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Hendricks libraries and Tsetlin piles

Published online by Cambridge University Press:  01 July 2016

Jacques-Edouard Dies
Jacques-Edouard Dies*
Affiliation:
Université Paul Sabatier
*
∗ Postal address: Laboratoire de Statistiques et Probabilitiés, Université Paul Sabatier, 118 route de Narbonne, 31077 Toulouse, France.
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Abstract

In order to study the transience of Hendricks libraries, we introduce and study a special class of Markov chains, the Tsetlin d-piles, generalizing Tsetlin libraries and briefly defined as follows: a 1-pile is a Tsetlin library and a d-pile is a Tsetlin library where each book is replaced by a (d − 1)-pile. We give a stationary measure of these chains and establish the necessary and sufficient conditions for positive recurrence and transience. Finally, the study of d-piles allows us to determine a sufficient condition for transience of quite a large class of Hendricks libraries.

Keywords

DENUMERABLE MARKOV CHAINSTSETLIN LIBRARYTRANSIENCEPAGING ALGORITHMS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 1 , March 1982, pp. 37 - 55
Copyright
Copyright © Applied Probability Trust 1982 

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References

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