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An All Geometric Discrete-Time Multiserver Queueing System

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Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12023))

Abstract

In this work we look at a discrete-time multiserver queueing system where the number of available servers is distributed according to one of two geometrics. The arrival process is assumed to be general independent, the service times deterministically equal to one slot and the buffer capacity infinite. The queueing system resides in one of two states and the number of available servers follows a geometric distribution with parameter determined by the system state. At the end of a slot there is a fixed probability that the system evolves from one state to the other, with this probability depending on the current system state only, resulting in geometrically distributed sojourn times.

We obtain the probability generating function (pgf) of the system content of an arbitrary slot in steady-state, as well as the pgf of the system content at the beginning of an arbitrary slot with a given state. Furthermore we obtain an approximation of the distribution of the delay a customer experiences in the proposed queueing system. This approximation is validated by simulation and the results are illustrated with a numerical example.

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Authors and Affiliations

  1. Department of Telecommunications and Information Processing (TELIN), SMACS Research Group, Ghent University (UGent), Sint-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Freek Verdonck, Herwig Bruneel & Sabine Wittevrongel

Authors
  1. Freek Verdonck
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  2. Herwig Bruneel
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  3. Sabine Wittevrongel
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Corresponding author

Correspondence to Freek Verdonck .

Editor information

Editors and Affiliations

  1. Politecnico di Milano, Milan, Italy

    Marco Gribaudo

  2. Peoples' Friendship University of Russia, Moscow, Russia

    Eduard Sopin

  3. Peoples' Friendship University of Russia, Moscow, Russia

    Irina Kochetkova

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Verdonck, F., Bruneel, H., Wittevrongel, S. (2020). An All Geometric Discrete-Time Multiserver Queueing System. In: Gribaudo, M., Sopin, E., Kochetkova, I. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2019. Lecture Notes in Computer Science(), vol 12023. Springer, Cham. https://doi.org/10.1007/978-3-030-62885-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-62885-7_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62884-0

  • Online ISBN: 978-3-030-62885-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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