CS457 - System Performance Evaluation - Winter 2010

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Lecture 21 - Binomial Distributions, Poisson Processes (pdf)

Other Distributions

The exponential distribution pretty well takes care of arrival events in open systems. What about

These are normally modelled based on distributions that are abstractions of behaviour observed in logs or traces. Here are a few that turn up from time to time.

Bernoulli & BinomialDistributions

Systems that are easily categorized into two distinct homogeneous classes.


Think times

Service times


Coin-flipping is the natural analogue, but it covers any binary choice made at (biased!) random.

How do you sample a Bernoulli distribution in practice


Make N binary choices at random, all identical.

How do you sample a binomial distribution in practice

  1. Small N: sample a Bernoulli N times,
  2. Medium N: divide the range [0,L) into N+1 parts proportional to (N choose k) and do binary search with u
  3. Large N: converge to another distribution

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