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

Author

Listed:
  • Justin A. Mulvany

    (University of Southern California)

  • Amber L. Puha

    (California State University San Marcos)

  • Ruth J. Williams

    (University of California, San Diego)

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.

Suggested Citation

  • Justin A. Mulvany & Amber L. Puha & Ruth J. Williams, 2019. "Asymptotic behavior of a critical fluid model for a multiclass processor sharing queue via relative entropy," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 351-397, December.
    • Handle: RePEc:spr:queues:v:93:y:2019:i:3:d:10.1007_s11134-019-09629-8
    DOI: 10.1007/s11134-019-09629-8
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