Skip to main content
SpringerLink
Log in

On the single server retrial queue with priority customers

  • Articles
  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

We consider anM 2/G 2/1 type queueing system which serves two types of calls. In the case of blocking the first type customers can be queued whereas the second type customers must leave the service area but return after some random period of time to try their luck again. This model is a natural generalization of the classicM 2/G 2/1 priority queue with the head-of-theline priority discipline and the classicM/G/1 retrial queue. We carry out an extensive analysis of the system, including existence of the stationary regime, embedded Markov chain, stochastic decomposition, limit theorems under high and low rates of retrials and heavy traffic analysis.

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. B.D. Choi and K.K. Park, TheM/G/1 retrial queue with Bernoulli schedule, Queueing Systems 7 (1990) 219–228.

    Google Scholar 

  2. G.I. Falin, A single-line system with secondary orders, Eng. Cybernet. Rev. 17 (1979) 76–83.

    Google Scholar 

  3. G.I. Falin, On a multiclass batch arrival retrial queue, Adv. Appl. Prob. 20 (1988) 483–487.

    Google Scholar 

  4. G.I. Falin, A survey of retrial queues, Queueing Systems 7 (1990) 127–168.

    Google Scholar 

  5. T. Hanschke, TheM/G/1/1 queue with repeated attempts and different types of feedback effects, OR Spectrum 7 (1985) 209–215.

    Google Scholar 

  6. N.K. Jaiswal, Time-dependent solution of the head-of-the-line priority queue, J. Roy. Stat. Soc. B24 (1962) 91–101.

    Google Scholar 

  7. Z. Khalil, G. Falin and T. Yang, Some analytical results for congestion in subscriber line modules, Queueing Systems 10 (1992) 381–402.

    Google Scholar 

  8. V.G. Kulkarni, On queueing systems with retrials, J. Appl. Prob. 20 (1983) 380–389.

    Google Scholar 

  9. T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987) 203–233.

    Google Scholar 

  10. T. Yang, M.J.M. Posner, J.G.C. Templeton and H. Li, An approximation method for theM/G/1 retrial queue with general service times, to appear in Eur. J. Oper. Res.

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Operations Research, Mathematics Faculty, Madrid University-Complutense, 28040, Madrid, Spain

    G. I. Falin, J. R. Artalejo & M. Martin

Authors
  1. G. I. Falin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. R. Artalejo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Visiting from: Department of Probability, Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Falin, G.I., Artalejo, J.R. & Martin, M. On the single server retrial queue with priority customers. Queueing Syst 14, 439–455 (1993). https://doi.org/10.1007/BF01158878

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158878

Keywords

Search

Navigation