Wavelet analysis of long-range-dependent traffic

Abry, Patrice; Veitch, Darryl

doi:10.1109/18.650984

Cited by 806 publications

(677 citation statements)

References 28 publications

(49 reference statements)

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“…A number of additional studies have also compared wavelet-based approaches to Whittle and other approaches [6,339,378]. These generally show the wavelet approach to be better, in terms of both reduced bias and variability (and hence, tighter confidence intervals).…”

Section: Comparison Of Resultsmentioning

confidence: 99%

“…The identification and analysis of such effects are done using wavelets [6,566,662]. Wavelet analysis (as described in Section 7.4.5) is reminiscent of spectral analysis in the sense that the signal being studied is expressed in terms of a set of basis functions, or, rather, in terms of the coefficients of the different basis functions.…”

Section: More Complex Scaling Behaviormentioning

confidence: 99%

“…A completely different approach to analyzing and measuring scaling effects is to use multiresolution analysis with wavelets [6,3,5]. The idea is to start with a basic oscillating pattern of limited duration -the wavelet -and check its correlation to the data at different scales and shifts.…”

Section: Using Wavelets and Logscale Diagramsmentioning

confidence: 99%

“…The procedure is simple [6,7,5]. For each scale j, we compute the average of the squares of the details at that scale d j,k .…”

Section: Logscale Diagrams and Self-similaritymentioning

confidence: 99%

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Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

191

131

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Reliable performance evaluations require the use of representative workloads. This is no easy task since modern computer systems and their workloads are complex, with many interrelated attributes and complicated structures. Experts often use sophisticated mathematics to analyze and describe workload models, making these models difficult for practitioners to grasp. This book aims to close this gap by emphasizing the intuition and the reasoning behind the definitions and derivations related to the workload models. It provides numerous examples from real production systems, with hundreds of graphs. Using this book, readers will be able to analyze collected workload data and clean it if necessary, derive statistical models that include skewed marginal distributions and correlations, and consider the need for generative models and feedback from the system. The descriptive statistics techniques covered are also useful for other domains.

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Section: Comparison Of Resultsmentioning

confidence: 99%

Section: More Complex Scaling Behaviormentioning

confidence: 99%

Section: Using Wavelets and Logscale Diagramsmentioning

confidence: 99%

“…The procedure is simple [6,7,5]. For each scale j, we compute the average of the squares of the details at that scale d j,k .…”

Section: Logscale Diagrams and Self-similaritymentioning

confidence: 99%

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Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

191

131

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“…Além disso, os coeficientes da DWT de um sinal 1/f são praticamente não-correlacionados (intra e inter-escalas) [4]. Por essa razão, as wavelets têm sido amplamente empregadas nas análise e síntese (simulação) de sinais fractais [52].…”

Section: Waveletunclassified

Contribuições à geração de tráfego fractal por meio da transformada wavelet.

Lund¹

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ResumoEstudos mostraram que o tráfego nas redes de dados tanto locais quanto de grandeárea, possui propriedades fractais como dependência de longa duração -Long-Range Dependence (LRD) e auto-similaridade. Devidoà heterogeneidade de aplicações nessas redes, os traces de tráfego podem apresentar dependência de longa duração -Long Range Dependence (LRD), dependência de curta duração -Short Range Dependence (SRD) ou uma mistura de LRD com SRD.Sendo assim, este trabalho tem como objetivo sintetizar séries temporais gaussianas com flexibilidade de processamento no plano tempo-freqüência a serem inseridas num gerador de tráfego com as características estatísticas específicas do tráfego encontrado em redes por comutação de pacotes reais, como autosimilaridade, LRD e SRD. Para isto foram desenvolvidos dois métodos para síntese de séries temporais gaussianas com LRD e simultânea introdução de SRD em diferentes faixas de freqüência: Discrete Wavelet Tansform (DWT) com mapa de variâncias e Discrete Wavelet Packet Tansform (DWPT). Estes métodos utilizaram o mapa de variâncias cujo conceito foi desenvolvido neste trabalho.A validação dos métodos foi feita através de análise estatística e comparação com resultados de séries geradas pelo método Discrete Wavelet Transfom (DWT) de Bäckar utilizado em [1]. Além disso, também foi validada a idéia de que a DWPTé mais interessante que a DWT por ser mais flexível e prover uma maior flexibilidade de processamento no plano tempo-freqüência.

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Self‐Similar Network Traffic: An Overview

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SELF-SIMILAR NETWORK TRAFFIC: AN OVERVIEWto the shape of the whole, i.e., it is self-similar. Of course, this is not too surprising since the constructive process-by its recursive action-endows the limiting object with the scale-invariance property.The 1-dimensional Cantor set, e.g., as obtained by projecting the 2-D Cantor set onto the line, can be given an interpretation as a traffic series Xt 2 f 0; 1g-call it "Cantor traffic"-where Xt = 1 means that there is a packet transmission at time t. This is depicted in Figure 1. 1.2 (left). If the constructive process is terminated at iteration n 0, then the contiguous line segments of length 1=3 n may be interpreted as on-periods or packet trains of duration 1=3 n , and the segments between successive on-periods as off-periods or absence of traffic activity. Nonuniform traffic intensities may be imparted by generalizing the constructive framework via the use of probability measures. For example, for the 1-dimensional Cantor set, instead of letting the left and right components after scaling have identical "mass," they may be assigned different mass, subject to the constraint that the total mass be preserved at each stage of the iterative construction. This modification corresponds to defining a probability measure on the Borel subsets of 0; 1 and distributing the measure at each iteration nonuniformly left and right. Note that the classical Cantor set construction-viewed as a map-is not measure-preserving. Figure 1shows such a construction with weights L = 2 =3, R = 1 =3 for the left and right components, respectively. The probability measure is represented by "height"; we observe that scale-invariance is exactly preserved. In general, the traffic patterns producible with fixed weights L , R are limited, but one can extend the framework by allowing possibly different weights associated with every edge in the weighted viii SELF-SIMILAR NETWORK TRAFFIC: AN OVERVIEW processes which are nondecreasing processes whose differences-also called increment process-constitute the original process. For example, for the on/off Cantor traffic construction (cf. Figure 1.1.2 (left)), let us assign the interpretation that time is discrete such that at step n 0, it ranges over the values t = 0; 1=3 n ; 2=3 n ; : : : ; 3 n , 1=3 n ; 1. Thus we can equivalently index the discrete time steps by i = 0; 1; 2; : : : ; 3 n . With a slight abuse of notation, let us redefine X as Xi = 1 if, and only if, in the original process Xi=3 n = 1 and Xi=3 n , " = 1 for all 0 " 1=3 n . That is, for i values for which an on-period in the original process Xt begins at t = i=3 n , Xi is defined to be zero. Thus, in the case of n = 2 , we have

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Wavelet analysis of long-range-dependent traffic

Cited by 806 publications

References 28 publications

Workload Modeling for Computer Systems Performance Evaluation

Workload Modeling for Computer Systems Performance Evaluation

Contribuições à geração de tráfego fractal por meio da transformada wavelet.

Self‐Similar Network Traffic: An Overview

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