Software Performance and Scalability: A Quantitative Approach

Appendix A. Stochastic Equilibrium and Ergodicity

	So much of life, it seems to me, is determined by pure randomness.
	--Sidney Poitier

In this appendix, a more thorough covering of random processes is provided to accommodate the needs of those who wish to dive deeper on the theories about random processes and those who wish to know more about how some of the important concepts derived thereof can be borrowed to help understand software performance and scalability challenges better. It is particularly important to understand the concepts of stochastic equilibrium and ergodicity, not only because they are the foundations on which most of the useful queuing models are built, but also because they represent the desirable conditions that many systems are designed to develop into.

BASIC CONCEPTS

We continue with where we left off in Section 4.2 by further elaborating on the concept of random variables.

Random Variables

In probability theory, a random variable is a variable whose values are random and to which a probability distribution is assigned. For example, when you access a Web application, there can only be one of the two outcomes: Available (A) or Unavailable (U). If you access the same Web application twice over a time period, based on the status of the Web application at the time it was accessed, then there could be two out of the four possible outcomes to describe your experience: (UU, UA, AU, AA). If we assign a random variable (X) to denote the number of times the Web application ...