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- Title
Asymptotic behavior of a critical fluid model for a multiclass processor sharing queue via relative entropy.
- Authors
Mulvany, Justin A.; Puha, Amber L.; Williams, Ruth J.
- 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.
- Subjects
ENTROPY; INVARIANT sets; TOPOLOGICAL entropy; ASYMPTOTIC efficiencies; BEHAVIOR
- Publication
Queueing Systems, 2019, Vol 93, Issue 3/4, p351
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-019-09629-8