Approximating Load Distributions in Time Sharing Systems

In studying the principle of decomposition Courtois suggested that the crossing point between the job-submission rate of time-sharing terminals and the job-completion rate of the computing system would approximate the mean number of active jobs. We have shown that the actual load distribution is approximated well by a normal distribution whose mean is calculated as Courtois suggested and whose variance is easily calculated from the parameters of the system. Numerical studies show that the approximation deteriorates when the coefficient of variation of the times between completions of jobs by the computing system gets too large