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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.

- 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)

- E. Crovella, Murad S. Taqqu
- 1998

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)

- Robert J. Adler, Raisa E. Feldman, Murad S. Taqqu, Mark E. Crovella, Azer Bestavros, Walter Willinger +11 others
- 1998