17: Common Distributions (Extremistan)

"Most quantities of interest, most projections, most numerical assessments are not point estimates. Rather they are rough distributions — not always normal, sometimes bi-modal, sometimes exponential, sometimes something else." - John Allen Paulos"We must be careful not to confuse data with the abstractions we use to analyze them" - William James.Lecture outline: What are some commonly used distributions that apply to performance evaluation studies of computer networks?

1. Exponential distribution and generalizations (still in the realm of mild randomness)

Exponential distribution;

Gamma distribution;

Phase type distributions;

Hypoexponential and Hyperexponential distributions;

Weibull distribution;

Comparison between Gamma and Weibull distributions

2. Extremistan: long tailed distributions

Weibull distribution (a long-tailed distribution)

Power-law vs. Exponential decay

Heavy-tailed (Power-Law) vs. Long-tailed distributions

Pareto distribution (a heavy tailed distribution)

Lognormal distribution (another long-tailed distribution)

Primary reference for this lecture:

“The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling” by Raj Jain; Chapter 29: “Commonly Used Distributions”.

Secondary references for this lecture:

“Fundamentals of Performance Evaluation of Computer and Telecommunication System”, by Obaidat and Boudriga; Chapter 10: “Commonly Used Distributions in Simulation and Their Applications”.