Invariant states and rates of Convergence for a critical fluid model of a processor sharing queue

Details Invariant states and rates of Convergence for a critical fluid model of a processor sharing queue Invariant states and rates of Convergence for a critical fluid model of a processor sharing queue

2004-05-14

arxiv.org/abs/math/0405289v1

Annals of Applied Probability 2004, Vol. 14, No. 2, 517-554

Mathematics

Probability

Scientific paper

10.1214/105051604000000017

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 \infty. 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.

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