Largest-first sequential selection with a sum constraint

Authors:
E. G. Coffman, Jr.;G. Fayolle;P. Jacquet;P. Robert
Affiliations:
AT&T Bell Laboratories, Murray Hill, NJ 07974, USA;INRIA, 78153 Le Chesnay, France;INRIA, 78153 Le Chesnay, France;INRIA, 78153 Le Chesnay, France
Venue:
Operations Research Letters
Year:
1990

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Abstract

Scan the order statistics X"("1") = X"("2") = ... = X"("n") of n independent samples from U[0, 1] in the order listed. The i-th number scanned, X"("i"), is selected if and only if the sum of X"("i") and the numbers already selected out of the first i -1 is no greater than 1. Let N(n) denote the total number selected. We prove that N~ @? lim"n"-"~E[N(n)] = 1 + @S"k"="1E[N(k)]/2^k^+^1 5/3, and that @bN"~ - E[N(n)] @b