English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This work considers a server that processes $J$ classes using the generalizedprocessor sharing discipline with base weight vector $\alpha=(\alpha_1,...,\alpha_J)$ and redistribution weight vector$\beta=(\beta_1,...,\beta_J)$. The invariant manifold $\mathcal{M}$ of theso-called fluid limit associated with this model is shown to have the form$\mathcal{M}=\{x\in\mathbb{R}_+^J:x_j=0 for j\in\mathcal{S}\}$, where$\mathcal{S}$ is the set of strictly subcritical classes, which is identifiedexplicitly in terms of the vectors $\alpha$ and $\beta$ and the long-runaverage work arrival rates $\gamma_j$ of each class $j$. In addition, undergeneral assumptions, it is shown that when the heavy traffic condition$\sum_{j=1}^J\gamma_j=\sum_{j=1}^J\alpha_j$ holds, the functional central limitof the scaled unfinished work process is a reflected diffusion process thatlies in $\mathcal{M}$. The reflected diffusion limit is characterized by theso-called extended Skorokhod map and may fail to be a semimartingale. Thisgeneralizes earlier results obtained for the simpler, balanced case where$\gamma_j=\alpha_j$ for $j=1,...,J$, in which case $\mathcal{M}=\mathbb{R}_+^J$and there is no state-space collapse. Standard techniques for obtainingdiffusion approximations cannot be applied in the unbalanced case due to theparticular structure of the GPS model. Along the way, this work alsoestablishes a comparison principle for solutions to the extended Skorokhod mapassociated with this model, which may be of independent interest.

The heavy traffic limit of an unbalanced generalized processor sharing model