On a BMAP/G/1 G-queue with setup times and multiple vacations |
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| Authors: | Yi Peng Xiang-qun Yang |
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| Institution: | Yi PENG 1,Xiang-qun YANG 2 1 School of Mathematical Science and Computing Technology,Central South University,Changsha 410075,Hunan,China 2 College of Mathematics and Computer Science,Hunan Normal University,Changsha 410081,China |
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| Abstract: | In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and
negative customers follow a batch Markovian arrival process (BMAP) and Markovian arrival process (MAP) respectively. The arrival
of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation
as soon as the system empties and is allowed to take repeated (multiple) vacations. By using the supplementary variables method
and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on
the renewal theory. |
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| Keywords: | G-queues batch Markovian arrival process(BMAP) setup times multiple vacations censoring technique Markov chains |
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