In this paper we investigate the stability of a class of two-station multiclass uid 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 VandeVate , 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
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