Long-range dependence - Ten years of Internet traffic modeling

Department of Computer Science and Engineering, University of California, Riverside, Riverside, California, United States
IEEE Internet Computing (Impact Factor: 1.71). 10/2004; 8(5):57- 64. DOI: 10.1109/MIC.2004.46
Source: DBLP


Self-similarity and scaling phenomena have dominated Internet traffic analysis for the past decade. With the identification of long-range dependence (LRD) in network traffic, the research community has undergone a mental shift from Poisson and memory-less processes to LRD and bursty processes. Despite its widespread use, though, LRD analysis is hindered by the difficulty of actually identifying dependence and estimating its parameters unambiguously. The authors outline LRD findings in network traffic and explore the current lack of accuracy and robustness in LRD estimation. In addition, they present recent evidence that packet arrivals appear to be in agreement with the Poisson assumption in the Internet core.

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    • "Complex systems with inherent LRD have been described in many other fields, and its mathematical concepts are fruitfully employed. Numerous studies demonstrate LRD for example in geological and climate research (Scheffer et al., 2009; Varotsos and Kirk-Davidoff, 2006), finance market fluctuations (Matteo et al., 2005; Robinson, 2003), in Internet modeling and network traffic analysis (Abry et al., 2002; Karagiannis et al., 2004; Riedi et al., 1999), or statistic analyses of human language (Alvarez-Lacalle et al., 2006; Petersen et al., 2012). Fig. 1A shows an example of an ethernet bytes-per-time arrival, at two different aggregation levels. "
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    ABSTRACT: Highlights • EEG microstate sequences of the resting brain exhibit long-range dependency (LRD). • We describe why LRD is important and provide comparisons to other complex systems. • Hidden Markov Models (HMM) do not normally capture LRD. • We propose to test whether the proposed model of Gärtner et al. captures LRD.
    NeuroImage 05/2015; DOI:10.1016/j.neuroimage.2015.05.062 · 6.36 Impact Factor
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    • "The latest findings in the field of neurobiology concerning the functional Magnetic Resonance Imaging technique, suggest that the Hurst coefficient (see definition below) can be used as a biomarker for certain disorders including Alzheimer (Maxim et al. 2005), Parkinson (Rassouli 2006), autism (Lai 2010) and impulsive traits (Hahn et al. 2012). Finally, it is remarkable that scaling behaviour has been also identified in certain artificial processes, such as network traffic (Leeland 1994; Karagiannis et al. 2004) or econometrics (Lo 1991; Baille 1996; Serinaldi 2010). For instance, in the field of economy, the scaling behaviour has been detected in energy prices (Serletis and Rosenberg 2007), financial markets (Gama et al. 2008) and Spanish electricity spot market (Norouzzadeh et al. 2007). "
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    ABSTRACT: We overview studies of the natural variability of past climate, as seen from available proxy information, and its attribution to deterministic or stochastic controls. Furthermore, we characterize this variability over the widest possible range of scales that the available information allows, and we try to connect the deterministic Milankovitch cycles with the Hurst–Kolmogorov (HK) stochastic dynamics. To this aim, we analyse two instrumental series of global temperature and eight proxy series with varying lengths from 2 thousand to 500 million years. In our analysis, we use a simple tool, the climacogram, which is the logarithmic plot of standard deviation versus time scale, and its slope can be used to identify the presence of HK dynamics. By superimposing the climacograms of the different series, we obtain an impressive overview of the variability for time scales spanning almost nine orders of magnitude—from 1 month to 50 million years. An overall climacogram slope of −0.08 supports the presence of HK dynamics with Hurst coefficient of at least 0.92. The orbital forcing (Milankovitch cycles) is also evident in the combined climacogram at time scales between 10 and 100 thousand years. While orbital forcing favours predictability at the scales it acts, the overview of climate variability at all scales suggests a big picture of irregular change and uncertainty of Earth’s climate.
    Surveys in Geophysics 01/2014; 34(2). DOI:10.1007/s10712-012-9208-9 · 3.45 Impact Factor
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    • "Long-range dependence (LRD) is a relative new statistical concept in time series analysis. The most well-known models of long-range dependent processes are fractional Brownian motion (fBm) and FARIMA, [5]. In [6] the asymptotically behavior of the autocorrelation of a fGn is analyzed. "
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    ABSTRACT: In the last few years the long-range dependence analysis of time-series became more important. A key parameter characterizing long-range dependent processes is the Hurst parameter H. The goal of this paper is to compare some estimation techniques for the Hurst parameter. We found that the best estimator is the one based on the second order discrete wavelet transform statistical analysis and works for second order wide sense stationary random processes.
    Optimization of Electrical and Electronic Equipment (OPTIM), 2012 13th International Conference on; 05/2012
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