Power law condition for stability of Poisson hail

Abstract

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.

15 pages, 1 figure

Cited by in corpus (2)

• Stable Systems with Power Law Conditions for Poisson Hail
• Shape Theorems for Poisson Hail on a Bivariate Ground