Volume 48, Number 3, July-September 2014
|Page(s)||399 - 413|
|Published online||30 April 2014|
The MX/M/1 queue with working breakdown
School of Mathematics and Statistics, Central South University, Changsha 410075, P.R. China
Received: 15 May 2013
Accepted: 24 February 2014
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.
Mathematics Subject Classification: 68M20 / 60K20 / 90B22
Key words: MX/M/1 queue / working breakdown / probability generating function (PGF) / Laplace–Stieltjes transform (LST) / waiting time distribution / stochastic decomposition
© EDP Sciences, ROADEF, SMAI, 2014
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