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The performance of the move-to-front scheme under some particular forms of Markov requests

Part of: Theory of data Computer system organization Markov processes

Published online by Cambridge University Press:  14 July 2016

Eliane R. Rodrigues
Eliane R. Rodrigues*
Affiliation:
Universidade de Brasília
*
∗Present address: Instituto de Matemáticas, UNAM, Area de la Investigación Científica, Circuita Exterior, Ciudad Universitaria, México DF 04510, México.
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Abstract

The move-to-front scheme is studied taking into account some forms of Markov dependence for the way items are requested. One of the dependences specifically rules out two consecutive requests for the same item. The other is the so-called p-correlation. An expression for the stationary distribution of the sequence of arrangements of items is given in each case. A necessary and sufficient condition for these distributions to belong to a particular class of distributions is also given. The mean search time for an item is calculated for each form of dependence and these are compared with the value obtained in the case of independent requests. Some properties of the sequence of requests are given. Finally, an expression for the variance of the search time is obtained.

Keywords

MARKOV DEPENDENCEMEAN SEARCH TIMESTATIONARY DISTRIBUTIONVARIANCE OF THE SEARCH TIME

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 68M20: Performance evaluation; queueing; scheduling 68P10: Searching and sorting
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1089 - 1102
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Most of this work was done while the author was doing her Ph.D. at Queen Mary and Westfield College, University of London, UK.

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