Asymptotic expansions for waiting time probabilities in an \(M/G/1\) queue with long-tailed service time

DOI10.1007/BF01193324zbMath0747.60092OpenAlexW2095916515MaRDI QIDQ1183672

S. Singh

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1007/bf01193324

zbMATH Keywords

subexponential distributionqueue with batch arrivalsapproximations to the waiting time distribution

Mathematics Subject Classification ID

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

Related Items (12)

ApproximatingM/G/1 Waiting Time Tail Probabilities ⋮ Waiting-time tail probabilities in queues with long-tail service-time distributions ⋮ Tandem queues with subexponential service times and finite buffers ⋮ How to measure the accuracy of the subexponential approximation for the stationary single server queue ⋮ A solution to the ruin problem for Pareto distributions. ⋮ On ruin probability and aggregate claim representations for Pareto claim size distributions ⋮ A General Class of Closed Fork and Join Queues with Subexponential Service Times ⋮ Second-order asymptotics for the ruin probability in the case of very large claims ⋮ Unnamed Item ⋮ Higher-order expansions for compound distributions and ruin probabilities with subexponential claims ⋮ Ultimate Ruin Probabilities for Generalized Gamma-Convolutions Claim Sizes ⋮ Explicit M/G/1 waiting-time distributions for a class of long-tail service-time distributions

Cites Work

• Second order behaviour of the tail of a subordinated probability distribution
• The structure of the class of subexponential distributions
• Algorithms for the state probabilities and waiting times in single server queueing systems with random and quasirandom input and phase-type service times
• On convolution tails
• Asymptotic behaviour of Wiener-Hopf factors of a random walk
• The class of subexponential distributions
• Functions of probability measures
• Some new results on the subexponential class
• Theory prob. appl.
• Subexponential distributions and integrated tails
• Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution
• Exponential expansion for the tail of the waiting-time probability in the single-server queue with batch arrivals
• On the tails of waiting-time distributions
• On a single-server queue with group arrivals
• Some results on regular variation for distributions in queueing and fluctuation theory
• Regular variation of the tail of a subordinated probability distribution
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