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The MX/M/1 queue with working breakdown

Zaiming Liu;  Yang Song — 2014

RAIRO - Operations Research - Recherche Opérationnelle

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

M/M/1 retrial queue with collisions and working vacation interruption under N-policy

Li Tao;  Zaiming Liu;  Zhizhong Wang — 2012

RAIRO - Operations Research - Recherche Opérationnelle

Consider an M/M/1 retrial queue with collisions and working vacation interruption under N-policy. We use a quasi birth and death process to describe the considered system and derive a condition for the stability of the model. Using the matrix-analytic method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, some numerical examples are presented.

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