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The transposition replacement policy with a partial memory

Published online by Cambridge University Press:  14 July 2016

Peter R. Nelson
Peter R. Nelson*
Affiliation:
G. D. Searle & Co.
*
∗Postal address: Searle Research and Development, Division of G.D. Searle & Co., Box 5110, Chicago, IL 60680, U.S.A.
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Abstract

Consider as a model for any serial list a bookshelf with books B1, ···, Bn. At each unit of time book is demanded with probability pi and is replaced one position to the left of where it was removed (or in the same position if it is already at the left-hand end). If this transposition is made only when Bi has been demanded k times in a row, we show that the average position of the next book demanded is a monotone decreasing function of k.

Keywords

DELAYED POLICIESPARTIAL MEMORYTRANSPOSITION POLICY
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 733 - 736
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research supported in part by NSF Grant No. MCS78–02634.

References

Hendricks, W. J. (1976) An account of self-organizing systems. SIAMJ. Computing 5,715–723.Google Scholar
Kan, Y. C. and Ross, S. M. (1980) Optimal list order under partial memory constraints. J. Appl. Prob. 17, 1004–1015.Google Scholar
Letac, G. (1978) Chaînes de Markov sur les Permutations. Séminaire de Mathématiques Supérieures, 63. Les Presses de l'Université de Montréal, Montréal, Québec.Google Scholar