On a model for the storage of files on a hardware II : Evolution of a   typical data block
  We consider a generalized 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, at the right of their arrival point. We study here the evolution of the extremities of the data block straddling 0, which is empty at time 0 and is equal to $\RRR$ at a deterministic time. 
Vincent Bansaye (PMA)