The Annals of Applied Probability

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

Amber L. Puha and 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 ∞. 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.

Article information

Source
Ann. Appl. Probab. Volume 14, Number 2 (2004), 517-554.

Dates
First available in Project Euclid: 23 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1082737103

Digital Object Identifier
doi:10.1214/105051604000000017

Mathematical Reviews number (MathSciNet)
MR2052894

Zentralblatt MATH identifier
1061.60098

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

Keywords
Processor sharing queue critical fluid model measure-valued solution invariant states coupling renewal processes renewal functions renewal measures

Citation

Puha, Amber L.; Williams, Ruth J. Invariant states and rates of convergence for a critical fluid model of a processor sharing queue. Ann. Appl. Probab. 14 (2004), no. 2, 517--554. doi:10.1214/105051604000000017. https://projecteuclid.org/euclid.aoap/1082737103


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