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/

Zendy Plus

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

Zendy Tools

Zendy Open

We introduce a "system-wide safety staffing" (SWSS) parameter for multiclassmulti-pool networks of any tree topology, Markovian or non-Markovian, in theHalfin-Whitt regime. This parameter can be regarded as the optimal reallocationof the capacity fluctuations (positive or negative) of order $\sqrt{n}$ wheneach server pool employs a square-root staffing rule. We provide an explicitform of the SWSS as a function of the system parameters, which is derived usinga graph theoretic approach based on Gaussian elimination.  For Markovian networks, we give an equivalent characterization of the SWSSparameter via the drift parameters of the limiting diffusion. We show that ifthe SWSS parameter is negative, the limiting diffusion and the diffusion-scaledqueueing processes are transient under any Markov control, and cannot have astationary distribution when this parameter is zero. If it is positive, we showthat the diffusion-scaled queueing processes are uniformly stabilizable, thatis, there exists a scheduling policy under which the stationary distributionsof the controlled processes are tight over the size of the network. Inaddition, there exists a control under which the limiting controlled diffusionis exponentially ergodic. Thus we have identified a necessary and sufficientcondition for the uniform stabilizability of such networks in the Halfin-Whittregime.  We use a constant control resulting from the leaf elimination algorithm tostabilize the limiting controlled diffusion, while a family of Markovscheduling policies which are easy to compute are used to stabilize thediffusion-scaled processes. Finally, we show that under these controls theprocesses are exponentially ergodic and the stationary distributions haveexponential tails.

On system-wide safety staffing of large-scale parallel server networks