Performance of Shared Memory in a Parallel Computer
Performance of Shared Memory in a Parallel Computer
Kevin Donovan
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In particular, we will see that the growth rate of the maximum queue length, and the fact that this value is concentrated at only a few values, is reflected in the propositions to be demonstrated in this section. 16 We start by defining the values ro and ri aiound which the maximum queue length clusters. ro = rj — 1, where Ti = min {r: F(l; n, m, r) n, and rj > A, the value Vi is well-defined. Before stating the theorem, we need to establish several lemmas. Lemma 10. Let A > be a rationai numb...er. Let n and m grow to infinity while maintaining a constant ratio A = n/m. Let tq and ri be defined as above. Then, as m goes to infinity, tq and ri also go to infinity. Proof. Assume the contrary. Suppose ri were bounded, say by ri 0m— e~^ • min{l, A^}, where = 1 + o(l).
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