Conditional limit theorems for queues with Gaussian input, a weak convergence approach

DOI10.1016/j.spa.2004.11.008zbMath1073.60085OpenAlexW1979498038MaRDI QIDQ2485854

A. B. Dieker

Publication date: 5 August 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://research.utwente.nl/en/publications/conditional-limit-theorems-for-queues-with-gaussian-input-a-weak-convergence-approach(cfba9bfd-804e-4c81-9784-21fac3fa7bab).html

zbMATH Keywords

Gaussian processesBusy periodLarge deviationsRegular variationMetric entropyOverflow probability

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25)

Related Items (15)

Minimizing Large Deviation Paths for a Family of Long-Range Dependent Processes and Their Fractional Brownian Approximations ⋮ On convergence to stationarity of fractional Brownian storage ⋮ Extremes of 𝛼(𝑡)-locally stationary Gaussian random fields ⋮ Large buffer asymptotics for generalized processor sharing queues with Gaussian inputs ⋮ Extremes of multidimensional Gaussian processes ⋮ Gaussian queues in light and heavy traffic ⋮ Steady-state GI/G/\(n\) queue in the Halfin-Whitt regime ⋮ On asymptotic constants in the theory of extremes for Gaussian processes ⋮ Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution ⋮ Generalized Pickands constants ⋮ Extremes of Gaussian processes over an infinite horizon ⋮ Reduced-load equivalence for Gaussian processes ⋮ Subexponential asymptotics of hybrid fluid and ruin models ⋮ Large deviations of infinite intersections of events in Gaussian processes ⋮ Reduced-load equivalence for queues with Gaussian input

Cites Work

• How large delays build up in a GI/G/1 queue
• A note on transient Gaussian fluid models
• A function space large deviation principle for certain stochastic integrals
• Path space large deviations of a large buffer with Gaussian input traffic
• On conditioning a random walk to stay nonnegative
• A note on LDP for supremum of Gaussian processes over infinite horizon
• Extremes of Gaussian processes over an infinite horizon
• Large deviations of infinite intersections of events in Gaussian processes
• Donsker theorems for diffusions: necessary and sufficient conditions
• Conditioned limit theorems for waiting-time processes of the M/G/1 queue
• Conditioned limit theorems relating a random walk to its associate, with applications to risk reserve processes and the GI/G/1 queue
• Large deviations for multi-dimensional reflected fractional Brownian motion
• A global asymptotic normality of the sample correlogram of a stationary Gaussian process
• Exact asymptotics for a queue with fractional Brownian input and applications in ATM networks
• Semi-Stable Stochastic Processes
• Large deviations and overflow probabilities for the general single-server queue, with applications
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