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Discrete Gamma Approximation in Retrial Queue MMPP/M/1 Based on Moments Calculation

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Analytical and Computational Methods in Probability Theory (ACMPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10684))

Abstract

In the paper, the retrial queueing system of MMPP/M/1 type is considered. The process of the number of calls in the system is analyzed. The method for the approximate calculation of the first and the second moments is suggested. We propose the method of the discrete gamma approximation based on obtained moments. The numerical analysis of the obtained results for different values of the system parameters is provided. Comparison of the distributions obtained by simulation and the approximate ones is presented.

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Acknowledgments

The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008).

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Authors and Affiliations

  1. Tomsk State University, 36 Lenina ave., Tomsk, 634050, Russian Federation

    Ekaterina Fedorova, Anatoly Nazarov & Svetlana Paul

  2. Peoples’ Friendship University of Russia, 6 Miklukho-Maklaya st., Moscow, 117198, Russian Federation

    Ekaterina Fedorova & Anatoly Nazarov

Authors
  1. Ekaterina Fedorova
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  2. Anatoly Nazarov
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  3. Svetlana Paul
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Corresponding author

Correspondence to Ekaterina Fedorova .

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Editors and Affiliations

  1. Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Vladimir V. Rykov

  2. City University of Hong Kong, Hong Kong, Hong Kong

    Nozer D. Singpurwalla

  3. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    Andrey M. Zubkov

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Fedorova, E., Nazarov, A., Paul, S. (2017). Discrete Gamma Approximation in Retrial Queue MMPP/M/1 Based on Moments Calculation. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-71504-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71503-2

  • Online ISBN: 978-3-319-71504-9

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