  This paper addresses the question when the underlying Markov process of a
multiclass queueing network is positive Harris recurrent. It is well-known that
stability of the fluid limit model is a sufficient condition for this. Hence,
stability of fluid (limit) models is of vital interest. Recently, it has been
shown that if the fluid model satisfies certain properties, it is stable if and
only if there exists a Lyapunov function. In this paper a new method is
provided to conclude that the underlying Markov process is positive Harris
recurrent if the fluid model is stable by using explicitly the Lyapunov
function of the fluid model.
