matrix-geometric solution; busy cycle; stochastic decomposition;
D O I：
10.1016/j.apm.2007.10.005
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, we study a discrete time Geom/Geom/1 queue with multiple working vacations. Using the quasi birth and death chain and matrix-geometric solution method, we give distributions for the number of customers in system and the waiting time of a customer and their stochastic decomposition structures, and obtain distributions of the additional number of customers and additional delay. Furthermore, we derive the formulae of expected regular busy period and expected busy cycle. Finally, by numerical examples, we analyze the effect of the parameters on the expected queue length and sojourn time. (C) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：2941 / 2953
页数：13
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