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SHIFT-GENERATED RANDOM PERMUTATIONS AND THE M/D/1 QUEUE

Published online by Cambridge University Press:  01 May 1998

WOLFGANG STADJE
WOLFGANG STADJE
Affiliation:
Fachbereich Mathematik/Informatik, Universität Osnabrück, D-49069 Osnabrück, Germany
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Abstract

We consider a simple shift procedure which transforms any mapping f[ratio ]{0, …, n}→{0, …, n} into a permutation of 0, …, n. We study this shift under the assumption that the values f(0), …, f(n) are uniformly and independently chosen random numbers in {0, …, n}. The exact and asymptotic distributions of the required shift sizes are derived, and a connection to queueing theory is exhibited.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 3 , May 1998 , pp. 297 - 304
Copyright
© The London Mathematical Society 1998

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