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Special Retrial Queues with State-Dependent Input Rate

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1109))

Abstract

This paper studies Markovian models of controlled systems with retrials, where the rate of the flow of retrials does not depend on the amount of their sources. The input flow of customers is controlled according to a multithreshold strategy. The conditions for the existence of a stationary regime are defined for this type of system, and clear formulae of vector-matrix type for stationary probabilities are obtained. The problem of multicriteria optimization of the system’s profit are also considered.

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References

  1. Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems: A Computational Approach. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78725-9

    Book  MATH  Google Scholar 

  2. Avrachenkov, K., Yechiali, U.: Retrial networks with finite buffers and their application to internet data traffic. Probab. Eng. Inf. Sci. 22, 519–536 (2008)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  4. Choi, B.D., Park, K.K., Pearce, C.E.M.: An M/M/1 Retrial queue with control policy and general retrial times. Queueing Syst. 14, 275–292 (1993)

    Article  MathSciNet  Google Scholar 

  5. Dudin, A.N., Klimenok, V.I.: Optimization of dynamic control of input load in node of informational-computing network. Autom. Technol. 3, 25–31 (1991)

    MATH  Google Scholar 

  6. Falin, G.: Heavy traffic analysis of a random walk on a lattice semi-trip. Stoch. Models 11(3), 395–409 (1995)

    Article  MathSciNet  Google Scholar 

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

    Book  Google Scholar 

  8. Lebedev, E.A., Usar, I.Y.: Retrial queues with variable rate of input flow. Cybern. Syst. Anal. 3, 151–159 (2013)

    Google Scholar 

  9. Phung-Duc, T.: Retrial queueing models: a survey on theory and applications. ArXiv abs arxiv:1906.09560, n. p. (2019)

  10. Ponomarov, V., Lebedev, E.: Finite source retrial queues with state-dependent service rate. Commun. Comput. Inf. Sci. 356, 140–146 (2013)

    MATH  Google Scholar 

  11. Roger, A.H., Charles, R.J.: Matrix Analysis. Cambridge University Press, Cambridge (1986)

    Google Scholar 

  12. Walrand, J.: An Introduction to Queueing Networks. Prentice Hall, Upper Saddle River (1988)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Higher Polytechnic School, University of Malaga, 29071, Malaga, Spain

    Ivan Atencia

  2. Applied Statistics Department, Taras Shevchenko National University of Kyiv, Volodymyrska Str., 64, Kyiv, 01601, Ukraine

    Eugene Lebedev, Vadym Ponomarov & Hanna Livinska

Authors
  1. Ivan Atencia
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  2. Eugene Lebedev
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  3. Vadym Ponomarov
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  4. Hanna Livinska
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Corresponding author

Correspondence to Vadym Ponomarov .

Editor information

Editors and Affiliations

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

    Alexander Dudin

  2. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Alexander Moiseev

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Atencia, I., Lebedev, E., Ponomarov, V., Livinska, H. (2019). Special Retrial Queues with State-Dependent Input Rate. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2019. Communications in Computer and Information Science, vol 1109. Springer, Cham. https://doi.org/10.1007/978-3-030-33388-1_7

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  • DOI: https://doi.org/10.1007/978-3-030-33388-1_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33387-4

  • Online ISBN: 978-3-030-33388-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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