Skip to main content
SpringerLink
Log in

M/M/1 Retrial Queueing System with Variable Service Rate

  • Published:
Ukrainian Mathematical Journal Aims and scope

We consider a queueing system of the M/M/1 type with repeated claims in the case where the service rate depends on the loading of the system, i.e., on the number of claims in the queue waiting for service. We establish the existence conditions and the formulas for the ergodic distribution of the number of claims in the system with bounded and unbounded queues of repeated claims.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. R. Artalejo and A. Gomes-Corral, Retrial Queueing Systems. A Computational Approach, Springer, Berlin (2008).

    Book  Google Scholar 

  2. G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman & Hall, London (1997).

    Book  Google Scholar 

  3. V. V. Anisimov and J. R. Artalejo, “Analysis of Markov multiserver retrial queues with negative arrivals,” Queueing Syst., 39, 157–182 (2001).

    Article  MathSciNet  Google Scholar 

  4. E. A. Lebedev, I. A. Makushenko, H. V. Livinska, and I. Ya. Usar, “On steady-state analysis of [M|M|m|m+n]-type retrial queueing systems,” Inform. Technol. Math. Model., Queueing Theory Appl., Comm. Comput. Inform. Sci., 800, 133–146 (2017).

    MATH  Google Scholar 

  5. D. Gross, J. F. Shortle, J. M. Thompson, and C. M. Harris, Fundamentals of Queueing Theory, Wiley, New Jersey (2008).

    Book  Google Scholar 

  6. A. Economu and S. Kanta, “Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs,” Oper. Res. Lett., 36, 696–699 (2008).

    Article  MathSciNet  Google Scholar 

  7. V. I. Klimenok, “Optimization of dynamic control over the conditions of operation of the information and computational systems with repeated calls,” Avtomat. Vychisl. Tekh., No. 1, 25–30 (1990).

  8. X. Zhang, J. Wang, and Q. Ma, “Optimal design for a retrial queueing system with state-dependent service rate,” J. Systems Sci. Complexity, 30, 883–900 (2017).

    Article  MathSciNet  Google Scholar 

  9. J. Warland, An Introduction to Queueing Networks, New Jersey, Prentice Hall (1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Silesian University of Technology, Gliwice, Poland

    M. S. Bratiichuk

  2. T. Shevchenko Kyiv National University, Kyiv, Ukraine

    A. A. Chechelnitsky

  3. T. Shevchenko Kyiv National University, Kyiv, Ukraine

    I. Ya. Usar

Authors
  1. M. S. Bratiichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Chechelnitsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. Ya. Usar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Ya. Usar.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 3, pp. 355–365, March, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bratiichuk, M.S., Chechelnitsky, A.A. & Usar, I.Y. M/M/1 Retrial Queueing System with Variable Service Rate. Ukr Math J 72, 403–415 (2020). https://doi.org/10.1007/s11253-020-01790-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-020-01790-1

Search

Navigation