Recent traffic measurement studies from a wide range of working packet networks have convincingly established the presence of significant statistical features that are characteristic of fractal traffic processes, in the sense that these features span many time scales. Of particular interest in packet traffic modeling is a property called long-range dependence, which is marked by the presence of correlations that can extend over many time scales. In this paper, we demonstrate empirically that, beyond its statistical significance in traffic measurements, long-range dependence has considerable impact on queueing performance, and is a dominant characteristic for a number of packet traffic engineering problems. In addition, we give conditions under which the use of compact and simple traffic models that incorporate long-range dependence in a parsimonious manner (e.g., fractional Brownian motion) is justified and can lead to new insights into the traffic management of high-speed networks. 1...

An abstract model for aggregated connectionless traffic, based on the fractional Brownian motion, is presented. Insight into the parameters is obtained by relating the model to an equivalent burst model. Results on a corresponding storage process are presented. The buffer occupancy distribution is approximated by a Weibull distribution. The model is compared with publicly available samples of real Ethernet traffic. The degree of the short-term predictability of the traffic model is clarified through an exact formula for the conditional variance of a future value given the past. The applicability and interpretation of the self-similar model are discussed extensively, and the notion of ideal Free Traffic is introduced. Keywords: LAN traffic, long-range dependence, self-similar, prediction 1 Introduction In this paper we are considering the modelling of traffical phenomena in a connectionless network. The principle of such a network is that all data is sent in relatively small independen...

A Wavelet based tool for the analysis of long range dependence is introduced and a related semiparametric estimator of the Hurst parameter. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono vs multi-fractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.

There is much experimental evidence that network traffic processes exhibit ubiquitous properties of selfsimilarity and long range dependence (LRD), i.e., of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much recent modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the first-order statistics such as the marginal distribution of the process.

Abstract- In this paper we demonstrate how TCP congestion control can show chaotic behavior. We demonstrate the major features of chaotic systems in TCPlIP networks with examples. These features include un-predictability, extreme sensitivity to initial conditions and odd periodicity. Previous work has shown the fractal nature of aggregate TCPAP traffic and one explanation to this phenomenon was that traffic can be approxi-mated by a large number of ON/OFF sources where the random ON and/or OFF periods are of length described by a heavy tailed distribution. In this paper we show that this argument is not necessary to explain self-similarity, neither randomness is required. Rather, TCP itself as a deter-ministic process creates chaos, which generates self-similarity. This prop-erty is inherent in todays TCPlIP networks and it is independent of higher layer applications or protocols. The two causes: heavy tailed ONlOFF and chaotic TCP together contribute to the phenomena, called fractal nature of Internet traffic. Keywords-TCP congestion control, fractal traffic, chaotic models. I.

A wavelet-based tool for the analysis of long-range dependence and a related semi-parametric estimator of the Hurst parameter is introduced. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational, and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long-range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono versus multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.

this paper. In 2 we summarize the considerable literature on the subject along with an introduction to our approach. 3 presents results indicating the traffic characteristics that can be generated with simple piecewise linear and nonlinear maps. 4 shows how a queueing system can be represented by a 2-D deterministic transformation, and outlines a potential performance analysis approach. 5 concludes this paper with a description of future directions for this work.

INTRODUCTION In the last decade a number of extensive studies of high resolution traffic measurements from a wide range of packet traffic networks have been reported [1,6,7,10,11,14,22]. The most important finding of these studies is the identified fractal-like behaviour implying the so called long-range dependence and self-similarity properties. As a result of intensive research at Bellcore a series of papers reported these findings in Ethernet LAN [7,9,11,12]. The comprehensive study of Leland's group with the conclusion that this traffic is self-similar was published in detail in [11]. The study of Duffy et al. [6] revealed the self-similarity traffic property in common-channel signalling network. Meier-Hellstern et al. [14] found that the Pareto distribution with infinite variance is applicable for characterizing the D-channel traffic in N-ISDN. Paxson et al. [20,22] reported the self-similar features of TCP traffic. The fractal properties also

Self-similar processes based on fractal point processes (FPPs) provide natural and attractive network tra#c models. We show that the point process formulation yields a wide range of FPPs which in turn yield a diversity of parsimonious, computationally e#cient, and highly practical asymptotic second-order self-similar processes. Using this framework, we show that the relevant second-order fractal characteristics such as long-range dependence (LRD), slowly-decaying variance, and 1/f noise are completely characterized by three fundamental quantities: mean arrival rate, Hurst parameter, and fractal onset time. Four models are proposed, and the relationship between their model parameters and the three fundamental quantities are analyzed. By successfully applying the proposed models to Bellcore's Ethernet traces, we show that the FPP models prove useful in evaluating and predicting the queueing performance of various types of fractal tra#c sources. Keywords: point process, fractal, self-similarity, long-range dependence, tra#c modeling 1 Throughout this paper, self-similarity refers to asymptotic second-order self-similarity [4], [13] unless otherwise defined. 1

Recent traffic measurement studies suggest that the self-similarity observed in packet traffic arises from aggregating individual sources which behave in an ON/OFF manner with heavy-tailed sojourn times in one or both of the states. In this paper, we investigate the connection between general ON/OFF behavior, self-similarity and queueing performance. We use chaotic maps to model general ON/OFF behavior with combinations of heavy tailed and light tailed sojourn time behavior. We present results which show that chaotic maps which capture the heavytailed sojourn time behavior in the OFF and/or ON states generate traffic that is asymptotically self-similar. However, the resulting queue length distribution decays as a power law with the heavy ON source, and as an exponential with the light ON source, even though both processes exhibit identical 1/f noise behavior. To resolve this apparent paradox, we consider aggregates of ON and OFF sources, and show that the nature of the ON period is le...