Large deviations of inverse processes with nonlinear scalings

DOI10.1214/aoap/1028903372zbMath0939.60011OpenAlexW1990016613MaRDI QIDQ1296714

N. G. Duffield, Ward Whitt

Publication date: 29 November 1999

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1028903372

zbMATH Keywords

renewal theorylarge deviationsqueueing theorycounting processesfractional Gaussian noiseregularly varying functionsinverse processes

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Large deviations (60F10) Self-similar stochastic processes (60G18)

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Large deviation principles for renewal-reward processes ⋮ Modeling LEAST RECENTLY USED caches with Shot Noise request processes ⋮ Large deviations for fractional Poisson processes ⋮ Efficient simulation of tail probabilities in a queueing model with heterogeneous servers ⋮ An extension of a logarithmic form of Cramér's ruin theorem to some FARIMA and related processes ⋮ Large Deviations for Clocks of Self-similar Processes ⋮ Large deviations in discrete-time renewal theory ⋮ Large deviations for a class of tempered subordinators and their inverse processes ⋮ How to estimate the rate function of a cumulative process ⋮ Asymptotic results for empirical means of independent geometric distributed random variables ⋮ Large deviation principles for the finite-dimensional distributions of compound renewal processes ⋮ Statistical fluctuations under resetting: rigorous results

Cites Work

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• A storage model with self-similar input
• Large deviations behavior of counting processes and their inverses
• Exponential bounds for queues with Markovian arrivals
• Functional large deviation principles for first-passage-time processes
• Unstable Asymptotics for Nonstationary Queues
• Stability, queue length, and delay of deterministic and stochastic queueing networks
• Logarithmic asymptotics for steady-state tail probabilities in a single-server queue
• Economies of scale in queues with sources having power-law large deviation scalings
• Large deviations and overflow probabilities for the general single-server queue, with applications
• Fractional Brownian Motions, Fractional Noises and Applications
• Convex Analysis

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