THE MX/M/1 QUEUE WITH WORKING BREAKDOWN

被引：18

作者：

Liu, Zaiming ^{[1
]}

Song, Yang ^{[1
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China

来源：

RAIRO-OPERATIONS RESEARCH | 2014年 / 48卷 / 03期

基金：

中国国家自然科学基金;

关键词：

M-X/M/1; queue; working breakdown; probability generating function (PGF); Laplace-Stieltjes transform (LST); waiting time distribution; stochastic decomposition; RETRIAL QUEUE;

D O I：

10.1051/ro/2014014

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 consider a batch arrival M-X/M/1 queue model with working breakdown. The server may be subject to a service breakdown when it is busy, rather than completely stoping service, it will decrease its service rate. For this model, we analyze a two-dimensional Markov chain and give its quasi upper triangle transition probability matrix. Under the system stability condition, we derive the probability generating function (PGF) of the stationary queue length, and then obtain its stochastic decomposition, which shows the relationship with that of the classical M-X/M/1 queue without vacation or breakdown. Besides, we also give the Laplace-Stieltjes transform (LST) of the stationary waiting time distribution of an arbitrary customer in a batch. Finally, some numerical examples are given to illustrate the effect of the parameters on the system performance measures.

引用

下载

页码：399 / 413

页数：15

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