Stochastic Systems

Asymptotic behavior of a critical fluid model for a processor sharing queue via relative entropy

Amber L. Puha and Ruth J. Williams

Full-text: Open access

Abstract

In this paper, we develop a new approach to studying the asymptotic behavior of fluid model solutions for critically loaded processor sharing queues. For this, we introduce a notion of relative entropy associated with measure-valued fluid model solutions. In contrast to the approach used in [12], which does not readily generalize to networks of processor sharing queues, we expect the approach developed in this paper to be more robust. Indeed, we anticipate that similar notions involving relative entropy may be helpful for understanding the asymptotic behavior of critical fluid model solutions for stochastic networks operating under various resource sharing protocols naturally described by measure-valued processes.

Article information

Source
Stoch. Syst., Volume 6, Number 2 (2016), 251-300.

Dates
Received: July 2015
First available in Project Euclid: 22 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1490148013

Digital Object Identifier
doi:10.1214/15-SSY198

Mathematical Reviews number (MathSciNet)
MR3633537

Zentralblatt MATH identifier
1359.60113

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60F17: Functional limit theorems; invariance principles
Secondary: 60G57: Random measures 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

Keywords
Queueing processor sharing critical fluid model fluid model asymptotics relative entropy

Rights
Creative Commons Attribution 4.0 International License.

Citation

Puha, Amber L.; Williams, Ruth J. Asymptotic behavior of a critical fluid model for a processor sharing queue via relative entropy. Stoch. Syst. 6 (2016), no. 2, 251--300. doi:10.1214/15-SSY198. https://projecteuclid.org/euclid.ssy/1490148013


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References

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