by Unknown Authors

by Unknown Authors

Basic notions of probability theory are applied to problems of performance analysis of on-line real-time systems. Frequently used is APL as both an analytical tool and as a scratch pad in working out the examples. Elements of probability for system design by A. 0. Allen Modern on-line computer systems are complex and, therefore, often difficult to analyze. This paper aims at providing a directed review of probability theory and problems that are necessary for further study of queuing theory and queuing models. The ap-proach here is to introduce the basic concepts through practical examples. It is important to have access to a computer when designing and analyzing computer systems. An APL terminal system was used in writing this paper. Therefore, suggestions, examples, and calculations are given in terms of that system. Of course, any programming language with computational capability, such as FORTRAN, ALGOL. BASIC or PL/l, may be used to Write programs for expressing the algorithms or models of this paper. Basic concepts of probability theory The most basic concept in probability theory is that of a sample space. The phenomenon under study is assumed to be described as an experiment that can be repeated under the same conditions. A sample space of such an experiment is a set S of sample points or elementary events so chosen that the outcome of each event of the experiment corresponds to exactly one element of the set S and vice versa. The concept of sample space is illustrated by the following example.

basic concept sample space probability theory apl terminal system vice versa on-line real-time system performance analysis system design elementary event directed review analytical tool basic notion write program scratch pad computer system allen modern on-line computer system programming language experiment corresponds computational capability practical example sample point following example

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