Fractional Brownian Motion withH< 1/2 as a Limit of Scheduled Traffic

DOI10.1239/jap/1346955328zbMath1255.60062OpenAlexW2130597161MaRDI QIDQ3165489

Victor F. Araman, Peter W. Glynn

Publication date: 29 October 2012

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

Full work available at URL: https://projecteuclid.org/euclid.jap/1346955328

zbMATH Keywords

functional limit theoremFractional Brownian motionheavy-traffic limit theoremscheduled traffic model

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Queueing theory (aspects of probability theory) (60K25) Brownian motion (60J65) Functional limit theorems; invariance principles (60F17) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (7)

On a single server queue fed by scheduled traffic with Pareto perturbations ⋮ Optimized appointment scheduling ⋮ New and refined bounds for expected maxima of fractional Brownian motion ⋮ Gaussian limits for scheduled traffic with super-heavy tailed perturbations ⋮ Asymptotically Optimal Appointment Schedules ⋮ A Data-Driven Model of an Appointment-Generated Arrival Process at an Outpatient Clinic ⋮ Optimal stationary appointment schedules

Cites Work

• On convergence to stationarity of fractional Brownian storage
• Slow, fast and arbitrary growth conditions for renewal-reward processes when both the renewals and the rewards are heavy-tailed
• Extremes of a certain class of Gaussian processes
• Is network traffic approximated by stable Lévy motion or fractional Brownian motion?
• Large deviations of infinite intersections of events in Gaussian processes
• Weak convergence to fractional brownian motion and to the rosenblatt process
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