Stability of fluid networks with proportional routing

In this paper we investigate the stability of a class of two-station multiclass fluid networks with proportional routing. We obtain explicit necessary and sufficient conditions for the global stability of such networks. By virtue of a stability theorem of Dai, these results also give sufficient conditions for the stability of a class of related multiclass queueing networks. Our study extends the results of Dai and Vande Vate, who provided a similar analysis for fluid models without proportional routing, which arise from queueing networks with deterministic routing. The models we investigate include fluid models which arise from a large class of two-station queueing networks with probabilistic routing. The stability conditions derived turn out to have an appealing intuitive interpretation in terms of virtual stations and push-starts which were introduced in earlier work on multiclass networks.