A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is self-similar or long-range 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 self-similarity 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 real-time 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...

Abstract — Most network traffic analysis and modeling studies lump all connections together into a single flow. Such aggregate traffic typically exhibits long-range-dependent (LRD) correlations and non-Gaussian 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 connection-level 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 high-volume 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 (non-Gaussian). 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 heavy-tailed 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.

In this paper, we develop a simple and powerful multiscale model for the synthesis of nonGaussian, long-range dependent (LRD) network traffic. Although wavelets effectively decorrelate LRD data, wavelet-based 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 N-point 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.

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Abstract—Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of long-range 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, wavelet-based model that captures the positivity, LRD, and “spikiness ” of non-Gaussian traffic. Using a binary tree, the model synthesizes an-point 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 tree-based 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 time-resolutions affects queuing and that a Gaussian assumption can lead to over-optimistic predictions of tail queue probability even when taking LRD into account. I.

We develop a simple multiscale model for the analysis and synthesis of nonGaussian, long-range-dependent (LRD) network traffic loads. The wavelet transform effectively decorrelates LRD signals and hence is well-suited to model such data. However, traditional wavelet-based 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 N-point 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 over-optimistic predictions of tail queue probability even when taking LRD into account.

Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and Long range dependence at very large time scales to highly non-Gaussian 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 tree-based model which is flexible enough to accommodate Gaussian as well as bursty behavior on different scales in a parsimonious way.

Developments in telecommunications technology have outpaced progress in teletraffic methods and practices. As a result, the planning and dimensioning of even the latest information-age 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 "real-life" packet switched networks.