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 study infinite server queues driven by Cox processes in a fast oscillatoryrandom environment. While exact performance analysis is difficult, we establishdiffusion approximations to the (re-scaled) number-in-system process by provingfunctional central limit theorems (FCLTs) using a stochastic homogenizationframework. This framework permits the establishment of quenched and annealedlimits in a unified manner. At the quantitative level, we identity twoparameter regimes, termed subcritical and supercritical indicating the relativedominance between the two underlying stochasticities driving our system: therandomness in the arrival intensity and that in the serivce times. We show thatwhile quenched FCLTs can only be established in the subcritical regime,annealed FCLTs can be proved in both cases. Furthermore, the limitingdiffusions in the annealed FCLTs display qualitatively different diffusivityproperties in the two regimes, even though the stochastic primitives areidentical. In particular, when the service time distribution is heavy-tailed,the diffusion is sub- and super-diffusive in the sub- and super-critical cases.The results illustrate intricate interactions between the underlying drivingforces of our system.

Diffusion Approximations for $\text{Cox}/G_t/\infty$ Queues In A Fast Oscillatory Random Environment