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Stability of Fluid Networks with Proportional Routing

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Abstract

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 [14], 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 [19], 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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  1. Graduate Program in Operations Research and Industrial Engineering, Department of Mechanical Engineering, University of Texas at Austin, Austin, TX, 78712-1063, USA

    John J. Hasenbein

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Hasenbein, J.J. Stability of Fluid Networks with Proportional Routing. Queueing Systems 38, 327–354 (2001). https://doi.org/10.1023/A:1010959706486

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