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A Retrial Queueing System with Renewal Input and Phase Type Service Time Distribution

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Information Technologies and Mathematical Modelling - Queueing Theory and Applications (ITMM 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 638))

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Abstract

In this paper, a single-server retrial queue with renewal input, phase type service time distribution and a constant retrial rate is analyzed. A constant retrial rate is typical for some real world systems where the intensity of individual retrials is inversely proportional to the number of customers in the orbit or only one customer from the orbit is allowed to make the retrials. A distinguishing feature of the system under consideration is an arbitrary distribution of inter-arrival times and phase type service time distribution while the vast majority of previous research is devoted to retrial systems with a stationary Poisson input or Markovian extensions and exponentially distributed service times. We derive the stationary distributions of the system states and the Laplace-Stieltjes transform of the sojourn time distribution.

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References

  1. Kulkarni, V.G., Liang, H.M.: Retrial queues revisited. In: Dshalalow, J.H. (ed.) Frontiers in Queueing: Models and Applications in Science and Engineering, pp. 19–34. CRC Press, Boca Raton (1997)

    Google Scholar 

  2. Falin, G., Templeton, J.: Retrial Queues. Chapman and Hall, London (1997)

    Book  MATH  Google Scholar 

  3. Gomez-Corral, A.: A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Ann. Oper. Res. 141, 163–191 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems: A Computational Approach. Springer, Heidelberg (2008)

    Book  MATH  Google Scholar 

  5. Fayolle, G.: A simple telephone exchange with delayed feedback. In: Boxma, O.J., Cohen, I.W., Tijms, M.C. (eds.) Teletraffic Analysis and Computer Performance Evaluation, pp. 245–253. North-Holland, Amsterdam (1986)

    Google Scholar 

  6. Farahmand, K.: Single line queue with repeated demands. Queueing Syst. 6, 223–228 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Choi, B.D., Shin, Y.W., Ahn, W.C.: Retrial queues with collision arising from unslotted CSMA/CD protocol. Queueing Syst. 11, 335–356 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dudin, A.N., Klimenok, V.I.: A retrial \(BMAP/SM/1\) system with linear repeated requests. Queueing Syst. 34, 47–66 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Artalejo, J., Gomez-Corral, A., Neuts, M.F.: Analysis of multiserver queues with constant retrial rate. Eur. J. Oper. Res. 135, 569–581 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, H., Zhao, Y.Q.: A retrial queue with constatnt retrial rate, server downs and impatient customers. Stoch. Models 21, 531–550 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Efrosinin, D., Winkler, A.: Queuing system with a constant retrial rate, non-reliable server and threshhold-based recovery. Eur. J. Oper. Res. 210, 594–605 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kim, C.S., Klimenok, V., Dudin, A.: A G/M/1 retrial queue with constant retrial rate. TOP 22, 509–529 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Neuts, M.: Matrix-geometric Solutions in Stochastic Models - An Algorithmic Approach. Johns Hopkins University Press, Baltimore (1981)

    MATH  Google Scholar 

  14. van Dantzig, D.: Chaines de Markof dans les ensembles abstraits et applications aux processus avec regions absorbantes et au probleme des boucles. Ann. de l’Inst. H. Pioncare 14(fasc. 3), 145–199 (1955)

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2014K2A1B8048465) and by Belarusian Republican Foundation of Fundamental Research (Grant No. F15KOR-001).

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, 220030, Minsk, Belarus

    Valentina Klimenok

Authors
  1. Valentina Klimenok
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Correspondence to Valentina Klimenok .

Editor information

Editors and Affiliations

  1. Belarusian State University , Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University , Tomsk, Russia

    Alexander Gortsev

  3. Tomsk State University , Tomsk, Russia

    Anatoly Nazarov

  4. Kemerovo State University , Anzhero-Sudzhensk, Russia

    Rafael Yakupov

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© 2016 Springer International Publishing Switzerland

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Klimenok, V. (2016). A Retrial Queueing System with Renewal Input and Phase Type Service Time Distribution. In: Dudin, A., Gortsev, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2016. Communications in Computer and Information Science, vol 638. Springer, Cham. https://doi.org/10.1007/978-3-319-44615-8_12

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  • DOI: https://doi.org/10.1007/978-3-319-44615-8_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44614-1

  • Online ISBN: 978-3-319-44615-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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