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130
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 213 (34 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.
On the Relevance of LongRange Dependence in Network Traffic
, 1996
"... There is much experimental evidence that network traffic processes exhibit ubiquitous properties of selfsimilarity and long range dependence (LRD), i.e., of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their im ..."
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Cited by 186 (1 self)
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There is much experimental evidence that network traffic processes exhibit ubiquitous properties of selfsimilarity and long range dependence (LRD), i.e., of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much recent modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the firstorder statistics such as the marginal distribution of the process.
The Importance of LongRange Dependence of VBR Video Traffic in ATM Traffic Engineering: Myths and Realities
 IN PROC. ACM SIGCOMM '96
, 1996
"... There has been a growing concern about the potential impact of longterm correlations (secondorder statistic) in variablebitrate (VBR) video traffic on ATM buffer dimensioning. Previous studies have shown that video traffic exhibits longrange dependence (LRD) (Hurst parameter large than 0.5). We ..."
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Cited by 145 (9 self)
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There has been a growing concern about the potential impact of longterm correlations (secondorder statistic) in variablebitrate (VBR) video traffic on ATM buffer dimensioning. Previous studies have shown that video traffic exhibits longrange dependence (LRD) (Hurst parameter large than 0.5). We investigate the practical implications of LRD in the context of realistic ATM traffic engineering by studying ATM multiplexers of VBR video sources over a range of desirable cell loss rates and buffer sizes (maximum delays). Using results based on large deviations theory, we introduce the notion of Critical Time Scale (CTS). For a given buffer size, link capacity, and the marginal distribution of frame size, the CTS of a VBR video source is defined as the number of frame correlations that contribute to the cell loss rate. In other words, secondorder behavior at the time scale beyond the CTS does not significantly affect the network performance. We show that whether the video source model i...
On the Effect of Traffic Selfsimilarity on Network Performance
, 1997
"... Recent measurements of network traffic have shown that selfsimilarity is an ubiquitous phenomenon present in both local area and wide area traffic traces. In previous work, we have shown a simple, robust application layer causal mechanism of traffic selfsimilarity, namely, the transfer of files i ..."
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Cited by 121 (10 self)
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Recent measurements of network traffic have shown that selfsimilarity is an ubiquitous phenomenon present in both local area and wide area traffic traces. In previous work, we have shown a simple, robust application layer causal mechanism of traffic selfsimilarity, namely, the transfer of files in a network system where the file size distributions are heavytailed. In this paper, we study the effect of scaleinvariant burstiness on network performance when the functionality of the transport layer and the nteraction of traffic sources sharing bounded network resources is incorporated. First, we show that transport layer mechanisms are important factors in translating the application layer causality into link traffic selfsimilarity. Network performance as captured by throughput, packet loss rate, and packet retransmission rate degrades gradually with increased heavytailedness while queueing delay, response time, and fairness deteriorate more drastically. The degree to which heavytailedness affects selfsimilarity is determined by how well congestion control is able to shape a source traffic into an onaverage constant output stream while conserving information. Second, we show that increasing network resources such as link bandwidth and buffer capacity results in a superlinear improvement in performance. When large file transfers occur with nonnegligible probability, the incremental
On multimedia networks: Selfsimilar traffic and network performance
 IEEE Communications Magazine
, 1999
"... he future will bring a wide variety of multimedia applications each with different traffic characteristics at optimized performance, to be carried by both wireless and wireline networks. In wireless mobile networks the offered traffic varies both temporally and spatially, with the spatial variation ..."
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Cited by 70 (0 self)
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he future will bring a wide variety of multimedia applications each with different traffic characteristics at optimized performance, to be carried by both wireless and wireline networks. In wireless mobile networks the offered traffic varies both temporally and spatially, with the spatial variation significantly higher than in wired networks. Models of the traffic offered to the network or a component of the network will be critical to providing high quality of service (QoS). Traffic models are used as the input to analytical or simulation studies of resource allocation strategies. We may view traffic at the application or packet level, where an applicationlevel view may simply describe the offered traffic as “a videoconference between three parties,” while the packetlevel view is given by a stochastic model
Point Process Approaches for Modeling and Analysis of SelfSimilar Traffic: Part II  Applications
, 1997
"... In previous work [24], Fractal Point Processes (FPPs) have been proposed as novel tools for understanding, modeling and analyzing diverse types of selfsimilar traffic behavior. We apply the FPP models in the context of network traffic modeling and performance analysis. Two qualitatively different f ..."
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Cited by 59 (8 self)
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In previous work [24], Fractal Point Processes (FPPs) have been proposed as novel tools for understanding, modeling and analyzing diverse types of selfsimilar traffic behavior. We apply the FPP models in the context of network traffic modeling and performance analysis. Two qualitatively different fractal data sets (Bellcore Ethernet traces) are characterized by FPP models. Comparison of modeldriven and tracedriven queueing simulation results show that the matched models yield close agreement with the traces over a wide range of system parameters. We also show that under suitable conditions, the FPP models yield Gaussian processes. Queueing simulation shows that the FPP models can be computationally efficient alternatives for generating fractional Gaussian noise processes. Finally, we divide fractal traffic into two types, applicationlevel fractal traffic and networklevel fractal traffic, and argue that each type has radically different implications for the design and control of fut...
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.
Practical TimeScale Fitting of SelfSimilar Traffic with MarkovModulated Poisson Process
, 2001
"... Recent measurements of packet/cell... In this paper, we first give some definitions of selfsimilarity. Then, we propose a fitting method for the selfsimilar traffic in terms of Markovmodulated Poisson process (MMPP). We construct an MMPP as the superposition of twostate MMPPs and fit it so as to ..."
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Cited by 33 (2 self)
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Recent measurements of packet/cell... In this paper, we first give some definitions of selfsimilarity. Then, we propose a fitting method for the selfsimilar traffic in terms of Markovmodulated Poisson process (MMPP). We construct an MMPP as the superposition of twostate MMPPs and fit it so as to match the variance function over several timescales. Numerical examples show that the variance function of the selfsimilar process can be well represented by that of resulting MMPPs. We also examine the queueing behavior of the resulting MMPP/D/1 queueing systems. We compare the analytical results of MMPP/D/1 with the simulation ones of the queueing system with selfsimilar input.
LongRange Dependence and HeavyTail Modeling for Teletraffic Data
 IEEE Signal Processing Magazine
, 2002
"... Analysis and modeling of computer network traffic is a daunting task considering the amount of available data. This is quite obvious when considering the spatial dimension of the problem, since the number of interacting computers, gateways and switches can easily reach several thousands, even in a L ..."
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Cited by 32 (3 self)
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Analysis and modeling of computer network traffic is a daunting task considering the amount of available data. This is quite obvious when considering the spatial dimension of the problem, since the number of interacting computers, gateways and switches can easily reach several thousands, even in a Local Area Network (LAN) setting. This is also true for the time dimension: W. Willinger and V. Paxson in [42] cite the figures of 439 million packets and 89 gigabytes of data for a single week record of the activity of a university gateway in 1995. The complexity of the problem further increases when considering Wide Area Network (WAN) data [28]. In light of the above, it is clear that a notion of importance for modern network engineering is that of invariants, i.e. characteristics that are observed with some reproducibility and independently of the precise settings of the network under consideration. In this tutorial paper, we focus on two such invariants related to the time d...
Internet Traffic Tends To Poisson and Independent as the Load Increases
, 2001
"... The burstiness of Internet traffic was established in pioneering work in the early 1990s, which demonstrated that packet arrival times are not Poisson, and packet and byte counts in fixedlength intervals are longrange dependent [17, 20]. Here we demonstrate that these results are one end of a con ..."
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Cited by 31 (1 self)
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The burstiness of Internet traffic was established in pioneering work in the early 1990s, which demonstrated that packet arrival times are not Poisson, and packet and byte counts in fixedlength intervals are longrange dependent [17, 20]. Here we demonstrate that these results are one end of a continuum of traffic characteristics. At the other end are Poisson behavior and independence. Our study focuses on packets, what devices actually see; we study the statistical properties of packet interarrival times and packet sizes. As the traffic load increases  that is, as the number of simultaneous transport connections increases  arrivals tend to Poisson and sizes tend to independence. More specifically, longrange dependence of interarrivals and sizes decreases to independence, and the marginal distribution of interarrivals tends toward exponential; this happens (1) through time on a single link as the load increases due to daily variation, or (2) at a single point in time as the load increases going from lightly loaded links at the edges of the Internet to heavily loaded links at the core. Convergence is rapid; the packet traffic gets quite close to Poisson and independent loads far less than the maximum we observe.