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Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs

Author

Listed:
  • Anatoly Nazarov

    (National Research Tomsk State University)

  • János Sztrik

    (University of Debrecen, Doctoral School of Informatics)

  • Anna Kvach

    (National Research Tomsk State University)

  • Ádám Tóth

    (University of Debrecen, Doctoral School of Informatics)

Abstract

This paper deals with a retrial queuing system with a finite number of sources and collision of the customers, where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. A significant difference of this system from the previous ones is that the service time is assumed to follow a general distribution while the server’s lifetime and repair time is supposed to be exponentially distributed. The considered system is investigated by the method of asymptotic analysis under the condition of an unlimited growing number of sources. As a result, it is proved that the limiting probability distribution of the number of customers in the system follows a Gaussian distribution with given parameters. The Gaussian approximation and the estimations obtained by stochastic simulations of the prelimit probability distribution are compared to each other and measured by the Kolmogorov distance. Several examples are treated and figures show the accuracy and area of applicability of the proposed asymptotic method.

Suggested Citation

  • Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2022. "Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1503-1518, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09870-w
    DOI: 10.1007/s11009-021-09870-w
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    References listed on IDEAS

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    1. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    2. Antonio Gómez-Corral & Tuan Phung-Duc, 2016. "Retrial queues and related models," Annals of Operations Research, Springer, vol. 247(1), pages 1-2, December.
    3. Velika I. Dragieva, 2014. "Number Of Retrials In A Finite Source Retrial Queue With Unreliable Server," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-23.
    4. Falin, G. I. & Artalejo, J. R., 1998. "A finite source retrial queue," European Journal of Operational Research, Elsevier, vol. 108(2), pages 409-424, July.
    5. Lyes Ikhlef & Ouiza Lekadir & Djamil Aïssani, 2016. "MRSPN analysis of Semi-Markovian finite source retrial queues," Annals of Operations Research, Springer, vol. 247(1), pages 141-167, December.
    6. Anatoly Nazarov & János Sztrik & Anna Kvach & Tamás Bérczes, 2019. "Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs," Annals of Operations Research, Springer, vol. 277(2), pages 213-229, June.
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    Cited by:

    1. Nikolaos Limnios & Bei Wu, 2025. "Diffusion Approximation of Loss Queueing Systems," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-5, March.

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