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Branching Processes, the Max-Plus Algebra and Network Calculus

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7314))

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Abstract

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory.

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Author information

Authors and Affiliations

  1. Maestro group, INRIA, 2004 Route des Lucioles, 06902, Sophia Antipolis Cedex, France

    Eitan Altman

  2. Department TELIN, Ghent University, St-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Dieter Fiems

Authors
  1. Eitan Altman
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  2. Dieter Fiems
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Editor information

Editors and Affiliations

  1. Faculty of Advanced Technology, University of Glamorgan, Pontypridd, UK

    Khalid Al-Begain

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

    Dieter Fiems

  3. LIG Laboratory - INRIA MESCAL Project,, Joseph Fourier University, 51, avenue Jean Kuntzmann, F-38330, Montbonnot, France

    Jean-Marc Vincent

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Altman, E., Fiems, D. (2012). Branching Processes, the Max-Plus Algebra and Network Calculus. In: Al-Begain, K., Fiems, D., Vincent, JM. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2012. Lecture Notes in Computer Science, vol 7314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30782-9_18

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  • DOI: https://doi.org/10.1007/978-3-642-30782-9_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30781-2

  • Online ISBN: 978-3-642-30782-9

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