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GI / G / 1 Lakatos-Type Queueing System with T-Retrials

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Cybernetics and Systems Analysis Aims and scope

Abstract

We consider the Lakatos-type GI / G /1 queueing system with T-retrials, i.e., the system with the FCFS service discipline and a constant orbit cycle time T. We have constructed a Markov chain for the system, proved its ergodicity condition, solved a system of equations for the stationary distributions of the system state probabilities, and derived formulas for the average number of requests and the average number of orbit cycles at specific relations of service and orbit time. We have developed an algorithm for statistical modeling of the considered system as well. Results of analytical and statistical modeling show consistency between them. We have indicated an essential property of the Lakatos-type system, namely, the fact that it can be used to evaluate a system in which the FCFS service discipline is not necessary.

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References

  1. J. Artalejo, “A classified bibliography of research in retrial queueing. Progress in 1990–1999,” Top, Vol. 7, Iss. 2, 187–211 (1999).

  2. J. Artalejo, “A classified bibliography of research in retrial queueing. Progress in 2000–2009,” Math. Comput. Model., Vol. 51, 1071–1081 (2010).

    Article  Google Scholar 

  3. S. V. Serebriakova, “Algorithm of the statistical modeling of retrial queuing system GI /G / m/ 0 / /K / D,” in: Proc. the 8th World Congress “Aviation in the XXI-st Century” — “Safety in Aviation and Space Technologies,” Vol. 4, Iss. 8 (Kyiv, Ukraine, 10–12 Oct, 2018), National Aviation University, Kyiv (2018), pp. 4.3.47–4.3.50.

  4. D. Yu. Kuznetsov and A. A. Nazarov, Adaptive Random Multiple Access Networks [in Russian], Del’taplan, Tomsk (2002).

  5. W. Rogiest, K. Laevens, D. Fiems, and H. Bruneel, “A performance model for an asynchronous optical buffer,” Performance Evaluation, Vol. 62, Nos. 1–4, 313–330 (2005).

  6. T. Rhung-Duc, W. Rogiest, Y. Takahashi, and H. Bruneel, “Retrial queues with balanced call blending analysis of single-server and multiserver model,” Ann. Oper. Res., Vol. 239, Iss. 2, 429–449 (2016).

  7. E. V. Koba and I. N. Kovalenko, “Three retrial queueing systems representing some special features of aircraft landing,” J. Autom. Inform. Sci., Vol. 34, Iss. 4, 1–4 (2002).

  8. What does a day of bad weather look like? (2014). URL: https://youtu.be/brX_VhOU3qQ.

  9. L. Lakatos, “A probability model connected with landing of airplanes,” in: A. A. Balkoma (ed.), Safety and Reliability, Brookfieled, Rotterdam (1999), pp. 151–154.

    Google Scholar 

  10. E. V. Koba and S. V. Pustova, “Lakatos queuing systems, their generalization and application,” Cybern. Syst. Analysis, Vol. 48, No. 3, 387–396 (2012). https://doi.org/10.1007/s10559-012-9418-7.

    Article  MathSciNet  MATH  Google Scholar 

  11. E. V. Koba, “Cyclic-retrial queuing systems with dispatching,” Cybern. Syst. Analysis, Vol. 55, No. 6, 926–932 (2019). https://doi.org/10.1007/s10559-019-00202-y.

    Article  MATH  Google Scholar 

  12. L. Lakatos, L. Szeidl, and M. Telek, Introduction to Queueing Systems with Telecommunication Applications, Springer, Cham (2019). https://doi.org/10.1007/978-3-030-15142-3.

    Book  MATH  Google Scholar 

  13. E. V. Koba, “Retrial queueing system M / M /1/ 0 with combined service discipline,” Cybern. Syst. Analysis, Vol. 53, No. 3, 387–391 (2017). https://doi.org/10.1007/s10559-017-9938-2.

    Article  MathSciNet  MATH  Google Scholar 

  14. P. P. Bocharov and A. V. Pechinkin, Queueing Theory [in Russian], Izd-vo RUDN, Moscow (1995).

  15. V. S. Koroliuk and Yu. V. Borovskikh, Analytic Asymptotics of Probability Distributions [in Russian], Naukova Dumka, Kyiv (1981).

  16. B. D. Riply, “Thoughts on pseudorandom number generators,” J. Comput. Appl. Math., Vol. 31, Iss. 1, 153–163 (1990).

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    O. V. Koba

  2. National Aviation University, Kyiv, Ukraine

    S. V. Serebriakova

Authors
  1. O. V. Koba
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  2. S. V. Serebriakova
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Correspondence to O. V. Koba.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2021, pp. 128–138.

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Koba, O.V., Serebriakova, S.V. GI / G / 1 Lakatos-Type Queueing System with T-Retrials. Cybern Syst Anal 57, 279–288 (2021). https://doi.org/10.1007/s10559-021-00353-x

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  • DOI: https://doi.org/10.1007/s10559-021-00353-x

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