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Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs

Author

Listed:
  • Anatoly Nazarov

    (National Research Tomsk State University)

  • János Sztrik

    (University of Debrecen)

  • Anna Kvach

    (National Research Tomsk State University)

  • Tamás Bérczes

    (University of Debrecen)

Abstract

The aim of the present paper is to investigate a finite-source M/M/1 retrial queuing system with collision of the customers where the server is subjects to random breakdowns and repairs depending on whether it is idle or busy. An asymptotic method is applied under the condition that the number of sources tends to infinity while the primary request generation rate, retrial rate tend to zero and service rate, failure rates, repair rate are fixed. It is proved that in steady state the limiting distribution of the centered and normalized number of customers in the system (orbit and service) follows a normal law with given parameters. The novelty of this investigation is the introduction of failure and repair of the service. Approximations of prelimiting distribution by asymptotic one are obtained and several illustrative examples show the accuracy and range of applicability of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:277:y:2019:i:2:d:10.1007_s10479-018-2894-z
    DOI: 10.1007/s10479-018-2894-z
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    References listed on IDEAS

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    1. B. Krishna Kumar & A. Thanikachalam & V. Kanakasabapathi & R. Rukmani, 2016. "Performance analysis of a multiprogramming–multiprocessor retrial queueing system with orderly reattempts," Annals of Operations Research, Springer, vol. 247(1), pages 319-364, December.
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    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.
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    Cited by:

    1. Chiu, Singa Wang & Chen, Hui-Cun & Wu, Hua-Yao & Chiu, Yuan-Shyi Peter, 2020. "A hybrid finite production rate system featuring random breakdown and rework," Operations Research Perspectives, Elsevier, vol. 7(C).
    2. Wang, Kuo-Hsiung & Wu, Chia-Huang & Yen, Tseng-Chang, 2022. "Comparative cost-benefit analysis of four retrial systems with preventive maintenance and unreliable service station," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    3. 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.
    4. Wu, Chia-Huang & Yen, Tseng-Chang & Wang, Kuo-Hsiung, 2021. "Availability and Comparison of Four Retrial Systems with Imperfect Coverage and General Repair Times," Reliability Engineering and System Safety, Elsevier, vol. 212(C).

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