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Abstrac(We demonstrate that Ethernet LAN traffic is statistically se~-simi/ar, that none of the commonly used traffic models is able to capture this fra([al-like behavior, that such behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks, and that aggregating streams of such traffic typically intensifies… (More)

A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is <i>self-similar</i> or <i>long-range dependent</i> in nature (i.e., bursty over a wide range of time scales) - in sharp contrast to commonly made traffic modeling assumptions. In this paper, we… (More)

We demonstrate that Ethernet local area network (LAN) traffic is statistically <i>self-similar,</i> that none of the commonly used traffic models is able to capture this fractal behavior, and that such behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks. Intuitively, the critical characteristic of this… (More)

We state and prove the following key mathematical result in self-similar traffic modeling: the superposition of many <i>ON/OFF</i> sources (also known as <i>packet trains</i>) with strictly alternating <i>ON</i>- and <i>OFF</i>-periods and whose <i>ON</i>-periods or <i>OFF</i>-periods exhibit the <i>Noah Effect</i> (i.e., have high variability or infinite… (More)

Let fB H (u)g u2R be a fractional Brownian motion (fBm) with index H 2 (0; 1) and sp(B H) be the closure in L 2 (() of the span sp(B H) of the increments of fBm B H. It is well-known that, when B H = B 1=2 is the usual Brownian motion (Bm), an element X 2 sp(B 1=2) can be characterized by a unique function f X 2 L 2 (R), in which case one writes X in an… (More)

- P Abry, P Flandrin, M S Taqqu, D Veitch
- 1999

Long-range dependence-Scaling phenomena-(Multi)fractal-Wavelet analysis Scaling analysis-Scaling parameters estimation-Robustness-Fractional Brownian motion synthesis-Fano factor-Aggregation procedure-Allan variance.

The explosion of the World Wide Web as a medium for information dissemination has made it important to understand its characteristics, in particular the distribution of its le sizes. This paper presents evidence that a number of le size distributions in the Web exhibit heavy tails, including les requested by users, les transmitted through the network,… (More)

High-resolution traac measurements from modern communications networks provide unique opportunities for developing and validating mathematical models for aggregate traac. To exploit these opportunities, we emphasize the need for structural models that take into account spe-ciic physical features of the underlying communication network structure. This… (More)

- E Moulines, F Roueff, M S Taqqu, Cédex, France
- 2006

In recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi-parametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this contribution, we adapt to the wavelet setting the classical semi-parametric… (More)