Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

DOI10.1239/jap/1101840559zbMath1076.60078OpenAlexW2154158675MaRDI QIDQ4660538

Ravi R. Mazumdar, Parijat Dube, Fabrice M. Guillemin

Publication date: 4 April 2005

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

Full work available at URL: https://semanticscholar.org/paper/a245154cd0bde8642434240ecaea7a25988a4e71

zbMATH Keywords

Laplace transformon-offM/G/1-fluid queue

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Boundary theory for Markov processes (60J50)

Related Items (5)

Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes ⋮ The \(M/G/\infty\) system revisited: finiteness, summability, long range dependence, and reverse engineering ⋮ Hysteretic Capacity Switching for M/G/1 Queues ⋮ Evaluating Scale Functions of Spectrally Negative Lévy Processes ⋮ Lévy Processes with Two-Sided Reflection

Cites Work

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• Dynamic, transient and stationary behavior of the M/GI/1 queue via martingales
• Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval
• Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options
• A new approach to the busy period of the M/M/1 queue
• On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum
• The expected wet period of finite dam with exponential inputs.
• Excursions of the workload process in \(G/GI/1\) queues
• On doubly reflected completely asymmetric Lévy processes.
• Exit problem for a spectrally positive process

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