Revisiting an old friend: On the observability of the relation between Long Range Dependence and Heavy Tail

Patrice Abry
École Normale Supérieure de Lyon
Physics Department - Statistical Signal Processing Group

Taqqu's Theorem plays a fundamental role in Internet
traffic modeling, for two reasons: First, its theoretical formulation
matches closely and in a meaningful manner some of the key network
mechanisms controlling traffic characteristics; Second, it offers a
plausible explanation for the origin of the long range dependence
property in relation with the heavy tail nature of the traffic
components. Numerous attempts have since been made to observe its predictions
empirically, either from real Internet traffic data or from numerical
simulations based on popular traffic models, yet rarely has this
resulted in a satisfactory quantitative agreement. This raised in the literature a
number of comments and questions, ranging from the adequacy of the
theorem to real world data to the relevance of the statistical tools
involved in practical analyses. The present contribution aims at
studying under which conditions this fundamental theorem can be
actually seen at work on real or simulated data.
P. Abry, P. Borgnat, A. Scherrer, (ENS Lyon, France)
and F. Ricciato (Univ. Salento, Italy, FTW, Austria), D. Veitch (Univ. melbourne, Australia)
(Work submitted to Telecommunication Systems)

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