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Self Similarity in World Wide Web: Traffic Evidence and Possible Causes
Mark E. Crovella and Azer Bestavros Computer Science Dept, Boston University Presented by Kalyan Boggavarapu CSC 497 Lehigh University
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Kalyan Boggavarapu CSC 497 Lehigh University
Self-Similarity Def: is an object whose appearance is unchanged regardless of the scale it is used. Heavy tailed: a function exhibiting the power laws. E.g.: The geographical distribution of the people in the world. World Wide Web traffic can show Self-Similarity 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Kalyan Boggavarapu CSC 497 Lehigh University
Data Set Traces from NCSA Mosaic Jan, Feb 1995 Logs: URL, session, User and workstation ID Experiment Environment: 37 SparkStation-2 workstations, 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Kalyan Boggavarapu CSC 497 Lehigh University
11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Self Similarity Characteristics
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Kalyan Boggavarapu CSC 497 Lehigh University
Parameters Degree of self Similarity - H Hurst parameter H ,range of (1/2 , 1) H->1 is the max self-similarity In this paper we would see 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Kalyan Boggavarapu CSC 497 Lehigh University
Analysis in two stages Stage 1: what is the appropriate value of H. Stage 2: Which parameter accurately measures this parameter H. 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Stage 1: Estimate the value of H
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Self Similarity for different time intervals
Step 1: Estimate for short intervals ( 1 sec and above ) using: web traffic data for a single hr Plot: Variance Time plot, Rescaled range plot Periodogram plot Step 2: Estimate for scaling to large intervals Whittle Estimator 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Self Similarity characteristics graphs 1
Slope => H This line is => H Slope is => H 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Kalyan Boggavarapu CSC 497 Lehigh University
Whilttle Estimator Estimates: the confidence range of H Based: a time series FGN – Fractional Gaussian Noise Model Now check: if timeseries aggregation or Estimated H is consistent or not ? Infer: www traffic at stub networks is self similar when traffic is high in demand. 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Kalyan Boggavarapu CSC 497 Lehigh University
Expected feature: aggregation => H Aggregation over a long range shows stability of the hypothesis Whittle estimator confirms our earlier calculations of H H Fully busy Variance of 95% Confidence Interval of H Least busy H decreasing as it becomes less busy 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Stage 2: Which parameter is useful to estimate the value of H
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Which parameter is responsible for self similarity?
File requests => file transfers => unique files distribution Alpha = 1.2 H (.7-.8) 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Kalyan Boggavarapu CSC 497 Lehigh University
Its Available files Available files => Heavy tailed behavior of file transfer Conclusion: Distribution of available files => ( Web traffic self similarity = Heavy tailed distribution of file transfers) 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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Kalyan Boggavarapu CSC 497 Lehigh University
Sources: “Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes” (1996) Mark Crovella, Azer Bestavros Proceedings of SIGMETRICS'96: The ACM International Conference on Measurement and Modeling of Computer Systems. 11/28/2018 Kalyan Boggavarapu CSC Lehigh University
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