Abstract
Two models involving multiprocessor systems with two different groups of processors are examined. In the first model, the processors which are in use break down from time to time; one of the two groups is used only when the other one is entirely inoperative. In the second model, the breakdowns are replaced by a Poisson stream of jobs. Again, one group of processors is used in preference to the other one. In both cases, the analysis is based on finding a polynomial in two variables which satisfies a partial differential-functional equation. Exact solutions are obtained.
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