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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