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Reliability Analysis of a Two-Server Heterogeneous Unreliable Queueing System with a Threshold Control Policy

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 800))

Abstract

Heterogeneous servers which can differ in service speed and reliability are getting more popular in modeling of modern communication systems. For a two-server queueing system with unreliable servers the allocation of customers between the servers is performed via a threshold control policy which prescribes to use the fastest server whenever it is free and the slower one only if the number of waiting customers exceeds some threshold level depending on the state of faster server. The main task of the paper consists in reliability analysis of the proposed system including evaluation of the stationary availability and reliability function. The effects of different parameters on introduced reliability characteristics are analyzed numerically.

D. Efrosinin—The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008), by the Russian Foundation for Basic Research, Project No. 16-37-60072 mol_a_dk and No. 15-08-08677 A, by the Austro-Hungarian Scientific Cooperation OMAA 96öu8.

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References

  1. Efrosinin, D.: Controlled queueing systems with heterogeneous servers. In: Dynamic Optimization and Monotonicity Properties, Saarbrücken. VDM (2008)

    Google Scholar 

  2. Efrosinin, D.: Queueing model of a hybrid channel with faster link subject to partial and complete failures. Ann. Oper. Res. 202, 75–102 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Efrosinin, D., Samouylov, K., Gudkova, I.: Busy period analysis of a queueing system with breakdowns and its application to wireless network under licensed shared access regime. In: Galinina, O., Balandin, S., Koucheryavy, Y. (eds.) NEW2AN/ruSMART -2016. LNCS, vol. 9870, pp. 426–439. Springer, Cham (2016). doi:10.1007/978-3-319-46301-8_36

    Chapter  Google Scholar 

  4. Efrosinin, D., Sztrik, J.: Optimal control of a two-server heterogeneous queueing system with breakdowns and constant retrials. In: Dudin, A., Gortsev, A., Nazarov, A., Yakupov, R. (eds.) ITMM 2016. CCIS, vol. 638, pp. 57–72. Springer, Cham (2016). doi:10.1007/978-3-319-44615-8_5

    Chapter  Google Scholar 

  5. Koole, G.: A simple proof of the optimality of a threshold policy in a two-server queueing system. Syst. Control Lett. 26, 301–303 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kumar, B.K., Madheswari, S.P.: An \(M/M/2\) queueing system with heterogeneous servers and multiple vacations. Math. Comput. Model. 41, 1415–1429 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kumar, B.K., Madheswari, S.P., Venkatakrishnan, K.S.: Transient solution of an \(M/M/2\) queue with heterogeneous servers subject to catastrophes. Inf. Manag. Sci. 18(1), 63–80 (2007)

    MathSciNet  MATH  Google Scholar 

  8. Legros, B., Jouini, O.: Routing in a queueing system with two heterogeneous servers in speed and in quality of resolution (2016). http://www.lgi.ecp.fr/~jouini

  9. Levy, J., Yehiali, U.: An \(M/M/s\) queue with servers’ vacations. Inf. Syst. Oper. Res. 14(2), 153–163 (1976)

    MathSciNet  MATH  Google Scholar 

  10. Lin, W., Kumar, P.R.: Optimal control of a queueing system with two heterogeneous servers. IEEE Trans. Autom. Control 29, 696–703 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mitrany, I.L., Avi-Itzhak, B.: A many server queue with service interruptions. Oper. Res. 16, 628–638 (1967)

    Article  MATH  Google Scholar 

  12. Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models. The John Hopkins University Press, Baltimore (1981)

    MATH  Google Scholar 

  13. Neuts, M.F., Lucantoni, D.M.: A Markovian queue with \(N\) servers subject to breakdowns and repairs. Manag. Sci. 25, 849–861 (1979)

    Article  MathSciNet  Google Scholar 

  14. Ozkan, E., Kharoufeh, J.: Optimal control of a two-server queueing system with failures. Probab. Eng. Inf. Sci. 28, 489–527 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rykov, V., Efrosinin, D.: On the slow server problem. Autom. Remote Control 70(12), 2013–2013 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yue, D., Yue, W., Yu, J., Tian, R.: A heterogeneous two-server queueing system with balking and server breakdowns. In: Proceedings of the Eighth International Symposium on Operations Research and Its Applications, China, pp. 230–244 (2009)

    Google Scholar 

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya Street 6, 117198, Moscow, Russia

    Dmitry Efrosinin

  2. Johannes Kepler University Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Dmitry Efrosinin

  3. University of Debrecen, Egyetem tér 1, Debrecen, 4032, Hungary

    Janos Sztrik

  4. Institute of Control Sciences, RAS, Profsoyuznaya Street 65, 117997, Moscow, Russia

    Mais Farkhadov & Natalia Stepanova

Authors
  1. Dmitry Efrosinin
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  2. Janos Sztrik
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  3. Mais Farkhadov
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  4. Natalia Stepanova
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Correspondence to Dmitry Efrosinin .

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Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kazan National Research Technological University, Kazan, Russia

    Alexander Kirpichnikov

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Efrosinin, D., Sztrik, J., Farkhadov, M., Stepanova, N. (2017). Reliability Analysis of a Two-Server Heterogeneous Unreliable Queueing System with a Threshold Control Policy. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2017. Communications in Computer and Information Science, vol 800. Springer, Cham. https://doi.org/10.1007/978-3-319-68069-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-68069-9_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68068-2

  • Online ISBN: 978-3-319-68069-9

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