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Simple Binomial Approximation |
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Suppose n is equal to 1. For a simple processor-memory configuration, there is no memory contention and the achieved bandwidth is B(m, 1) = 1. Now if m = 1 and n > 1, there is contention but the achieved bandwidth is the same, B(1, n) = 1. Simple processor configurations do not randomly generate requests each cycle, and hence the queueing models do not accurately describe behavior for low values of n and m. For small n or m (since any solution is symmetric), the binomial rather than the Poisson is a better characterization of the request distribution. |
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Suppose we now substitute the queue size for the MB/D/1 (binomial arrivals) for the M/D/1 as used in the development of the asymptotic solution. |
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and for this the processor always (Prob = 1) makes one request each Tc. As seen from a given module: |
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Note now that if either n or m = 1, B(m, n) = 1, since |
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