Abstract
This paper presents results of diffusion approximations which may be used in the analysis of multiprogrammed computer systems. First of all we give a mathematical proof for the best CPU utilization under different priority rules in the case of one CPU and more DTU-s. With the help of the Brownian motion approximation we get an explicit result for a model considered by Gaver and Shedler in priority queues, without using the Wald identity. Some examples are given when the diffusion approximation is more complicated than the Brownian motion one.
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