Skip to main content
SpringerLink
Log in

Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

This study considers a multi-class single-server retrial queue with constant retrial rates in which service times are generally distributed with different service rates for each class. Avrachenkov (Queueing Systems 100:177–179, 2022) formulated the conjecture on the stability of this queueing system. We completely resolve the conjecture by using the fluid limit approach.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Avrachenkov, K.: Stability and partial instability of multi-class retrial queues. Queueing Syst. 100, 177–179 (2022)

    Article  Google Scholar 

  2. Avrachenkov, K., Morozov, E., Nekrasova, R.: Stability analysis of two-class retrial systems with constant retrial rates and general service times. Perform. Eval. 159, 19 (2023)

    Article  Google Scholar 

  3. Avrachenkov, K., Morozov, E., Nekrasova, R., Steyaert, B.: Stability analysis and simulation of \(N\)-class retrial system with constant retrial rates and Poisson inputs. Asia-Pac. J. Oper. Res. 31, 18 (2014)

    Article  Google Scholar 

  4. Avrachenkov, K., Nain, P., Yechiali, U.: A retrial system with two input streams and two orbit queues. Queueing Syst. 77, 1–31 (2014)

    Article  Google Scholar 

  5. Bramson, M.: Stability of two families of queueing networks and a discussion of fluid limits. Queueing Syst. 28, 7–31 (1998)

    Article  Google Scholar 

  6. Dai, J.G.: On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. 5, 49–77 (1995)

    Article  Google Scholar 

  7. Kim, B.: Stability of a retrial queueing network with different classes of customers and restricted resource pooling. J. Ind. Manag. Optim. 7, 753–765 (2011)

    Article  Google Scholar 

  8. Kim, B., Kim, J.: Stability of a multi-class multi-server retrial queueing system with service times depending on classes and servers. Queueing Syst. 94, 129–146 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful to the reviewers for their valuable comments and suggestions. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864). J. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568).

Author information

Authors and Affiliations

  1. Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Republic of Korea

    Bara Kim

  2. Department of Mathematics Education, Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju, Chungbuk, 28644, Republic of Korea

    Jeongsim Kim

Authors
  1. Bara Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeongsim Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeongsim Kim.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, B., Kim, J. Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates. Queueing Syst 104, 175–185 (2023). https://doi.org/10.1007/s11134-023-09881-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11134-023-09881-z

Keywords

Mathematics Subject Classification

Search

Navigation