Results 1  10
of
30
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.
Multiresolution markov models for signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 121 (17 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for selfsimilar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
Fast Approximation of SelfSimilar Network Traffic
, 1995
"... Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically selfsimilar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample ..."
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Cited by 94 (0 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 [LTWW94a, PF94]. 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 and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate a closer approximation to true selfsimilar sample paths than the other known fast method (Random Midpoint Displacement). We then 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 s...
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.
SmallTime Scaling Behaviors of Internet Backbone Traffic: An Empirical Study
 In Proceedings of the IEEE Infocom
, 2003
"... Abstract — We study the smalltime (subseconds) scaling behaviors of Internet backbone traffic, based on traces collected from OC3/12/48 links in a tier1 ISP. We observe that for a majority of these traces, the (secondorder) scaling exponents at small time scales (1ms 100ms) are fairly close to ..."
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Cited by 59 (5 self)
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Abstract — We study the smalltime (subseconds) scaling behaviors of Internet backbone traffic, based on traces collected from OC3/12/48 links in a tier1 ISP. We observe that for a majority of these traces, the (secondorder) scaling exponents at small time scales (1ms 100ms) are fairly close to 0.5, indicating that traffic fluctuations at these time scales are (nearly) uncorrelated. In addition, the traces manifest mostly monofractal behaviors at small time scales. The objective of the paper is to understand the potential causes or factors that influence the smalltime scalings of Internet backbone traffic via empirical data analysis. We analyze the traffic composition of the traces along two dimensions – flow size and flow density. Our study uncovers dense flows (i.e., flows with bursts of densely clustered packets) as the correlationcausing factor in small time scales, and reveals that the traffic composition in terms of proportions of dense vs. sparse flows plays a major role in influencing the smalltime scalings of aggregate traffic. I.
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
A survey on wavelet applications in data mining
 SIGKDD Explor. Newsl
"... Recently there has been significant development in the use of wavelet methods in various data mining processes. However, there has been written no comprehensive survey available on the topic. The goal of this is paper to fill the void. First, the paper presents a highlevel datamining framework tha ..."
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Cited by 30 (3 self)
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Recently there has been significant development in the use of wavelet methods in various data mining processes. However, there has been written no comprehensive survey available on the topic. The goal of this is paper to fill the void. First, the paper presents a highlevel datamining framework that reduces the overall process into smaller components. Then applications of wavelets for each component are reviewd. The paper concludes by discussing the impact of wavelets on data mining research and outlining potential future research directions and applications. 1.
Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Longmemory Parameter
 Journal of Forecasting
, 1999
"... We develop an ordinary least squares estimator of the long memory parameter from a fractionally integrated process that is an alternative to the Geweke PorterHudak estimator. Using the wavelet transform from a fractionally integrated process, we establish a loglinear relationship between the wavel ..."
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Cited by 29 (6 self)
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We develop an ordinary least squares estimator of the long memory parameter from a fractionally integrated process that is an alternative to the Geweke PorterHudak estimator. Using the wavelet transform from a fractionally integrated process, we establish a loglinear relationship between the wavelet coe cients ' variance and the scaling parameter equal to the long memory parameter. This loglinear relationship yields a consistent ordinary least squares estimator of the long memory parameter when the wavelet coe cients ' population variance is replaced by their sample variance. We derive the small sample bias and variance of the ordinary least squares estimator and test it against the Geweke PorterHudak estimator and the McCoy Walden maximum likelihood wavelet estimator by conducting a numberofMonte Carlo experiments. Based upon the criterion of choosing the estimator which minimizes the mean squared error, the wavelet OLS approach was superior to the Geweke PorterHudak estimator, but inferior to the McCoy Walden wavelet estimator for the processes simulated. However, given the simplicity of programming and running the wavelet OLS estimator and its statistical inference of the long memory parameter we feel the general practitioner will be attracted to wavelet OLS estimator. Keywords
Multifractal Processes
, 1999
"... This paper has two main objectives. First, it develops the multifractal formalism in a context suitable for both, measures and functions, deterministic as well as random, thereby emphasizing an intuitive approach. Second, it carefully discusses several examples, such as the binomial cascades and sel ..."
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Cited by 28 (6 self)
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This paper has two main objectives. First, it develops the multifractal formalism in a context suitable for both, measures and functions, deterministic as well as random, thereby emphasizing an intuitive approach. Second, it carefully discusses several examples, such as the binomial cascades and selfsimilar processes with a special eye on the use of wavelets. Particular attention is given to a novel class of multifractal processes which combine the attractive features of cascades and selfsimilar processes. Statistical properties of estimators as well as modelling issues are addressed.
Multiscale queuing analysis of longrangedependent network traffic
 Proc. IEEE INFOCOM
, 2000
"... Abstract—Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of longrange dependence (LRD) and marginal statistics still remains on unsure footing. In this paper, we study these two issues by introducing a multiscale traffic ..."
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Cited by 25 (6 self)
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Abstract—Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of longrange dependence (LRD) and marginal statistics still remains on unsure footing. In this paper, we study these two issues by introducing a multiscale traffic model and a novel multiscale approach to queuing analysis. The multifractal wavelet model (MWM) is a multiplicative, waveletbased model that captures the positivity, LRD, and “spikiness ” of nonGaussian traffic. Using a binary tree, the model synthesizes anpoint data set with only computations. Leveraging the tree structure of the model, we derive a multiscale queuing analysis that provides a simple closed form approximation to the tail queue probability, valid for any given buffer size. The analysis is applicable not only to the MWM but to treebased models in general, including fractional Gaussian noise. Simulated queuing experiments demonstrate the accuracy of the MWM for matching real data traces and the precision of our theoretical queuing formula. Thus, the MWM is useful not only for fast synthesis of data for simulation purposes but also for applications requiring accurate queuing formulas such as call admission control. Our results clearly indicate that the marginal distribution of traffic at different timeresolutions affects queuing and that a Gaussian assumption can lead to overoptimistic predictions of tail queue probability even when taking LRD into account. I.