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On a Model for the Storage of Files on a Hardware. II. Evolution of a Typical Data Block

Part of: Markov processes Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Vincent Bansaye
Vincent Bansaye*
Affiliation:
Université Pierre et Marie Curie and CNRS
*
∗Postal address: Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, UMR 7599, 175 rue du Chevaleret, 75013 Paris, France. Email address: bansaye@ccr.jussieu.fr
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Abstract

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We consider the generalized version in continuous time of the parking problem of Knuth introduced in Bansaye (2006). Files arrive following a Poisson point process and are stored on a hardware identified with the real line, at the right of their arrival point. Here we study the evolution of the endpoints of the data block straddling 0, which is empty at time 0 and is equal to R at a deterministic time.

Keywords

Parking problemdata storagerandom coveringPoisson point processLévy process

MSC classification

Secondary: 60D05: Geometric probability and stochastic geometry 60G55: Point processes 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 901 - 927
Copyright
Copyright © Applied Probability Trust 2007 

References

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