ApproximatingM/G/1 Waiting Time Tail Probabilities

DOI10.1081/STM-120034127zbMath1057.60091OpenAlexW2054542768MaRDI QIDQ3157853

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Publication date: 19 January 2005

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/stm-120034127

zbMATH Keywords

heavy-tailed distributionM/G/1 queueCramér-Lundberg approximationnon-exponential asymptotics

Mathematics Subject Classification ID

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

Related Items (3)

Exact waiting time and queue size distributions for equilibrium \(M/G/1\) queues with Pareto service ⋮ Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model ⋮ Refinements of bounds for tails of compound distributions and ruin probabilities

Uses Software

• QUADPACK

Cites Work

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• Estimates for the probability of ruin with special emphasis on the possibility of large claims
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• The Fourier-series method for inverting transforms of probability distributions
• Waiting-time tail probabilities in queues with long-tail service-time distributions
• Asymptotics for M/G/1 low-priority waiting-time tail probabilities
• Asymptotic analysis of tail probabilities based on the computation of moments
• On the tails of waiting-time distributions
• Modeling service–time distributions with non–exponential tails:beta mixtures of exponentials
• Two-Sided Bounds for Ruin Probabilities when the Adjustment Coefficient does not Exist
• Computing Laplace Transforms for Numerical Inversion Via Continued Fractions
• Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times
• Numerical Computation of the Moments of a Probability Distribution from its Transform
• A unified approach to the study of tail probabilities of compound distributions
• Some estimates of geometric sums

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