Advertisement

Cybernetics and Systems Analysis

, Volume 49, Issue 4, pp 578–583 | Cite as

Periodic discrete-time one-channel GI/G/1 retrial queuing system with FCFS service discipline

  • I. N. Kovalenko
  • E. V. Koba
  • O. N. Dyshliuk
Article
  • 50 Downloads

Abstract

A discrete-time one-channel queuing system with general inter-arrival, service, and orbit times periodically dependent on the number of arrival is considered. The service discipline is assumed to be FCFS. The sufficient condition for the ergodicity of an embedded Markov chain is derived.

Keywords

queuing systems repeated calls stability of queuing systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. M. Glushkov, Synthesis of Digital Automata [in Rusian], Fizmatgiz, Moscow (1962).Google Scholar
  2. 2.
    T. Yang and J. G. C. Templeton, “A survey on retrial queues,” Queueing Systems, No. 3, 201–233 (1987).Google Scholar
  3. 3.
    G. Falin, “A survey of retrial queues,” Queueing Systems, No. 7, 127–167 (1990).Google Scholar
  4. 4.
    G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapmen & Hall, London (1997).MATHGoogle Scholar
  5. 5.
    J. R. Artalejo and A. Gomez-Corral, Retrial Queueing Systems: A Computational Approach, Springer, Berlin (2008).MATHCrossRefGoogle Scholar
  6. 6.
    J. R. Artalejo, “Accessible bibliography on retrial queues,” Math. and Comput. Model., 30, No. 3–4, 1–6 (1999).CrossRefGoogle Scholar
  7. 7.
    J. R. Artalejo, “A classified bibliography of research on retrial queues: Progress in 1990–1999,” Top 7, 187–211 (1999).Google Scholar
  8. 8.
    J. R. Artalejo, “Accessible bibliography on retrial queues: Progress in 2000–2009,” Math. and Comput. Model., 51, No. 9–10, 1071–1081 (2010).MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    A. N. Dudin and V. I. Klimenok, “A retrial BMAP/SM/1 system with linear repeated requests,” Queueing Systems, 34, 47–66 (2000).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    D. Yu. Kuznetsov and A. A. Nazarov, Adaptive Random Access Networks [in Russian], Del’taplan, Tomsk (2002).Google Scholar
  11. 11.
    V. V. Anisimov and E. A. Lebedev, Stochastic Queuing Networks: Markov Models [in Russian], Lybid’, Kyiv (1992).Google Scholar
  12. 12.
    L. Lakatos and A. A. Balkema, “A probability model connected with landing of airplanes,” in: Safety and Reliability, Brookfield, Rotterdam (1999), pp. 151–154.Google Scholar
  13. 13.
    E. V. Koba, “A GI/G/1retrial queuing system with FIFO service discipline,” Dop. NAN Ukrainy, No. 6, 101–103 (2000).Google Scholar
  14. 14.
    E. V. Koba, “On a GI/G/1retrial queueing system with a FIFO queueing discipline,” Theory Stochast. Proces., 24, No. 8, 201–207 (2002).MathSciNetGoogle Scholar
  15. 15.
    A. A. Borovkov, Ergodicity and Stability of Random Processes [in Russian], Editorial USSR, Moscow (1999).Google Scholar
  16. 16.
    G. P. Klimov, Stochastic Queuing Systems [in Russian], Nauka, Moscow (1966).Google Scholar
  17. 17.
    B. V. Gnedenko and I. N. Kovalenko, An Introduction to the Queuing Theory [in Russian], LKI, Moscow (2007).Google Scholar
  18. 18.
    W. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, Wiley (1971).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • I. N. Kovalenko
    • 1
  • E. V. Koba
    • 1
  • O. N. Dyshliuk
    • 2
  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.National Aviation UniversityKyivUkraine

Personalised recommendations