Abstract
A class of piecewise linear Lyapunov functions are used to obtain the sufficient conditions for the stability of multiclass fluid networks under priority service disciplines. This extends and generalizes existing work that is based on a linear Lyapunov function. This also complements the existing work that uses the piecewise linear Lyapunov function approach to study the global stability of multiclass queueing networks. A three-station network example is used to illustrate the quality of this sufficient condition. The preliminary results indicate that the piecewise linear Lyapunov function approach yields better sufficient conditions and provides a promising approach.
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