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An extension of a theorem concerning an interesting Markov chain

Published online by Cambridge University Press:  14 July 2016

W. J. Hendricks
W. J. Hendricks*
Affiliation:
Case Western Reserve University
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Abstract

In a single-shelf library of N books we suppose that books are selected one at a time and returned to the kth position on the shelf before another selection is made. Books are moved to the right or left as necessary to vacate position k. The probability of selecting each book is assumed to be known, and the N! arrangements of the books are considered as states of an ergodic Markov chain for which we find the stationary distribution.

Keywords

ERGODIC MARKOV CHAINSTORAGE AND SEARCHINVENTORY
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 886 - 890
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Burville, P. J. and Kingman, J. F. C. (1973) On a model for storage and search. J. Appl. Prob. 10, 697–701.Google Scholar
[2] Hendricks, W. J. (1972) The stationary distribution of an interesting Markov chain. J. Appl. Prob. 9, 231–233.Google Scholar