A Lyapunov view on positive Harris recurrence of multiclass queueing networks

In this paper we prove the positive Harris recurrence of the underlying Markov process of a multiclass queueing network. Using the fact that under certain conditions the stability of a fluid network is equivalent to the existence of a continuous Lyapunov function, we propose a new method to conclude that the underlying Markov process is positive Harris recurrent if the associated fluid network model is stable by using explicitly the Lyapunov function of the fluid network.