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SelfSimilarity in World Wide Web Traffic: Evidence and Possible Causes
, 1996
"... Recently the notion of selfsimilarity has been shown to apply to widearea and localarea network traffic. In this paper we examine the mechanisms that give rise to the selfsimilarity of network traffic. We present a hypothesized explanation for the possible selfsimilarity of traffic by using a p ..."
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Cited by 1129 (24 self)
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Recently the notion of selfsimilarity has been shown to apply to widearea and localarea network traffic. In this paper we examine the mechanisms that give rise to the selfsimilarity of network traffic. We present a hypothesized explanation for the possible selfsimilarity of traffic by using a particular subset of wide area traffic: traffic due to the World Wide Web (WWW). Using an extensive set of traces of actual user executions of NCSA Mosaic, reflecting over half a million requests for WWW documents, we examine the dependence structure of WWW traffic. While our measurements are not conclusive, we show evidence that WWW traffic exhibits behavior that is consistent with selfsimilar traffic models. Then we show that the selfsimilarity insuch traffic can be explained based on the underlying distributions of WWW document sizes, the effects of caching and user preference in le transfer, the effect of user "think time", and the superimposition of many such transfers in a local area network. To do this we rely on empirically measured distributions both from our traces and from data independently collected at over thirty WWW sites.
On the Relationship Between File Sizes, Transport Protocols, and SelfSimilar Network Traffic
 In Proc. IEEE International Conference on Network Protocols
, 1996
"... Recent measurements of localarea and widearea traffic have shown that network traffic exhibits variability at a wide range of scales. In this paper, we examine a mechanism that gives rise to selfsimilar network traffic and present some of its performance implications. The mechanism we study is th ..."
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Cited by 210 (21 self)
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Recent measurements of localarea and widearea traffic have shown that network traffic exhibits variability at a wide range of scales. In this paper, we examine a mechanism that gives rise to selfsimilar network traffic and present some of its performance implications. The mechanism we study is the transfer of files or messages whose size is drawn from a heavytailed distribution. First, we show that in a “realistic ” client/server network environment—i.e., one with bounded resources and coupling among traffic sources competing for resources—the degree to which file sizes are heavytailed can directly determine the degree of traffic selfsimilarity at the link level. We show that this causal relationship is robust with respect to changes in network resources (bottleneck bandwidth and
A multifractal wavelet model with application to TCP network traffic
 IEEE TRANS. INFORM. THEORY
, 1999
"... In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the mo ..."
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Cited by 171 (30 self)
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In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing Npoint data sets. We study both the secondorder and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variancetime plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.
The chaotic nature of TCP congestion control
, 2000
"... 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 unpredictability, extreme sensitivity to initial conditions and odd periodicity. Previous work h ..."
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Cited by 118 (4 self)
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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 unpredictability, 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 approximated 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 selfsimilarity, neither randomness is required. Rather, TCP itself as a deterministic process creates chaos, which generates selfsimilarity. This property 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. KeywordsTCP congestion control, fractal traffic, chaotic models. I.
Connectionlevel Analysis and Modeling of Network Traffic
 in ACM SIGCOMM Internet Measurement Workshop
, 2001
"... Abstract — Most network traffic analysis and modeling studies lump all connections together into a single flow. Such aggregate traffic typically exhibits longrangedependent (LRD) correlations and nonGaussian marginal distributions. Importantly, in a typical aggregate traffic model, traffic bursts ..."
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Cited by 78 (5 self)
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Abstract — Most network traffic analysis and modeling studies lump all connections together into a single flow. Such aggregate traffic typically exhibits longrangedependent (LRD) correlations and nonGaussian marginal distributions. Importantly, in a typical aggregate traffic model, traffic bursts arise from many connections being active simultaneously. In this paper, we develop a new framework for analyzing and modeling network traffic that moves beyond aggregation by incorporating connectionlevel information. A careful study of many traffic traces acquired in different networking situations reveals (in opposition to the aggregate modeling ideal) that traffic bursts typically arise from just a few highvolume connections that dominate all others. We term such dominating connections alpha traffic. Alpha traffic is caused by large file transmissions over high bandwidth links and is extremely bursty (nonGaussian). Stripping the alpha traffic from an aggregate trace leaves a beta traffic residual that is Gaussian, LRD, and shares the same fractal scaling exponent as the aggregate traffic. Beta traffic is caused by both small and large file transmissions over low bandwidth links. In our alpha/beta traffic model, the heterogeneity of the network resources give rise to burstiness and heavytailed connection durations give rise to LRD. Queuing experiments suggest that the alpha component dictates the tail queue behavior for large queue sizes, whereas the beta component controls the tail queue behavior for small queue sizes. Keywords—network traffic modeling, animal kingdom I.
Explaining World Wide Web Traffic SelfSimilarity
, 1995
"... Recently the notion of selfsimilarity has been shown to apply to widearea and localarea network traffic. In this paper we examine the mechanisms that give rise to selfsimilar network traffic. We present an explanation for traffic selfsimilarity by using a particular subset of wide area traffic: ..."
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Cited by 73 (2 self)
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Recently the notion of selfsimilarity has been shown to apply to widearea and localarea network traffic. In this paper we examine the mechanisms that give rise to selfsimilar network traffic. We present an explanation for traffic selfsimilarity by using a particular subset of wide area traffic: traffic due to the World Wide Web (WWW). Using an extensive set of traces of actual user executions of NCSA Mosaic, reflecting over half a million requests for WWW documents, we show evidence that WWW traffic is selfsimilar. Then we show that the selfsimilarity in such traffic can be explained based on the underlying distributions of WWW document sizes, the effects of caching and user preference in file transfer, the effect of user "think time", and the superimposition of many such transfers in a local area network. To do this we rely on empirically measured distributions both from our traces and from data independently collected at over thirty WWW sites. 1 Introduction Understanding the ...
SelfSimilar Network Traffic: An Overview
, 1999
"... INTRODUCTION 1.1.1 Background Since the seminal study of Leland, Taqqu, Willinger and Wilson [41] which set the groundwork for considering selfsimilarity an important notion in the understanding of network traffic including the modeling and analysis of network performance, an explosion of work ha ..."
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Cited by 72 (5 self)
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INTRODUCTION 1.1.1 Background Since the seminal study of Leland, Taqqu, Willinger and Wilson [41] which set the groundwork for considering selfsimilarity an important notion in the understanding of network traffic including the modeling and analysis of network performance, an explosion of work has ensued investigating the multifaceted nature of this phenomenon. 1 The long held paradigm in the communication and performance communities has been that voice traffic and, by extension, data traffic are adequately described by certain Markovian models (e.g., Poisson) which are amenable to accurate analysis and efficient control. The first property stems from the welldeveloped field of Markovian analysis which allows tight equilibrium bounds on performance variables such as the waiting time in various queueing systems to be found. This also 1 For a nontechnical account of the discovery of the selfsimilar nature of network traffic, including parallel effort
Fast, Approximate Synthesis of Fractional Gaussian Noise for Generating SelfSimilar Network Traffic
 ACM SIGCOMM, Computer Communication Review
, 1997
"... Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically selfsimilar processes instead of traditional Poisson processes [LTWW94, PF95]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample p ..."
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Cited by 58 (2 self)
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Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically selfsimilar processes instead of traditional Poisson processes [LTWW94, PF95]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample paths) corresponding to selfsimilar traffic. We present a fast Fourier transform method for synthesizing approximate selfsimilar sample paths for one type of selfsimilar process, Fractional Gaussian Noise, and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate close approximations to true selfsimilar sample paths. We also discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle's estimator for H, the Hurst parameter giving the strength of longrange dependence present in a selfsimilar time series. 1
SelfSimilarity and LongRange Dependence Through the Wavelet Lens
, 2000
"... Selfsimilar and longrange dependent processes are the most important kinds of random processes possessing scale invariance. We describe how to analyze them using the discrete wavelet transform. We have chosen a didactic approach, useful to practitioners. Focusing on the Discrete Wavelet Transform, ..."
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Cited by 43 (7 self)
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Selfsimilar and longrange dependent processes are the most important kinds of random processes possessing scale invariance. We describe how to analyze them using the discrete wavelet transform. We have chosen a didactic approach, useful to practitioners. Focusing on the Discrete Wavelet Transform, we describe the nature of the wavelet coefficients and their statistical properties. Pitfalls in understanding and key features are highlighted and we sketch some proofs to provide additional insight. The Logscale Diagram is introduced as a natural means to study scaling data and we show how it can be used to obtain unbiased semiparametric estimates of the scaling exponent. We then focus on the case of longrange dependence and address the problem of defining a lower cutoff scale corresponding to where scaling starts. We also discuss some related problems arising from the application of wavelet analysis to discrete time series. Numerical examples using many discrete time models are th...
An Evaluation of Linear Models for Host Load Prediction
, 1998
"... This paper evaluates linear models for predicting the Digital Unix fivesecond load average from 1 to 30 seconds into the future. A detailed statistical study of a large number of load traces leads to consideration of the BoxJenkins models (AR, MA, ARMA, ARIMA), and the ARFIMA models (due to selfs ..."
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Cited by 43 (7 self)
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This paper evaluates linear models for predicting the Digital Unix fivesecond load average from 1 to 30 seconds into the future. A detailed statistical study of a large number of load traces leads to consideration of the BoxJenkins models (AR, MA, ARMA, ARIMA), and the ARFIMA models (due to selfsimilarity.) These models, as well as a simple windowedmean scheme, are evaluated by running a large number of randomized testcases on the load traces. The main conclusions are that load is consistently predictable to a useful degree, and that the simpler models such as AR are sufficient for doing this prediction.