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Peng, Yi; Yang, Xiang-Qun

On a BMAP/G/1 G-queue with setup times and multiple vacations. (English) Zbl 1262.60088

Acta Math. Appl. Sin., Engl. Ser. 27, No. 4, 625-638 (2011).
Summary: We consider a BMAP/G/1 G-queue with setup times and multiple vacations. The arrivals of positive customers and negative customers follow a batch Markovian arrival process (BMAP) and a 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.

Cited in 5 Documents

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research

Keywords:

G-queues; batch Markovian arrival process (BMAP); setup times; multiple vacations; censoring technique; Markov chains
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References:

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