3.7 Independence

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3.7 Independence

Another very important concept in performance modeling and analysis is that of independence. An action or event is considered independent of another event or action if the occurrence of one does not influence the outcome of the other. For example, the tossing of a coin followed by the rolling of a die are independent, since the coin's toss has no impact on the outcome. If we look at these events as two separate sample spaces, the interaction of these events becomes clearer. The sample space for the coin's toss is simply the set {H,T}, and the sample space for the die is simply the set {1,2,3,4,5,6}. The sample space in Figure 3.5 is the Cartesian product of these two independent spaces.

Figure 3.5: Cartesian product of two independent sample spaces.

The independence of events in a system is an important concept to consider when evaluating systems. If two events are independent, we need not consider these as related items requiring us to examine their response in relation to each other and their environment.

In a computer system, two programs that cannot run concurrently with each other can be viewed as independent items and analyzed as such. Even though they run on the same hardware and possibly use the same operating systems software, since they cannot interfere with each other and are not dependent in terms of sequencing, they can be evaluated as separate, unrelated items. It becomes an important part of our modeling and analysis of a system to define all elements and their relationship to each other. These definitions can then be used to aid in the determination of independence. We will discuss this property of events further when we look at probability and then map this to computer systems elements.

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