Calculating the \(M/G/1\) busy-period density and LIFO waiting-time distribution by direct numerical transform inversion

DOI10.1016/0167-6377(95)00049-6zbMath0854.60095OpenAlexW1981798262WikidataQ56763789 ScholiaQ56763789MaRDI QIDQ1919174

Gagan L. Choudhury, Joseph Abate, Ward Whitt

Publication date: 13 January 1997

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

Full work available at URL: https://doi.org/10.1016/0167-6377(95)00049-6

zbMATH Keywords

Laplace transformsnumerical transform inversionqueuebusy periodlast-in-first-out service disciplineprobability of emptiness

Mathematics Subject Classification ID

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

Related Items

Limits and approximants for the M/G/1 LIFO waiting-time distribution, Ruin probability in the dual risk model with two revenue streams, Ultimate Ruin Probabilities for Generalized Gamma-Convolutions Claim Sizes, USING SINGULARITY ANALYSIS TO APPROXIMATE TRANSIENT CHARACTERISTICS IN QUEUEING SYSTEMS, Relaxation time for the discrete \(D/G/1\) queue, On the numerical inversion of busy-period related transforms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Fourier-series method for inverting transforms of probability distributions
• Solving probability transform functional equations for numerical inversion
• Waiting-time tail probabilities in queues with long-tail service-time distributions
• Convergence rates for M/G/1 queues and ruin problems with heavy tails
• The Probability Law of the Busy Period for Two Types of Queuing Processes
• On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1
• Transient Behavior of the M/G/1 Workload Process
• Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times
• Markov Processes Representing Traffic in Connecting Networks
• Queuing Systems in Which the Discipline is “Last-Come, First-Served”
• A Combinatorial Method in the Theory of Queues