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The MX/M/1 queue with working breakdown

Published online by Cambridge University Press:  30 April 2014

Zaiming Liu  and
Yang Song
Yang Song
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha 410075, P.R. China. [email protected]
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Abstract

In this paper, we consider a batch arrival MX/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 MX/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.

Keywords

MX/M/1 queueworking breakdownprobability generating function (PGF)Laplace–Stieltjes transform (LST)waiting time distributionstochastic decomposition
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 3 , July 2014 , pp. 399 - 413
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

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