TABLE OF CONTENTS Markov processes are powerful analytical tools applicable to the analysis of computer systems. They provide accurate, yet relatively simple means to construct representations of systems and to mathematically analyze a computer system. Markov processes require that we have an understanding of stochastic processes and their analysis. This chapter provides the background necessary to perform the modeling and analysis of such systems.
A stochastic process involves the representation of a family of random variables. A random variable is represented as a function on a variable, f( x), which approximates a number with the result of some experiment. The variable X is one possible value from a family of variables, from a sample space represented as ?. For example, for a toss of a coin the entire sample space is ? = {heads, tails}, and the random variable X may equal the mapping x = {1,0}, representing the functional mapping of the event set {heads, tails} to the event random variable mapping set {1,0}. (SeeTable 6.1.)
| Events | = | Heads | Tails |
|---|---|---|---|
| ? | ? | ||
| X | = | 0 | 1 |
A stochastic process is represented or described as a family of random variables, denoted X( t), where one value of the random variable X exists for each value of t. The random variable, X, has a set of possible values defined by the state space, X( t), for the random variable
