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This paper studies the fluid approximation (also known as the functionalstrong law-of-large-numbers) and the stability (positive Harris recurrent) for a multiclassqueueing network. Both of these are related to the stabilities of a linear fluid model,constructed from the first-order parameters (i.e., long-run average arrivals, services androutings) of the queueing network. It is proved that the fluid approximation for thequeueing network exists if the corresponding linear fluid model is...

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