A heavy-traffic theorem for the GI/G/1 queue with a Pareto-type service time distribution
type: Item
instance of: scholarly article
title: A heavy-traffic theorem for the GI/G/1 queue with a Pareto-type service time distribution
zbMATH Open document ID: 0913.60083
DOI: 10.1155/S1048953398000215
author: J. W. Cohen
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1999-05-26T00:00:00Z
full work available at URL: https://eudml.org/doc/48145
review text: The author considers a GI/G/1 queueing model, with traffic load \(a\), in which the service time distribution \(B(t)\) has a Pareto-type tail (i.e., for \(t \rightarrow \infty, 1-B(t) \sim \frac{c}{t^\nu}+ O[e^{-\delta t}], c>0, 1<\nu<2, \delta>0\)) and the \(\mu\)th moment of the interarrival time distribution \(A(t)\) exists for \(\mu>\nu\). The author proves that \((1-a)^{1/(\nu-1)} {\mathbf w}\) converges in distribution for \(a \uparrow 1\), where \({\mathbf w}\) is distributed as the stationary waiting time distribution. He obtains the Laplace-Stieltjes transform of the limiting distribution and an asymptotic series for its tail probabilities.
reviewed by: P. R. Parthasarathy
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 1221902
zbMATH Keywords: GI/G/1 model
zbMATH Keywords: Pareto-type service time distribution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1221902