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

Justin A. Mulvany (), Amber L. Puha () and Ruth J. Williams ()
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Justin A. Mulvany: University of Southern California
Amber L. Puha: California State University San Marcos
Ruth J. Williams: University of California, San Diego

Queueing Systems: Theory and Applications, 2019, vol. 93, issue 3, No 7, 397 pages

Abstract: 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; Primary 60K25; 60F17; Secondary 60G57; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11134-019-09629-8

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