An ergodic result for queue length processes of state-dependent queueing networks in the heavy-traffic diffusion limit

We consider state-dependent queueing networks in the heavy-traffic diffusion limit. Specifically, we consider queue length processes jointly satisfying a reflecting stochastic differential equation in the non-negative orthant with state-dependent drift vector and state-dependent diffusion and reflection matrices. Such state-dependence arises in queueing networks when the subjacent network parameters, such as arrival and service rates and routing probabilities, depend on the states of other queues in the network. For this class of networks, we provide a useful ergodicity criterium characterizing the main stability properties in such diffusion limit regime.