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Asymptotic Analysis of Retrial Queueing System M/GI/1 with Collisions and Impatient Calls

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1109))

Abstract

In the paper, the retrial queueing system of M/GI/1 type with input Poison flow of events, collisions and impatient calls is considered. The delay time of calls in the orbit and the impatience time of calls in the orbit have exponential distribution. Service time on server is with any distribution function. Asymptotic analysis method is proposed for the solving problem of finding distribution of the number of calls in the orbit under a long delay of calls in orbit and long time patience of calls in the orbit condition. The theorem about the Gauss form of the asymptotic probability distribution of the number of calls in the orbit is formulated and proved. Numerical illustrations, results are also given.

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Acknowledgments

This work is financially supported by the Russian Foundation for Basic Research according to the research project No. 19-41-703002.

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Authors and Affiliations

  1. National Research Tomsk State University, Lenina Avenue, 36, 634050, Tomsk, Russia

    Elena Danilyuk, Svetlana Moiseeva & Anatoly Nazarov

Authors
  1. Elena Danilyuk
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  2. Svetlana Moiseeva
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  3. Anatoly Nazarov
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Corresponding author

Correspondence to Elena Danilyuk .

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Editors and Affiliations

  1. Faculty of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Alexander Moiseev

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Danilyuk, E., Moiseeva, S., Nazarov, A. (2019). Asymptotic Analysis of Retrial Queueing System M/GI/1 with Collisions and Impatient Calls. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2019. Communications in Computer and Information Science, vol 1109. Springer, Cham. https://doi.org/10.1007/978-3-030-33388-1_19

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  • DOI: https://doi.org/10.1007/978-3-030-33388-1_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33387-4

  • Online ISBN: 978-3-030-33388-1

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