Stability of multiclass queueing networks under priority service disciplines

In this paper, we establish a sufficient condition for the stability of a multiclass fluid network and queueing network under priority service disciplines. The sufficient condition is based on the existence of a linear Lyapunov function, and it is stated in terms of the feasibility of a set of linear inequalities that are defined by network parameters. In all the networks we have tested, this sufficient condition actually gives a necessary and sufficient condition for their stability.