Application of $$\varphi$$ -Sub-Gaussian Random Processes in Queueing Theory

DOI10.1007/978-3-319-03512-3_2zbMath1322.60196OpenAlexW2236599745MaRDI QIDQ2946083

Rostyslav E. Yamnenko, Yuriy Vasil'ovich Kozachenko

Publication date: 16 September 2015

Published in: Modern Stochastics and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-03512-3_2

zbMATH Keywords

queueing theorysub-Gaussian random processesgeneralized fractional Brownian motion

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (2)

The distribution of the supremum of a $\gamma $-reflected stochastic process with an input process belonging to some exponential type Orlicz space ⋮ A bound for norms in \(L_p(T)\) of deviations of \(\varphi\)-sub-Gaussian stochastic processes

Cites Work

• On average losses in the ruin problem with fractional Brownian motion as input
• A storage model with self-similar input
• Bounds for the distribution of some functionals of processes with $\varphi $-sub-Gaussian increments
• On the distribution of storage processes from the class $V(𝜙,𝜓)$
• Boundary-Value problems with random initial conditions and functional series from subφ (Ω). I
• Large buffer asymptotics for the queue with fractional Brownian input
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