Moment Stability Properties of State-dependent Queueing Networks

We consider a class of queueing networks with state-dependent arrival and service rates. Under the uniform (in state) stability condition, we establish several moment stability properties of the queue length process: (i) the unique invariant measure of the queue length process admits a finite moment generating function in a neighborhood of zero; (ii) the expected value of unbounded (and possibly exponentially growing) functionals of the state process converges to the expectation under the invariant measure at an exponential rate; (iii) uniform (in time and initial condition in a compact set) estimates on exponential moments of the process; (iv) growth estimates of polynomial moments of the process as a function of the initial conditions. We note that our approach provides elementary proofs of these stability properties without resorting to the convergence of the scaled process to a stable fluid limit model.