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- W1569202264 abstract "We consider the process [ A(t)=mt+sigma int _0^t X(u) d u,qquad tgeq 0, ] describing the queue length, where $m$ and $sigma$ are positive constants, $X(u)$ is a $varphi$-sub-Gaussian generalized OrnsteinâUhlenbeck stochastic process, and [ varphi (u)= begin {cases} u^r, & |u| >1, u^2, & |u|le 1, end {cases}] $rgeq 2$. The classes of $varphi$-sub-Gaussian and strictly $varphi$-sub-Gaussian stochastic processes are wider than the class of Gaussian processes and are of interest for modeling stochastic processes appearing in queueing theory and in the mathematics of finance. We obtain an estimate of the probability that the queue length exceeds the maximum allowed for it, namely, [ mathsf {P}left {sup _{tgeq 0}left (A(t) -c t right )>x right }le L(gamma ) x^{r/(r-1)}exp left {-kappa (gamma )x^{r/(2(r-1))}right }, ] where $c>m$ is the service intensity, $x>0$ is the maximum queue length, and $L(gamma )$ and $kappa (gamma )$ are some finite constants." @default.
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- W1569202264 date "2007-01-22" @default.
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- W1569202264 doi "https://doi.org/10.1090/s0094-9000-07-00691-6" @default.
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