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Asymptotic Analysis of Queueing Systems with Finite Buffer Space

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Computer Networks (CN 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 431))

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Abstract

In the paper, we consider a single-server loss system in which each customer has both service time and a random volume. The total volume of the customers present in the system is limited by a finite constant (the system’s capacity). For this system, we apply renewal theory and regenerative processes to establish a relation which connects the stationary idle probability P 0 with the limiting fraction of the lost volume, Q loss, provided the service time and the volume are proportional. Moreover, we use the inspection paradox to deduce an asymptotic relation between Q loss and the stationary loss probability P loss. An accuracy of this approximation is verified by simulation.

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematical Research, Karelian Research Centre RAS, Petrozavodsk State University, Lenin 33, 185910, Petrozavodsk, Russia

    Evsey Morozov, Ruslana Nekrasova & Lyubov Potakhina

  2. Institute of Mathematics, Czestochowa University of Technology, Al. Armii Krajowej 21, 42-200, Czestochowa, Poland

    Oleg Tikhonenko

Authors
  1. Evsey Morozov
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  2. Ruslana Nekrasova
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  3. Lyubov Potakhina
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  4. Oleg Tikhonenko
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, Silesian University of Technology, Akademicka 16, 44-100, Gliwice, Poland

    Andrzej Kwiecień

  2. Institute of Informatics, Silesian University of Technology, ul. Akademicka 16, 44-100, Gliwice, Poland

    Piotr Gaj

  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Piotr Stera

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© 2014 Springer International Publishing Switzerland

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Morozov, E., Nekrasova, R., Potakhina, L., Tikhonenko, O. (2014). Asymptotic Analysis of Queueing Systems with Finite Buffer Space. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2014. Communications in Computer and Information Science, vol 431. Springer, Cham. https://doi.org/10.1007/978-3-319-07941-7_23

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  • DOI: https://doi.org/10.1007/978-3-319-07941-7_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07940-0

  • Online ISBN: 978-3-319-07941-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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