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International Conference on Information Technologies and Mathematical Modelling

ITMM 2016: Information Technologies and Mathematical Modelling - Queueing Theory and Applications pp 83–93Cite as

Quasi-Geometric, Gamma and Gaussian Approximations for Multiserver Retrial Queueing Systems

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

Abstract

In the paper, methods of quasi-geometric, gamma and Gaussian approximation of the probability distribution of the calls number in the orbit for multiserver retrial queueing systems are proposed. A description and analysis of the application area of each method for retrial queueing system M|M|N are given. In addition, the results of approximations are compared and a table of decision making on the choice of the approximation type has been composed.

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References

  1. Wilkinson, R.I.: Theories for toll traffic engineering in the USA. Bell Syst. Techn. J. 35(2), 421–507 (1956)

    Article  MathSciNet  Google Scholar 

  2. Cohen, J.W.: Basic problems of telephone trafic and the influence of repeated calls. Philips Telecommun. Rev. 18(2), 49–100 (1957)

    Google Scholar 

  3. Elldin, A., Lind, G.: Elementary Telephone Trafic Theory. Ericsson Public Telecommunications, Stockholm (1971)

    Google Scholar 

  4. Gosztony, G.: Repeated call attempts and their efect on trafic engineering. Budavox Telecommun. Rev. 2, 16–26 (1976)

    Google Scholar 

  5. Kuznetsov, D.Y., Nazarov, A.A.: Analysis of non-Markovian models of communication networks with adaptive protocols of multiple random access. Avtomatika i Telemekhanika 5, 124–146 (2001)

    MathSciNet  MATH  Google Scholar 

  6. Nazarov, A.A., Tsoj, S.A.: Common approach to studies of Markov models for data transmission networks controlled by the static random multiple access protocols. Avtomatika i Vychislitel’naya Tekhnika 4, 73–85 (2004)

    Google Scholar 

  7. Artalejo, J.R., Gómez-Corral, A.: Retrial Queueing Systems. A Computational Approach. Springer, New York (2008)

    Book  MATH  Google Scholar 

  8. Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman & Hall, London (1997)

    Book  MATH  Google Scholar 

  9. Artalejo, J.R., Falin, G.I.: Standard and retrial queueing systems: a comparative analysis. Revista Matematica Complutense 15, 101–129 (2002)

    MathSciNet  MATH  Google Scholar 

  10. Neuts, M.F., Rao, B.M.: Numerical investigation of a multiserver retrial model. Queueing Syst. 7(2), 169–189 (2002)

    Article  MATH  Google Scholar 

  11. Ridder, A.: Fast simulation of retrial queues. In: Third Workshop on Rare Event Simulation and Related Combinatorial Optimization Problems, pp. 1–5, Pisa (2000)

    Google Scholar 

  12. Kim, C.S., Mushko, V.V., Dudin, A.: Computation of the steady state distribution for multi-server retrial queues with phase type service process. Ann. Oper. Res. 201(1), 307–323 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gómez-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 

  14. Falin, G.I.: Asymptotic properties of probability distribution of the number of request in system M/G/1/1 with repeated calls. VINITI, pp. 5418–5483 (In Russian) (1983)

    Google Scholar 

  15. Artalejo, J.R.: Information theoretic approximations for retrial queueing systems. In: Transactions of the 11th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, pp. 263–270. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  16. Anisimov, V.V.: Asymptotic analysis of highly reliable retrial systems with finite capacity. In: Queues, Flows, Systems, Networks: Proceedings of the International Conference Modern Mathematical Methods of Investigating the Telecommunication Networks, pp. 7–12, Minsk (1999)

    Google Scholar 

  17. Yang, T., Posner, M.J.M., Templeton, J.G.C., Li, H.: An approximation method for the M/G/1 retrial queue with general retrial times. Eur. J. Oper. Res. 76, 552–562 (1994)

    Article  MATH  Google Scholar 

  18. Diamond, J.E., Alfa, A.S.: Approximation method for M/PH/1 retrial queues with phase type inter-retrial times. Eur. J. Oper. Res. 113, 620–631 (1999)

    Article  MATH  Google Scholar 

  19. Moiseeva, E., Nazarov, A.: Asymptotic Analysis of RQ-systems M/M/1 on heavy load condition. In: Proceedings of the IV International Conference Problems of Cybernetics and Informatics, pp. 164–166, Baku, Azerbaijan (2012)

    Google Scholar 

  20. Fedorova, E.: Quasi-geometric and gamma approximation for retrial queueing systems. In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds.) ITMM 2014. CCIS, vol. 487, pp. 123–136. Springer, Heidelberg (2014)

    Google Scholar 

  21. Kovalenko, I.N., Filippova, A.A.: Probability Theory and Mathematical Statistics. A Textbook. Vyschaya shkola, Moscow (1982). (In Russian)

    MATH  Google Scholar 

  22. Nazarov, A.A., Lyubina, T.V.: The non-Markov dynamic RQ system with the incoming MMP flow of requests. Autom. Remote Control 74(7), 1132–1143 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Nazarov, A., Chernikova, Y.: Gaussian approximations of probabilities distribution of states of the retrial queueing system with r-persistent exclusion of alternative customers. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. CCIS, vol. 564, pp. 200–208. Springer, Switzerland (2015)

    Chapter  Google Scholar 

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Acknowledgments

The reported study was funded by RFBR according to the research project No. 16-31-00292 mol-a.

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Authors and Affiliations

  1. Tomsk State University, Tomsk, Russia

    Ekaterina Fedorova

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  1. Ekaterina Fedorova
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Correspondence to Ekaterina Fedorova .

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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Fedorova, E. (2016). Quasi-Geometric, Gamma and Gaussian Approximations for Multiserver Retrial Queueing Systems. 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_7

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  • DOI: https://doi.org/10.1007/978-3-319-44615-8_7

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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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