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1 results

  • Extremal behavior of heavy-tailed ON-periods in a superposition of ON/OFF processes

  • Part of
  • Alwin Stegeman
  • Journal:
    Advances in Applied Probability / Volume 34 / Issue 1 / March 2002
    Published online by Cambridge University Press:
    01 July 2016, pp. 179-204
    Print publication:
    March 2002

  • Empirical studies of data traffic in high-speed networks suggest that network traffic exhibits self-similarity and long-range dependence. Cumulative network traffic has been modeled using the so-called ON/OFF model. It was shown that cumulative network traffic can be approximated by either fractional Brownian motion or stable Lévy motion, depending on how many sources are active in the model. In this paper we consider exceedances of a high threshold by the sequence of lengths of ON-periods. If the cumulative network traffic converges to stable Lévy motion, the number of exceedances converges to a Poisson limit. The same holds in the fractional Brownian motion case, provided a very high threshold is used. Finally, we show that the number of exceedances obeys the central limit theorem.