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Regenerative Analysis of a System with a Random Volume of Customers

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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))

Abstract

We study a general multi-server system in which each customer has service time and a random volume. We consider two main cases: (i) the total volume of the present customers is unlimited and (ii) this volume is upper bounded by a finite constant. For this system, using the regenerative approach, we develop performance analysis. We establish a solidarity property of the basic processes: accumulated volume, waiting time (workload) and queue size. In case (i), we prove an analog of Little’s formula and, provided the system is single-server and the input is Poisson, the Pollaczeck-Khintchine formula. In case (ii), we suggest an approximation of the Pollaczeck-Khintchine formula, which is then verified by simulation.

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References

  1. Asmussen, S.: Applied Probability and Queues. Springer, New York (2003)

    MATH  Google Scholar 

  2. Morozov, E.: The tightness in the ergodic analysis of regenerative queueing processes. Queueing Syst. 27, 179–203 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Morozov, E., Delgado, R.: Stability analysis of regenerative queueing systems. Autom. Remote Control 70(12), 1977–1991 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Morozov, E., Potakhina, L., Rumyantsev, A.: Stability analysis and simulation of a state-dependent transmission rate system. ManMach. Interact. 4, 673–683 (2015)

    Google Scholar 

  5. Morozov, E., Nekrasova, R., Potakhina, L., Tikhonenko, O.: Asymptotic analysis of queueing systems with finite buffer space. Commun. Comput. Inf. Sci. 431, 223–232 (2014)

    Article  Google Scholar 

  6. Tikhonenko, O.M.: An analog of littles formula for queueing systems with nonhomogeneous tasks. Autom. Remote Control 57(1), 85–88 (1996)

    MathSciNet  MATH  Google Scholar 

  7. Tikhonenko, O.M.: The problem of determination of the summarized messages volume in queueing systems and its applications. J. Inf. Process. Cybern. 32(7), 339–352 (1987)

    MathSciNet  MATH  Google Scholar 

  8. Tikhonenko, O.: Computer Systems Probability Analysis. Akademicka Oficyna Wydawnicza EXIT, Warsaw (2006). (in Polish)

    Google Scholar 

  9. Center for collective use of Karelian Research Centre of Russian Academy of Science. http://cluster.krc.karelia.ru/

  10. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. http://www.R-project.org/

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Acknowledgements

Research is supported by Russian Foundation for Basic Research, projects 15-07-02341, 15-07-02354, 15-07-02360 and the Program of Strategy Development of Petrozavodsk State University.

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Authors and Affiliations

  1. Institute of Applied Mathematical Research, Karelian Research Centre, Petrozavodsk State University, Petrozavodsk, Russia

    Evsey Morozov & Lyubov Potakhina

  2. Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University in Warsaw, Warsaw, Poland

    Oleg Tikhonenko

Authors
  1. Evsey Morozov
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  2. Lyubov Potakhina
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  3. Oleg Tikhonenko
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Corresponding author

Correspondence to Lyubov Potakhina .

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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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Morozov, E., Potakhina, L., Tikhonenko, O. (2016). Regenerative Analysis of a System with a Random Volume of Customers. 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_23

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  • DOI: https://doi.org/10.1007/978-3-319-44615-8_23

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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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