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Simulation of requests for service from a large number of low duty cycle independent users is apt to cause a severe computational load. A method is presented for the software implementation of an efficient simulator. It can be applied to the investigation of many time-sharing systems, such as satellite demand assignment (DA), computer time sharing, and traffic routing. More generally, the method generates independent multivariate Poisson distributions when the number of variables is very large and the value of the parameter in each distribution is very small.