Invariant states and rates of convergence for a critical fluid model of a processor sharing queue
Amber L. Puha and Ruth J. Williams
Source: Ann. Appl. Probab. Volume 14, Number 2
(2004), 517-554.
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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Keywords: Processor sharing queue; critical fluid model; measure-valued solution; invariant states; coupling renewal processes; renewal functions; renewal measures
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1082737103
Digital Object Identifier: doi:10.1214/105051604000000017
Mathematical Reviews number (MathSciNet): MR2052894
Zentralblatt MATH identifier: 02100746
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