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
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.
Published in Queueing Systems, 93 (2019), 351-397.
For access to the published paper, please
click here.