Copyright © 2009 Vincent Bansaye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line, in the closest free portions at the right of the arrival location. We specify the distribution of the space of unoccupied locations at a fixed time and give asymptotic regimes when the hardware is becoming full.