Thomas Mountford (Polytechnique Fédérale de Lausanne)
Stability results for queues
We consider the Poisson rain model for queues introduced by Bacceli and Foss: points in Z^d represent servers. Jobs arrive as a Poisson process. Each job has an associated service time and a team (subset of Z^d) that are required to work on it. We suppose this Poisson process is invariant with respect to lattice shifts. The questions addressed are when (given the law of teams and job length) the system is stable for sufficiently small arrival rate and this being so, can we say that the stable workload distribution is unique.