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Analysis of the BMAP/G/1 queue with gated service and adaptive vacations duration

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Abstract

We consider a BMAP/G/1 type queueing model with gated service and duration of vacations depending on how many times in turn the system was empty at the previous vacation completion moments. We compute stationary distributions of the queue length at the embedded moments (vacation completions) and at arbitrary time as well as of a customer waiting time. The results of our analysis can be useful for determining strategy of adaptive choosing duration of sleep periods, e.g., in mobile networks where power consumption is an important issue.

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Acknowledgments

The research is supported by the Russian Foundation for Basic Research (grant no. 14-07-90015) and the Belarusian Republican Foundation for Fundamental Research (grant no. F14R-126).

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030, Minsk, Belarus

    Alexander N. Dudin & Julia V. Sinjugina

  2. Institute of Control Sciences of Russian Academy of Sciences and Closed Corporation “Information and Networking Technologies”, Moscow, Russia

    Vladimir M. Vishnevsky

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  1. Alexander N. Dudin
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  2. Vladimir M. Vishnevsky
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  3. Julia V. Sinjugina
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Correspondence to Alexander N. Dudin.

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Dudin, A.N., Vishnevsky, V.M. & Sinjugina, J.V. Analysis of the BMAP/G/1 queue with gated service and adaptive vacations duration. Telecommun Syst 61, 403–415 (2016). https://doi.org/10.1007/s11235-014-9946-8

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  • DOI: https://doi.org/10.1007/s11235-014-9946-8

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