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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)

We model the workload of a network device responding to a random flux of work requests with various intensities and durations in two ways, a conventional univariate stochastic integral approach (" downstairs ") and a higher-dimensional random field approach (" upstairs "). The models feature Gaussian, stable, Poisson and, more generally, infinitely… (More)

The fluctuations of Internet traffic possess an intricate structure which cannot be simply explained by long–range dependence and self–similarity. In this work, we explore the use of the wavelet spectrum, whose slope is commonly used to estimate the Hurst parameter of long–range dependence. We show that much more than simple slope estimates are needed for… (More)

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… (More)

- Brendan O Bradley, Murad S Taqqu
- 2001

It is of great importance for those in charge of managing risk to understand how financial asset returns are distributed. Practitioners often assume for convenience that the distribution is normal. Since the 1960s, however, empirical evidence has led many to reject this assumption in favor of various heavy-tailed alternatives. In a heavy-tailed distribution… (More)

The Hurst parameter H characterizes the degree of long-range dependence (and asymp-totic self-similarity) in stationary time series. Many methods have been developed for the estimation of H from data. In practice, however, the classical estimation techniques can be severely affected by non-stationary artifacts in the time series. In fact, the assumption… (More)