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Convergence to Fractional Brownian Motion and to the Telecom Process: the Integral Representation Approach

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In and Out of Equilibrium 2

Part of the book series: Progress in Probability ((PRPR,volume 60))

Abstract

It has become common practice to use heavy-tailed distributions in order to describe the variations in time and space of network traffic workloads. The asymptotic behavior of these workloads is complex; different limit processes emerge depending on the specifics of the work arrival structure and the nature of the asymptotic scaling. We focus on two variants of the infinite source Poisson model and provide a coherent and unified presentation of the scaling theory by using integral representations. This allows us to understand physically why the various limit processes arise.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Uppsala University, Box 480, SE 751 06, Uppsala, Sweden

    Ingemar Kaj

  2. Department of Mathematics, Boston University, Boston, MA, 02215-2411, USA

    Murad S. Taqqu

Authors
  1. Ingemar Kaj
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  2. Murad S. Taqqu
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Editor information

Editors and Affiliations

  1. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina, 110 Jardim Botanico, CEP 22460-320, Rio de Janeiro, RJ, Brasil

    Vladas Sidoravicius

  2. Centro Brasileiro de Pesquisas FĂ­sicas, Rua Dr. Xavier Sigaud, 150 Urca, 22290-180, Rio de Janeiro, RJ, Brasil

    Maria Eulália Vares

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Kaj, I., Taqqu, M.S. (2008). Convergence to Fractional Brownian Motion and to the Telecom Process: the Integral Representation Approach. In: Sidoravicius, V., Vares, M.E. (eds) In and Out of Equilibrium 2. Progress in Probability, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8786-0_19

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