  We consider a queue where the server is the Euclidean space, and the
customers are random closed sets (RACS) of the Euclidean space. These RACS
arrive according to a Poisson rain and each of them has a random service time
(in the case of hail falling on the Euclidean plane, this is the height of the
hailstone, whereas the RACS is its footprint). The Euclidean space serves
customers at speed 1. The service discipline is a hard exclusion rule: no two
intersecting RACS can be served simultaneously and service is in the First In
First Out order: only the hailstones in contact with the ground melt at speed
1, whereas the other ones are queued; a tagged RACS waits until all RACS
arrived before it and intersecting it have fully melted before starting its own
melting. We give the evolution equations for this queue. We prove that it is
stable for a sufficiently small arrival intensity, provided the typical
diameter of the RACS and the typical service time have finite exponential
moments. We also discuss the percolation properties of the stationary regime of
the RACS in the queue.
