V-uniform ergodicity for state-dependent single class queueing networks

We consider single class queueing networks with state-dependent arrival and service rates. Under the uniform (in state) stability condition, it is shown that the queue length process is V-uniformly ergodic; that is, it has a transition probability kernel which converges to its limit geometrically quickly in the V-norm sense. Among several asymptotic properties of V-uniformly ergodic processes, we present a Strassen-type functional law of the iterated logarithm result.