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].