Advertisement

Cybernetics and Systems Analysis

, Volume 53, Issue 3, pp 387–391 | Cite as

Retrial Queueing System M / M / 1 / 0 with Combined Service Discipline

  • E. V. KobaEmail author
Article

Abstract

The paper considers retrial queueing system M /M /1/ 0 with combined service discipline, namely, a customer from the orbit is serviced in its turn, but in case of a free channel an arrival from the original flow is serviced immediately. The author obtains the expressions for state probabilities as well as ergodicity conditions. The system is compared with the Lakatos-type system.

Keywords

queueing system retrial queueing system orbit cyclic-waiting queueing system combined service discipline system ergodicity condition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Yang and J. G. C. Templeton, “A survey on retrial queues,” Queueing Systems, No. 3, 201–233 (1987).Google Scholar
  2. 2.
    I. N. Kovalenko and E. V. Koba, “On the classification of retrial queuing systems,” Cybern. Syst. Analysis, Vol. 46, No. 3, 420–425 (2010).MathSciNetCrossRefGoogle Scholar
  3. 3.
    J. Artalejo and G. Falin, “Standard and retrial queueing systems: A comparative analysis,” Revista matemática complutense, Vol. XV, No. 1, 101–129 (2002).MathSciNetzbMATHGoogle Scholar
  4. 4.
    J. Artalejo, “A classified bibliography of research in retrial queueing,” Progress in 1990-1999. Top. No. 7, 187–211 (1999).Google Scholar
  5. 5.
    J. Artalejo, “A classified bibliography of research in retrial queueing,” Progress in 2000-2009, Mathematical and Computer Modeling, Vol. 51, 1071–1081 (2010).Google Scholar
  6. 6.
    V. V. Anisimov, “Analysis of retrial queueing systems in asymptotically aggregated environment,” 3rd Intern. Workshop on Retrial Queues, Amsterdam (2000), pp. 43–46.Google Scholar
  7. 7.
    V. V. Anisimov and M. Kurtulush, “Some Markovian queueing retrial systems under light-traffic conditions,” Cybern. Syst. Analysis, Vol. 37, No. 6, 876–887 (2001).CrossRefGoogle Scholar
  8. 8.
    I. N. Kovalenko, “Loss probability in queueing system M/G/m with T-retrial of calls under light traffic conditions,” Dopovidi NAN Ukrainy, No. 5, 77–80 (2002).Google Scholar
  9. 9.
    I. N. Kovalenko, “A two-cyclic queueing system,” Cybern. Syst. Analysis, Vol. 51, No. 1, 51–55 (2015).CrossRefGoogle Scholar
  10. 10.
    E. V. Koba, “Stability condition for some typical retrial queues,” Cybern. Syst. Analysis, Vol. 41, No. 1, 100–103 (2005).CrossRefGoogle Scholar
  11. 11.
    E. A. Lebedev, “On the first passage time of removing level for retrial queues,” Dopovidi NAN Ukrainy, No. 3, 47–50 (2002).Google Scholar
  12. 12.
    I. Ya. Usar and E. A. Lebedev, “Retrial queueing systems with variable arrival rate,” Cybern. Syst. Analysis, Vol. 49, No. 3, 457–464 (2013).CrossRefGoogle Scholar
  13. 13.
    L. Laekatos, “On a simple continuous cyclic-waiting problem,” Annales Univ. Sci. Budapest, Sect. Comp., No. 14, 105–113 (1994).Google Scholar
  14. 14.
    L. Lakatos, “A probability model connected with landing of airplanes,” in: A.A. Balkoma (ed.), Safety and Reliability, Brookfieled, Rotherdam (1999), pp. 151–154.Google Scholar
  15. 15.
    E. V. Koba and I. N. Kovalenko, “Three retrial queueing systems representing some special features of aircraft landing,” J. Autom. Inform. Sci., Vol. 34, No. 4, 1–8 (2002).CrossRefGoogle Scholar
  16. 16.
    E. V. Koba, “On a GI /G /1 retrial queueing system with a FIFO queueing discipline,” Theory of Stochastic Processes, No. 8, 201–207 (2002).Google Scholar
  17. 17.
    S. V. Serebryakova, “Application of cyclic queueing systems,” Dopovidi NAN Ukrainy, No. 3, 32–37 (2016).Google Scholar
  18. 18.
    P. P. Bocharov and A.V. Pechinkin, Queuing Theory [in Russian], Izd. RUDN, Moscow (1995).Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations