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

A Lyapunov view on positive Harris recurrence of multiclass queueing networks