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Distribution-free bounds on the expectation of the maximum with scheduling applications. (English) Zbl 0715.90068
Summary: Let $$X_ 1,X_ 2,...,X_ n$$ be independent random variables with a fixed, common parent distribution for which the p-th moment $$E| X|^ p$$ is defined. Then the maximum order statistic $$X_{(n)}$$ grows at a rate that is $$o(n^{1/p})$$ in expectation, in probability and a.e. Explicit bounds of this order can be given for $$EX_{(n)}$$ in terms of the moments of X. Thus the expectation of the extreme grows slowly with the sample size. This observation is applied to the speed-up realized by parallel computation, and to the performance of scheduling policies.

##### MSC:
 90B35 Deterministic scheduling theory in operations research 68W15 Distributed algorithms
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##### References:
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