Long-range dependence ten years of Internet traffic modeling

Dept. of Comput. Sci. & Eng., California Univ., Riverside, CA, USA;
IEEE Internet Computing (Impact Factor: 2.04). 10/2004; 8(5):57- 64. DOI: 10.1109/MIC.2004.46
Source: DBLP

ABSTRACT 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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    ABSTRACT: It has been previously shown that actual network traffic exhibits long–range dependence. The Hurst parameter captures the degree of long–range dependence; however, because of the nature of computer network traffic, the Hurst parameter may not remain constant over a long period of time. An iterative method to compute the value of the Hurst parameter as a function of time is presented and analyzed. Experimental results show that the proposed method provides a good estimation of the Hurst parameter as a function of time. Additionally, this method allows the detection on changes of the Hurst parameter for long data series. The proposed method is compared with traditional methods for Hurst parameter estimation. Actual and synthetic traffic traces are used to validate our results. The proposed method allows detecting the changing points on the Hurst parameter, and better results can be obtained when modeling self–similar series using several values of the Hurst parameter instead of only one for the entire series. A new graphical tool to analyze long–range dependent series is proposed. Because of the nature of this plot, it is called the transition–variance plot. This tool may be helpful to distinguish between LAN and WAN traffic. Finally, the software LRD Lab* is deployed to analyze and synthesize long–range dependent series. The LRD Lab includes a simple interface to easily generate, analyze, visualize and save long–range dependent series.
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    Michael A Kouritzin, Samira Sadeghi
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    ABSTRACT: The Marcinkiewicz Strong Law, lim n→∞ 1 n 1 p n ∑ k=1 (D k − D) = 0 a.s. with p ∈ (1, 2), is studied for outer products D k = X k X T k , where {X k }, {X k } are both two-sided (multivariate) linear processes (with coefficient matrices (C l), (C l) and i.i.d. zero-mean innovations {Ξ}, {Ξ}). Matrix sequences C l and C l can decay slowly enough (as |l| → ∞) that {X k , X k } have long-range dependence while {D k } can have heavy tails. In particular, the heavy-tail and long-range-dependence phenomena for {D k } are handled simultaneously and a new decoupling property is proved that shows the convergence rate is determined by the worst of the heavy-tails or the long-range dependence, but not the combination. The main result is applied to obtain Marcinkiewicz Strong Law of Large Numbers for stochastic approximation, non-linear functions forms and autocovariances.
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    Michael Kouritzin, Samira Sadeghi


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