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Estimation and identification of long-range dependence in Internet traffic

Estimation and identification of long-range dependence in Internet traffic. Thomas Karagiannis ( tkarag@cs.ucr.edu ) University of California, Riverside / CAIDA. Long-range dependence (LRD). LRD captures the “memory” of the behavior Past values affect the present

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Estimation and identification of long-range dependence in Internet traffic

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  1. Estimation and identification of long-range dependence in Internet traffic Thomas Karagiannis (tkarag@cs.ucr.edu) University of California, Riverside / CAIDA

  2. Long-range dependence (LRD) • LRD captures the “memory” of the behavior • Past values affect the present • LRD describes scaling properties of a series • Statistical properties are independent of scale of observation • It is quantified by a single scalar number • Hurst power-law exponent • LRD appears in many aspects of networks • Traffic load, arrival times, delays • Shift from the traditional Poisson modeling and independence assumption to LRD and heavy tail modeling samsi 2003

  3. Questions regarding LRD • How can we identify LRD? • How can we estimate the intensity of LRD? • Where does LRD exist? • What causes LRD? • What are the effects of LRD? • How can we use LRD? samsi 2003

  4. LRD estimation • Long-range dependence: • Demonstrate the failure of the estimators • Inaccuracy • Sensitivity • Provide practical guidelines in LRD estimation • SELFIS (Self – Similarity Analsysis) • Software tool for LRD estimation • http://www.cs.ucr.edu/~tkarag/Selfis/Selfis.html samsi 2003

  5. LRD estimation • Evaluating the accuracy of the estimators • Synthetic fractional Gaussian noise (FGN) and fractional ARIMA time-series • Large difference in estimator results for synthesized LRD series with known Hurst exponent • Evaluating the robustness of the estimators • Periodicity, noise, trend, short-term correlations • Estimation methodologies significantly affected • Towards robust estimation: • Provide practical guidelines and algorithms to achieve robust estimation (under submission) samsi 2003

  6. LRD Estimation: The SELFIS tool samsi 2003

  7. LRD Estimation: The SELFIS tool • Design: • Java-based, platform-independent • Free, modular • Classes of function • Self-Similarity and long-range dependence analysis • Fractional Gaussian noise generators • Data processing algorithms (smoothing, stationarity tests) • Benefits: • Repeatability and consistency • Leverage of expertise among different disciplines • Ease of use • 200 Downloads from researchers spanning various disciplines and organizations samsi 2003

  8. LRD in backbone traffic • Examine Internet traffic in the backbone (to appear in INFOCOM 2004) : • OC48 link (2.4Gbps) traces taken by CAIDA monitors at a Tier 1 Internet Service Provider (ISP) • Traces from the WIDE backbone (WIDE project) • Large number of independent sources • Huge traffic multiplexing samsi 2003

  9. LRD in backbone traffic • Examine Poisson assumptions • Study LRD in byte/packet counts at different time-scales • Compare findings to “historical” Bellcore traces • Identify the relevant time scale for LRD samsi 2003

  10. LRD in backbone traffic: Findings • Time dependent Poisson characterization of network traffic that when viewed across very long time scales, exhibits the observed long-range dependence • Backbone traffic • Sub-second time-scales : Poisson • Multi-second time-scales : Piecewise-linear nonstationarity • Large time-scales : Long-range dependence samsi 2003

  11. Conclusions • LRD estimation: • Identify caveats • Propose solutions • LRD identification: • LRD in backbone traffic • Identify characteristics in different time-scales samsi 2003

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