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Queueing Systems

, Volume 93, Issue 3–4, pp 351–397 | Cite as

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

  • Justin A. Mulvany
  • Amber L. PuhaEmail author
  • Ruth J. Williams
Article
  • 37 Downloads

Abstract

This work concerns the asymptotic behavior of critical fluid model solutions for a multiclass processor sharing queue under general distributional assumptions. Such critical fluid model solutions are measure-valued functions of time. We prove that critical fluid model solutions converge to the set of invariant states as time goes to infinity, uniformly for all initial conditions lying in certain relatively compact sets. This generalizes an earlier single-class result of Puha and Williams to the more complex multiclass setting. In particular, several new challenges are overcome, including formulation of a suitable relative entropy functional and identifying a convenient form of the time derivative of the relative entropy applied to trajectories of critical fluid model solutions.

Keywords

Queueing Multiclass processor sharing Critical fluid model Fluid model asymptotics Relative entropy 

Mathematics Subject Classification

Primary 60K25 60F17 Secondary 60G57 68M20 90B22 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Marshall School of BusinessUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsCalifornia State University San MarcosSan MarcosUSA
  3. 3.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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