The stationary G/G/\(s\) queue
type: Item
instance of: scholarly article
title: The stationary G/G/\(s\) queue
zbMATH Open document ID: 0910.60071
DOI: 10.1155/S1048953398000057
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1999-04-06T00:00:00Z
full work available at URL: https://eudml.org/doc/48109
review text: The paper deals with the Laplace-Stieltjes transform (LST) of the stationary waiting time in the G/G/\(s\) queue with FCFS discipline. (The arrival process is strictly stationary and ergodic, the service times are i.i.d. and independent of the arrival process.) First, all singularities of the LST are evaluated and constraints are derived, ensuring that the LST is holomorphic. Then, a factorization method, which is more general than the Wiener-Hopf type decomposition, is proposed. Further, an expression is given for the LST and its asymptotic behaviour for long delays. Finally, the results are applied to the GI/G/\(s\) queue (the interarrival times are additionally independent) as well as to the case of the M/G/\(s\) queue.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 1204251
zbMATH Keywords: G/G/\(s\) queue
zbMATH Keywords: GI/G/\(s\) queue
zbMATH Keywords: first come-first served
zbMATH Keywords: factorization
zbMATH Keywords: singular points
zbMATH Keywords: M/G/\(s\) queue
zbMATH Keywords: Laplace-Stieltjes transform
zbMATH Keywords: Wiener-Hopf type decomposition
author: Pierre-Yves Le Gall
reviewed by: Andreas Brandt
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1204251