Queueing approximation of suprema of spectrally positive Lévy process

DOI10.1007/S11134-009-9160-7zbMath1196.60150OpenAlexW2069796594MaRDI QIDQ967283

Marek Czystolowski, Władysław Szczotka

Publication date: 28 April 2010

Published in: Queueing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11134-009-9160-7

zbMATH Keywords

heavy trafficLévy processLévy measurequeueing systemsMittag-Leffler distributionstationary waiting time

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Functional limit theorems; invariance principles (60F17)

Related Items (2)

The Class of Distributions Associated with the Generalized Pollaczek-Khinchine Formula ⋮ Convergence of the all-time supremum of a Lévy process in the heavy-traffic regime

Cites Work

• Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions
• Queues with server vacations and Lévy processes with secondary jump input
• Stochastic-Process Limits
• A Heavy Traffic Approximation for Workload Processes with Heavy Tailed Service Requirements
• On the Distribution of the Supremum Functional for Processes with Stationary Independent Increments
• The Supremum and Infimum of the Poisson Process
• Fluctuation theory in continuous time
• The supremum distribution of a Lévy process with no negative jumps
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