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SelfSimilarity Through HighVariability: Statistical Analysis of Ethernet LAN Traffic at the Source Level
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is selfsimilar or longrange dependent in nature (i.e., bursty over a wide range of time scales)  in sharp contrast to commonly made tr ..."
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Cited by 740 (24 self)
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A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is selfsimilar or longrange dependent 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 provide a plausible physical explanation for the occurrence of selfsimilarity in LAN traffic. Our explanation is based on new convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical analyses of realtime traffic measurements from Ethernet LAN's at the level of individual sources. This paper is an extended version of [53] and differs from it in significant ways. In particular, we develop here the mathematical results concerning the superposition of strictly alternating ON/OFF sources. Our key mathematical result states that the superposition of many ON/OFF sources (also k...
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 98 (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.
The Importance of Powertail Distributions for Modeling Queueing Systems
, 1999
"... Powertail distributions are those for which the reliability function is of the form x \Gammaff for large x. Although they look well behaved, they have the singular property that E(X ` ) = 1 for all ` ff. Thus it is possible to have a distribution with an infinite variance, or even an infinite ..."
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Cited by 35 (11 self)
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Powertail distributions are those for which the reliability function is of the form x \Gammaff for large x. Although they look well behaved, they have the singular property that E(X ` ) = 1 for all ` ff. Thus it is possible to have a distribution with an infinite variance, or even an infinite mean. As pathological as these distributions seem to be, they occur everywhere in nature, from the CPU time used by jobs on mainframe computers to sizes of files stored on discs, earthquakes, or even healthinsurance claims. Recently, traffic on the "electronic super highway" was revealed to be of this type, too. In this paper we first describe these distributions in detail and show their suitability to model selfsimilar behavior e.g. of the traffic stated above. Then we show how these distributions can occur in computersystem environments and develop a socalled truncated analytical model that in the limit is powertail. We study and compare the effects on system performance of a GI/M/1 ...
Simulation of nonGaussian LongRangeDependent Traffic using Wavelets
, 1999
"... In this paper, we develop a simple and powerful multiscale model for the synthesis of nonGaussian, longrange dependent (LRD) network traffic. Although wavelets effectively decorrelate LRD data, waveletbased models have generally been restricted by a Gaussianity assumption that can be unrealistic f ..."
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Cited by 35 (4 self)
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In this paper, we develop a simple and powerful multiscale model for the synthesis of nonGaussian, longrange dependent (LRD) network traffic. Although wavelets effectively decorrelate LRD data, waveletbased models have generally been restricted by a Gaussianity assumption that can be unrealistic for traffic. Using a multiplicative superstructure on top of the Haar wavelet transform, we exploit the decorrelating properties of wavelets while simultaneously capturing the positivity and "spikiness" of nonGaussian traffic. This leads to a swift O(N) algorithm for fitting and synthesizing Npoint data sets. The resulting model belongs to the class of multifractal cascades, a set of processes with rich statistical properties. We elucidate our model's ability to capture the covariance structure of real data and then fit it to real traffic traces. Queueing experiments demonstrate the accuracy of the model for matching real data. Our results indicate that the nonGaussian nature of traffic has a significant effect on queuing.
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 31 (9 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.
Additive and multiplicative mixture trees for network traffic modeling
 in Proceedings ICASSP
, 2002
"... Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and Long range dependence at very large time scales to highly nonGaussian marginals and multifractal scaling on small scales. This behavior can be explained by forming two components of the traffic acc ..."
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Cited by 3 (1 self)
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Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and Long range dependence at very large time scales to highly nonGaussian marginals and multifractal scaling on small scales. This behavior can be explained by forming two components of the traffic according to the speed of connections, one component absorbing most traffic and being mostly Gaussian, the other constituting virtually all the small scale bursts. Towards a better understanding of this phenomenon, we propose a novel treebased model which is flexible enough to accommodate Gaussian as well as bursty behavior on different scales in a parsimonious way.
Multiscale Modeling and Queuing Analysis of LongRangeDependent Network Traffic
, 1999
"... We develop a simple multiscale model for the analysis and synthesis of nonGaussian, longrangedependent (LRD) network traffic loads. The wavelet transform effectively decorrelates LRD signals and hence is wellsuited to model such data. However, traditional waveletbased models are Gaussian in n ..."
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Cited by 2 (1 self)
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We develop a simple multiscale model for the analysis and synthesis of nonGaussian, longrangedependent (LRD) network traffic loads. The wavelet transform effectively decorrelates LRD signals and hence is wellsuited to model such data. However, traditional waveletbased models are Gaussian in nature which one may at the most hope to match second order statistics of inherently nonGaussian traffic loads. Using a multiplicative superstructure atop the Haar wavelet tree, we retain the decorrelating properties of wavelets while simultaneously capturing the positivity and "spikiness" of nonGaussian traffic. This leads to a swift O(N) algorithm for fitting and synthesizing Npoint data sets. The resulting model belongs to the class of multifractal cascades, a set of processes with rich scaling properties which are better suited than LRD to capture burstiness. We elucidate our model's ability to capture the covariance structure of real data and then fit it to real traffic traces. We derive approximate analytical queuing formulas for our model, also applicable to other multiscale models, by exploiting its multiscale construction scheme. Queuing experiments demonstrate the accuracy of the model for matching real data and the precision of our theoretical queuing results, thus revealing the potential use of the model for numerous networking applications. Our results indicate that a Gaussian assumption can lead to overoptimistic predictions of tail queue probability even when taking LRD into account.
A Case For Fractal Traffic Modeling
 II Australian Telecommunication and Network Applications Conference `96
, 1996
"... Developments in telecommunications technology have outpaced progress in teletraffic methods and practices. As a result, the planning and dimensioning of even the latest informationage services is, by default, commonly done on the basis of classical teletraffic methods developed for circuit switched ..."
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Cited by 1 (0 self)
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Developments in telecommunications technology have outpaced progress in teletraffic methods and practices. As a result, the planning and dimensioning of even the latest informationage services is, by default, commonly done on the basis of classical teletraffic methods developed for circuit switched voice networks. In this paper, we will discuss recent traffic measurement studies which have demonstrated that measured traffic streams from working packet switched networks exhibit variations and fluctuations over a wide range of time scales. We motivate the application of fractal models to parsimoniously represent this apparent complexity of actual network traffic, illustrate some immediate benefits that arise from moving beyond traditional traffic modeling concepts and accepting the idea of the fractal nature of network traffic dynamics, and discuss the use of fractal models to develop traffic management methods that are accurate, practical, and based on a solid understanding of the traffic observed in "reallife" packet switched networks.