Hostname: page-component-7dd5485656-kp629 Total loading time: 0 Render date: 2025-10-29T12:03:27.754Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Hendricks, W. J. (1972) The stationary distribution of an interesting Markov chain. J. Appl. Prob. 9, 231–233.Google Scholar
Hendricks, W. J. (1973) An extension of a theorem concerning an interesting Markov chain. J. Appl. Prob. 10, 886–890.Google Scholar
Lauvergnat, G. (1976) Etude de méthodes de réorganisation automatique pour des structures d'information. Thèse de spécialité, Clermont-Ferrand.Google Scholar
Letac, G. (1974) Transience and recurrence of an interesting Markov chain. J. Appl. Prob. 11, 818–824.Google Scholar
Letac, G. (1978) Chaînes de Markov sur les permutations. SMS. Presses de l'Université de Montréal.Google Scholar
Nelson, P. R. (1975) Library Type Markov chains. Ph.D. Dissertation, Case Western Reserve University, Cleveland.Google Scholar
Tsetlin, M. L. (1963) Finite automata and models of simple form of behavior. Russian Math. Surveys 18 (4), 1–28.Google Scholar