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

Amber L. Puha; Ruth J. Williams

doi:10.1214/105051604000000017

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

Amber L. Puha·Ruth J. Williams

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Abstract

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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BibTeX RIS

Amber L. Puha, Ruth J. Williams. 2004-05-14. Invariant states and rates of Convergence for a critical fluid model of a processor sharing queue. https://doi.org/10.1214/105051604000000017

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