Power law condition for stability of Poisson hail
  We consider the Poisson hail model introduced by Baccelli and Foss. We give a power law condition for the tails (spatial and temporal) of the distribution of jobs to ensure stability as the rate parameter $\lambda $ tends to zero. We then show that in a weak sense it is optimal. 
Sergey Foss, Takis Konstantopoulos, Thomas Mountford
math.PR