Conditions for finite moments of waiting times in \(G/G/1\) queues
type: Item
instance of: scholarly article
title: Conditions for finite moments of waiting times in \(G/G/1\) queues
zbMATH Open document ID: 0809.60094
DOI: 10.1007/BF01158690
author: Robert D. Foley
author: Tomasz Rolski
author: D. J. Daley
published in: Queueing Systems
publication date: 1995-03-28T00:00:00Z
review text: \textit{J. Kiefer} and \textit{J. Wolfowitz} [Ann. Math. Stat. 27, 147-161 (1956; Zbl 0070.366)] proved that the \(\gamma\)-th moment of the stationary waiting time \(W\) in a stable \(GI/GI/1\) queue is finite if and only if the \((R+1)\)st moment of the service time is finite. The authors find sufficient conditions for the \(\gamma\)-th moment to be finite in a stable \(G/G/1\) queue with dependent service and interarrival times. This extends the earlier work of the first and third authors [Ann. Appl. Prob. 2, No. 4, 987-1008 (1992; Zbl 0772.60073)] on \(G/GI/1\) systems.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 698848
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: stationary waiting time
reviewed by: P. R. Parthasarathy
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01158690
OpenAlex ID: W2074250342
description: scientific article; zbMATH DE number 698848