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Branching Processes, the Max-Plus Algebra and Network Calculus

  • Eitan Altman
  • Dieter Fiems
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7314)

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.

Keywords

Stochastic recursive equations Branching processes Max-plus algebra Network calculus 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eitan Altman
    • 1
  • Dieter Fiems
    • 2
  1. 1.Maestro group, INRIASophia Antipolis CedexFrance
  2. 2.Department TELINGhent UniversityGentBelgium

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