Invariant States and Rates of Convergence for a Critical Fluid Model of a Processor Sharing Queue
A. L. Puha and R. J. Williams

This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid models as time approaches infinity. The main theorems of the paper provide sufficient conditions for a fluid model solution to converge to an invariant state and, under slightly more restrictive assumptions, provide a rate of convergence. These results are used in a related work by Gromoll for establishing a heavy traffic diffusion approximation for a processor sharing queue.

Annals of Applied Probability, 14 (2004), 517-554.
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