Abstract
In this paper, we analyze an M/M/1 queue with batch arrival and multiple working vacations. We describe the queueing model by a special GI/M/1 type Markov process with infinite phases, and by the matrix analytic method, we not only give the stationary queue length distribution of the model, but also obtain the exact number of vacations completed by the server.
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Acknowledgements
The author are grateful to the editor and the anonymous referees for their careful reading and invaluable comments and suggestions, which are helpful to improve the paper. This research was supported by the key technologies research and development program of Henan province (172102210242) and the foundation for university key research project of Henan province (16A110002). This research was completed when the author was a visiting scholar in School of Finance and Statistics, East China Normal University.
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Zhang, H. An analysis of the M\(^X\)/M/1 queue with multiple working vacations by GI/M/1 type Markov process. Acta Informatica 55, 613–624 (2018). https://doi.org/10.1007/s00236-018-0316-y
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DOI: https://doi.org/10.1007/s00236-018-0316-y