Asymptotic Behavior of the Thermodynamical Limit for Symmetric Closed Queueing Networks

We study the thermodynamical limit for a mean-field model describing how a closed symmetric queueing network operates. The Markov process under consideration is invariant under the action of a certain symmetry group $G$ in the phase space. We prove that the quotient process on the space of orbits of the $G$-action converges to a limit deterministic dynamical system.