1. 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

2. 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

3. 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

4. Kalyan Boggavarapu CSC 497 Lehigh University
11/28/2018
Kalyan Boggavarapu CSC Lehigh University

5. Self Similarity Characteristics

6. 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

7. 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

8. Stage 1: Estimate the value of H

9. 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

10. Self Similarity characteristics graphs 1
Slope => H
This line is => H
Slope is => H
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Kalyan Boggavarapu CSC Lehigh University

11. 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

12. 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

13. Stage 2: Which parameter is useful to estimate the value of H

14. 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

15. 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

16. 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