Performance and cost analysis of GeomX/G/1 queue with exhaustive service rule and multiple vacations

被引：1

作者：

Ma, Zhanyou ^{[1
]}

Yue, Wuyi ^{[2
]}

Cui, Guanghong ^{[1
]}

Hao, Yong ^{[1
]}

机构：

[1] Yanshan Univ, Coll Sci, Dept Appl Math, Qinhuangdao, Peoples R China

[2] Konan Univ, Dept Intelligence & Informat, Kobe, Hyogo, Japan

来源：

OPTIMIZATION | 2015年 / 64卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Geom(X)/G/1 queue; multiple vacations; embedded Markov chain; exhaustive service rule; performance analysis;

D O I：

10.1080/02331934.2013.811663

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：

We present a new discrete-time Geom(X)/G/1 queueing model with multiple vacations. We obtain the Probability Generating Function (PGF) of the queue length by using the method of an embedded Markov chain, and give the mean of the queue length. Then we study the PGF of the waiting time based on the independence of the arrival process and the waiting time. And we derive the PGF of the busy period, and the probabilities for the system being in a busy state or in a vacation state. Moreover, we formulate a cost model in order to determine the optimal expected parameter of the system. Finally, we show some numerical results to compare the means of the queue length and the waiting time in special cases.

引用

页码：2511 / 2528

页数：18

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