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 paper considers the tail asymptotics for a cumulative process $\{B(t); t\ge 0\}$ sampled at a heavy-tailed random time $T$. The main contribution ofthis paper is to establish several sufficient conditions for the asymptoticequality ${\sf P}(B(T) > bx) \sim {\sf P}(M(T) > bx) \sim {\sf P}(T>x)$ as $x\to \infty$, where $M(t) = \sup_{0 \le u \le t}B(u)$ and $b$ is a certainpositive constant. The main results of this paper can be used to obtain thesubexponential asymptotics for various queueing models in Markovianenvironments. As an example, using the main results, we derive subexponentialasymptotic formulas for the loss probability of a single-server finite-bufferqueue with an on/off arrival process in a Markovian environment.

Tail asymptotics for cumulative processes sampled at heavy-tailed random times with applications to queueing models in Markovian environments