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A Tight Bound on the Throughput of Queueing Networks with Blocking

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7984))

Abstract

In this paper, we present a bounding methodology that allows to compute a tight bound on the throughput of fork-join queueing networks with blocking and with general service time distributions. No exact models exist for queueing networks with general service time distributions and, consequently, bounds are the only certain information available. The methodology relies on two ideas. First, probability mass fitting (PMF) discretizes the service time distributions so that the evolution of the modified system can be modelled by a discrete Markov chain. Second, we show that the critical path can be computed with the discretized distributions and that the same sequence of jobs offers a bound on the original throughput. The tightness of the bound is shown on computational experiments (error on the order of one percent). Finally, we discuss the extension to split-and-merge networks and the approximate estimations of the throughput.

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Author information

Authors and Affiliations

  1. Louvain School of Management, Université catholique de Louvain (UCL), Belgium

    Jean-Sébastien Tancrez, Philippe Chevalier & Pierre Semal

  2. Center for Operations Research and Econometrics (CORE), UCL, Belgium

    Philippe Chevalier

Authors
  1. Jean-Sébastien Tancrez
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  2. Philippe Chevalier
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  3. Pierre Semal
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Editor information

Editors and Affiliations

  1. Belarusian State University, Nezavisimosti Ave. 4, 220030, Minsk, Belarus

    Alexander Dudin

  2. Department of Telecommunications and Information Processing, Ghent University, Sint-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Koen De Turck

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Tancrez, JS., Chevalier, P., Semal, P. (2013). A Tight Bound on the Throughput of Queueing Networks with Blocking. In: Dudin, A., De Turck, K. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2013. Lecture Notes in Computer Science, vol 7984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39408-9_28

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  • DOI: https://doi.org/10.1007/978-3-642-39408-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39407-2

  • Online ISBN: 978-3-642-39408-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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