Waiting-time tail probabilities in queues with long-tail service-time distributions

DOI10.1007/BF01158960zbMath0805.60097OpenAlexW1986582466MaRDI QIDQ1331293

Joseph Abate, Gagan L. Choudhury, Ward Whitt

Publication date: 2 February 1995

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

Full work available at URL: https://doi.org/10.1007/bf01158960

zbMATH Keywords

queueswaiting-time distributionPareto mixture of exponential distributionPollachek contour integralswaiting-time tail probabilities

Mathematics Subject Classification ID

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

Related Items (28)

ApproximatingM/G/1 Waiting Time Tail Probabilities ⋮ Some Results for the Actual Waiting Time in Batch Arrival Queueing Systems ⋮ Large claims approximations for risk processes in a Markovian environment ⋮ An application of deterministic chaotic maps to model packet traffic ⋮ Large deviation analysis of the single server queue ⋮ Calculating the \(M/G/1\) busy-period density and LIFO waiting-time distribution by direct numerical transform inversion ⋮ Patterns of buffer overflow in a class of queues with long memory in the input stream ⋮ The single server queue with mixing dependencies ⋮ How to measure the accuracy of the subexponential approximation for the stationary single server queue ⋮ A ruin model with a resampled environment ⋮ Processor sharing: a survey of the mathematical theory ⋮ Analysis of the queue lengths in a priority retrial queue with constant retrial policy ⋮ Statistical analysis of video frame size distribution originating from scalable video codec (SVC) ⋮ SOJOURN TIME TAILS IN THE M/D/1 PROCESSOR SHARING QUEUE ⋮ Modelling and estimating heavy-tailed non-homogeneous correlated queues: Pareto-inverse gamma HGLM with covariates ⋮ PIECEWISE POLYNOMIAL APPROXIMATIONS FOR HEAVY-TAILED DISTRIBUTIONS IN QUEUEING ANALYSIS ⋮ Maximum Values in Queueing Processes ⋮ On a generic class of two-node queueing systems ⋮ Higher-order expansions for compound distributions and ruin probabilities with subexponential claims ⋮ Open problems in queueing theory inspired by datacenter computing ⋮ Light-tailed asymptotics of stationary probability vectors of Markov chains of GI/G/1 type ⋮ Bayesian prediction of the transient behaviour and busy period in short- and long-tailed GI/G/1 queueing systems ⋮ Ultimate Ruin Probabilities for Generalized Gamma-Convolutions Claim Sizes ⋮ Improved algorithms for rare event simulation with heavy tails ⋮ On upper bounds for the tail distribution of geometric sums of subexponential random variables ⋮ Single-server queues under overdispersion in the heavy-traffic regime ⋮ Stochastic grey-box modeling of queueing systems: fitting birth-and-death processes to data ⋮ Explicit M/G/1 waiting-time distributions for a class of long-tail service-time distributions

Cites Work

• 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
• On Approximations for Queues, I: Extremal Distributions
• Asymptotic properties of supercritical branching processes I: The Galton-Watson process
• On the tails of waiting-time distributions
• Asymptotics for steady-state tail probabilities in structured markov queueing models
• Heavy-traffic asymptotic expansions for the asymptotic decay rates in theBMAP/G/1 queue
• Planning Queueing Simulations
• Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times
• The Pareto Distribution as a Queue Service Discipline
• Some results on regular variation for distributions in queueing and fluctuation theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Waiting-time tail probabilities in queues with long-tail service-time distributions