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Numerical Analysis of a Retrial System with Unreliable Servers Based on Laplace Domain Description

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Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 13144))

Abstract

In this paper, we consider a retrial queuing system with unreliable servers and analyze the distribution of the stationary generalized service time which includes also the unavailable periods (setup times) occurring during service of the customer. We consider three service interruption disciplines: preemptive resume (PRS), preemptive repeat different (PRD), and preemptive repeat identical (PRI); and provide the stationary distribution of the generalized service time and the remaining generalized service time for these disciplines in Laplace transform (LT) domain.

The main focus of the paper is on the numerical analysis based on LT domain descriptions, which we evaluate for various numerical examples.

This work is partially supported by the OTKA K-123914 project and the Artificial Intelligence National Laboratory Programme of Hungary and by the Russian Science Foundation, Project No. 21-71-10135, https://rscf.ru/en/project/21-71-10135/.

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References

  1. Abate, J., Whitt, W.: A unified framework for numerically inverting laplace transforms. INFORMS J. Comput. 18(4), 408–421 (2006)

    Article  MathSciNet  Google Scholar 

  2. Dimitriou, I., Morozov, E., Morozova, T.: Multiclass retrial system with coupled orbits and service interruptions: verification of stability conditions. In: Conference of Open Innovations, pp. 75–81 (2019)

    Google Scholar 

  3. Gaver, D.P.: Observing stochastic processes and approximate transform inversion. Oper. Res. 14, 444–459 (1966)

    Article  MathSciNet  Google Scholar 

  4. Horváth, I., Horváth, G., Almousa, S.A.D., Telek, M.: Numerical inverse Laplace transformation using concentrated matrix exponential distributions. Perf. Eval. (2019). https://doi.org/10.1016/j.peva.2019.102067

    Article  Google Scholar 

  5. Kulkarni, V.: Modeling and Analysis of Stochastic Systems. Chapman & Hall, London (1995)

    MATH  Google Scholar 

  6. Morozov, E., Morozova, T.: On stationary remaining service time in queuieng systems. In: Proceedings of SMARTY: International Conference Stochastic Modeling and Applied Research of Technology, Petrozavodsk, Russia, pp. pp. 1–12 (2020)

    Google Scholar 

  7. Ross, S.: Introduction to Probability Models, 8th edn. Academic Press, San Diego (2003)

    MATH  Google Scholar 

  8. Talbot, A.: The accurate numerical inversion of laplace transforms. IMA J. Appl. Math. 23(1), 97–120 (1979). https://doi.org/10.1093/imamat/23.1.97

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, Hungary

    András Mészáros & Miklós Telek

  2. MTA-BME Information Systems Research Group, ELKH, Budapest, Hungary

    András Mészáros & Miklós Telek

  3. Petrozavodsk State University, Lenin Street 33, Petrozavodsk, 185910, Russia

    Evsey Morozov & Taisia Morozova

  4. Institute of Applied Mathematical Research of the Karelian Research Centre of RAS, Pushkinskaya Street 11, Petrozavodsk, 185910, Russia

    Evsey Morozov

  5. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, 119991, Russia

    Evsey Morozov

  6. Uppsala University, Uppsala, Sweden

    Taisia Morozova

Authors
  1. András Mészáros
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  2. Evsey Morozov
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  3. Taisia Morozova
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  4. Miklós Telek
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Corresponding author

Correspondence to András Mészáros .

Editor information

Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. Applied Probability and Informatics Department, RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Mészáros, A., Morozov, E., Morozova, T., Telek, M. (2021). Numerical Analysis of a Retrial System with Unreliable Servers Based on Laplace Domain Description. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_19

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  • DOI: https://doi.org/10.1007/978-3-030-92507-9_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92506-2

  • Online ISBN: 978-3-030-92507-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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