The Joint Distribution of Internet Flow Sizes and Durations

1
The Joint Distribution of Internet Flow Sizes
and Durations

• CHEOLWOO PARK
• J. STEPHEN MARRON
• The University of North Carolina at Chapel Hill

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The Joint Distribution of Internet Flow Sizes and
Durations

• Motivation of the study
• Data description, scatter plots and density
  estimation
• Correlation plots
• Conclusions and future plans

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The Joint Distribution of Internet Flow Sizes and
Durations

• Started from conflict between two papers
• Extremal Dependence Internet Traffic
  Applications (2002) - Felix Hernandez Campos, J.
  S. Marron, Sidney I. Resnick and Kevin Jeffay
• On the Characteristics and Origins of Internet
  Flow Rates (2002) - Yin Zhang, Lee Breslau, Vern
  Paxson and Scott Shenker, SIGCOMM02

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The Joint Distribution of Internet Flow Sizes and
Durations

• Why interested in this topic?
• Size and rate are naturally considered as
  independent
• Users determine sizes of files transferred
  depending on their available bandwidths?
• Modeling of Internet traffic

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The Joint Distribution of Internet Flow Sizes and
Durations

• Different earlier analyses of Internet Flow Sizes
  and Durations

S Size, D Duration, R (S/D) Rate, IR
Inverse Rate

• Nearly contradictory answers!

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The Joint Distribution of Internet Flow Sizes and
Durations

• Why? Possibilities
• Data from different sources?
• Different types of data? (HTTP Resp. vs all web
  traces)
• Different correlation measure?

• Different threshold values?

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The Joint Distribution of Internet Flow Sizes and
Durations

• Threshold values

• applied thresholding to different variables
• used different threshold values

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The Joint Distribution of Internet Flow Sizes and
Durations

• Motivation of the study
• Data description, scatter plots and density
  estimation
• Correlation plots
• Conclusions and future plans

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The Joint Distribution of Internet Flow Sizes and
Durations

• Data
• HTTP responses
• Sunday Morning (800 AM 1200 PM)
• In April 2001
• From UNC Main Link

• Variables of Interest
• S  Size (bytes)
• D  Duration (time in seconds)
• R  Rate (throughput, byte/sec)
• IR  Inverse Rate (sec/byte)

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The Joint Distribution of Internet Flow Sizes and
Durations

• Scatterplot log10(Size) vs. log10(Duration)

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The Joint Distribution of Internet Flow Sizes and
Durations

• Scatterplot log10(Size) vs. log10(Rate)

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The Joint Distribution of Internet Flow Sizes and
Durations

• Scatterplot log10(Duration) vs. log10(Inv. Rate)

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The Joint Distribution of Internet Flow Sizes and
Durations

• Motivation of the Study
• Data description and scatter plots
• Log-log correlation plots with global
  thresholdings
• Conclusions and future plans

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The Joint Distribution of Internet Flow Sizes and
Durations
log10(Size) vs. log10(Duration)
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The Joint Distribution of Internet Flow Sizes and
Durations
log10(Size) vs. log10(Rate)
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The Joint Distribution of Internet Flow Sizes and
Durations
log10(Duration) vs. log10(Inv. Rate)
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The Joint Distribution of Internet Flow Sizes and
Durations
Simulated bivariate normal
log10(Size) vs. log10(Rate)
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The Joint Distribution of Internet Flow Sizes and
Durations

• Motivation of the Study
• Data description and scatter plots
• Log-log correlation plots with global
  thresholdings
• Conclusions and future plans

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The Joint Distribution of Internet Flow Sizes and
Durations

• Conclusions
• The blind men and the elephant
• Thresholding is CRITICAL

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The Joint Distribution of Internet Flow Sizes and
Durations

• Deeper investigation
• What values should we use ?
• On Size ?
• On Duration ?
• On Both ?
• How to handle 0 durations ?
• Which methods are robust to thresholding?