Fluid Approximations and Stability of Multiclass Queueing Networks: Work-Conserving Disciplines

This paper studies the uid approximation (also known as the functional strong law-of-large-numbers) and the stability (positive Harris recurrent) for a multiclass queueing network. Both of these are related to the stabilities of a linear uid model, constructed from the rst-order parameters (i.e., long-run average arrivals, services and routings) of the queueing network. It is proved that the uid approximation for the queueing network exists if the corresponding linear uid model is weakly stable, and that the queueing network is stable if the corresponding linear uid model is (strongly) stable. Suucient conditions are found for the stabilities of a linear uid model.

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