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May 2004 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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Ann. Appl. Probab. 14(2): 517-554 (May 2004). DOI: 10.1214/105051604000000017

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 ∞. 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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Amber L. Puha. Ruth J. Williams. "Invariant states and rates of convergence for a critical fluid model of a processor sharing queue." Ann. Appl. Probab. 14 (2) 517 - 554, May 2004. https://doi.org/10.1214/105051604000000017

Information

Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1061.60098
MathSciNet: MR2052894
Digital Object Identifier: 10.1214/105051604000000017

Subjects:
Primary: 60K25
Secondary: 68M20, 90B22

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 2 • May 2004
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