19: Self-similarity and LRD

"Unfortunately, the world has not been designed for the convenience of mathematicians." - Benoit MandelbrotLecture outline: What is self-similar traffic and how can it be modeled mathematically? What effects does it have on network performance and design?

Preamble: Voice vs. data networks. Data networks belong to extremistan (contains wild randomness).

1. Self-similarity in network traffic

Spot the computer generated fake (two examples: natural scenery, and a time-series)

Poisson modeling of network traffic: why Poisson models are poor models of network traffic?

Fractal models of network traffic: how they are better models of network traffic?

How to establish self-similarity? 1) Aggregated and original time-series 2) Autocorrelation function (ACF), and 3) Variance Plots.

2. Long range dependence (LRD)

Self-similarity, heavy tails and long-range dependence.

LRD: ACF decays like a power-law.

Rescaled adjusted range (R/S) statistics.

3. SS/LRD and network traffic

LAN/ WAN traffic is Fractal and not Poisson.

Web (HTTP) traffic is Fractal.

Fractal topology of the Internet.

Implications of self-similarity on network performance.

Primary reference for this lecture:

“High Speed Networks and Internets: Performance and Quality of Service” by William Stallings; Chapter 9: “Self-Similar Traffic”

Secondary references for this lecture:

1. “Wide-Area Traffic: The Failure of Poisson Modeling” by Vern Paxson and Sally Floyd [link].

2. “Internet Traffic Measurement” by Carey Williamson [link].

3. “Self-similarity in World Wide Web traffic: evidence and possible causes” by Crovella et al. [link].

4. “On the Self-similar Nature of Ethernet Traffic” by Leland et al. [link].