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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. Self-Similarity.

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self similarity in world wide web traffic evidence and possible causes

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

self similarity
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

Kalyan Boggavarapu CSC 497 Lehigh University

data set
Data Set
  • Traces from NCSA Mosaic
  • Jan, Feb 1995
  • Logs: URL, session, User and workstation ID
  • Experiment Environment:
    • 37 SparkStation-2 workstations,

Kalyan Boggavarapu CSC 497 Lehigh University

parameters
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

Kalyan Boggavarapu CSC 497 Lehigh University

analysis in two stages
Analysis in two stages
  • Stage 1:
    • what is the appropriate value of H.
  • Stage 2:
    • Which parameter accurately measures this parameter H.

Kalyan Boggavarapu CSC 497 Lehigh University

self similarity for different time intervals
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

Kalyan Boggavarapu CSC 497 Lehigh University

self similarity characteristics graphs 1
Self Similarity characteristics graphs 1

Slope => H

This line is => H

Slope is => H

Kalyan Boggavarapu CSC 497 Lehigh University

whilttle estimator
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.

Kalyan Boggavarapu CSC 497 Lehigh University

slide12

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

Kalyan Boggavarapu CSC 497 Lehigh University

which parameter is responsible for self similarity
Which parameter is responsible for self similarity?

File requests => file transfers => unique files distribution

Alpha = 1.2

H (.7-.8)

Kalyan Boggavarapu CSC 497 Lehigh University

its available files
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)

Kalyan Boggavarapu CSC 497 Lehigh University

sources
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.

Kalyan Boggavarapu CSC 497 Lehigh University

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