Explicit M/G/1 waiting-time distributions for a class of long-tail service-time distributions

DOI10.1016/S0167-6377(99)00014-0zbMath0967.90021OpenAlexW1972441433WikidataQ126857832 ScholiaQ126857832MaRDI QIDQ1306347

Joseph Abate, Ward Whitt

Publication date: 1999

Published in: Operations Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-6377(99)00014-0

zbMATH Keywords

M/G/1 queuewaiting-time distributionPollaczek-Khintchine formulaexponential mixture of inverse Gaussian distributionslong-tail distributionspower-tail distributions

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (7)

Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes ⋮ Corrected Phase-Type Approximations of Heavy-Tailed Queueing Models in a Markovian Environment ⋮ On the accuracy of phase-type approximations of heavy-tailed risk models ⋮ Importance of verifying queue model assumptions before planning with simulation software ⋮ Exact waiting time and queue size distributions for equilibrium \(M/G/1\) queues with Pareto service ⋮ Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis ⋮ On corrected phase-type approximations of the time value of ruin with heavy tails

Uses Software

• OEIS

Cites Work

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• Asymptotic expansions for waiting time probabilities in an \(M/G/1\) queue with long-tailed service time
• The Fourier-series method for inverting transforms of probability distributions
• Waiting-time tail probabilities in queues with long-tail service-time distributions
• Limits and Approximations for the Busy-Period Distribution in Single-Server Queues
• Modeling service–time distributions with non–exponential tails:beta mixtures of exponentials
• An operational calculus for probability distributions via Laplace transforms

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