A simple cyclic-queue model of a multiprogramming system with a fixed number of tasks is analyzed in its steady state. Expressions for queue-size distribution, average rate of job completions, and average stay-in-the-system time are derived. A measure of system efficiency alternative to processor utilization is suggested and optimal values for the degree of multiprogramming are given for various values of the parameters.
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Isi Mitrani (1972) studied this question.
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