Waiting-time tail probabilities in queues with long-tail service-time distributions
type: Item
instance of: scholarly article
title: Waiting-time tail probabilities in queues with long-tail service-time distributions
zbMATH Open document ID: 0805.60097
DOI: 10.1007/BF01158960
author: Joseph Abate
author: Gagan L. Choudhury
author: Ward Whitt
published in: Queueing Systems
publication date: 1995-02-02T00:00:00Z
review text: The authors have recently developed algorithms for the waiting-time tail probabilities \(P (W>x)\) in a large class of single-server queues [Oper. Res (1994), and Commun. Stat., Stochastic Models 10, No. 1, 99-143 (1994; Zbl 0801.60082)]. In this paper, the authors consider a \(GI/G/1\) queueing model assuming that the service time distribution is a Pareto mixture of exponential distribution with mean 1. They develop algorithms for computing the waiting-time distribution. They investigate the quality of approximations based on asymptotics for \(P (W>x)\), as \(x\to\infty\). They also derive multi-term asymptotic expansions for the \(M/G/1\) queue.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 622033
zbMATH Keywords: Pollachek contour integrals
zbMATH Keywords: waiting-time tail probabilities
zbMATH Keywords: queues
zbMATH Keywords: Pareto mixture of exponential distribution
zbMATH Keywords: waiting-time distribution
reviewed by: P. R. Parthasarathy
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01158960
OpenAlex ID: W1986582466
description: scientific article; zbMATH DE number 622033