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

We say that a random variable is $light$-$tailed$ if moments of order$2+\epsilon$ are finite for some $\epsilon>0$; otherwise, we say that it is$heavy$-$tailed$. We study queueing networks that operate under the Max-Weightscheduling policy, for the case where some queues receive heavy-tailed and somereceive light-tailed traffic. Queues with light-tailed arrivals are often delaystable (that is, expected queue sizes are uniformly bounded over time) but canalso become delay unstable because of resource-sharing with other queues thatreceive heavy-tailed arrivals.  Within this context, and for any given "tail exponents" of the input traffic,we develop a necessary and sufficient condition under which a queue is robustlydelay stable, in terms of $jumping$ $fluid$ models - an extension oftraditional fluid models that allows for jumps along coordinates associatedwith heavy-tailed flows. Our result elucidates the precise mechanism that leadsto delay instability, through a coordination of multiple abnormally largearrivals at possibly different times and queues and settles an earlier openquestion on the sufficiency of a particular fluid-based criterion. Finally, weexplore the power of Lyapunov functions in the study of delay stability.

Jumping Fluid Models and Delay Stability of Max-Weight Dynamics under Heavy-Tailed Traffic