Finiteness of waiting-time moments in general stationary single-server queues
type: Item
instance of: scholarly article
title: Finiteness of waiting-time moments in general stationary single-server queues
zbMATH Open document ID: 0772.60073
author: Tomasz Rolski
author: D. J. Daley
published in: The Annals of Applied Probability
publication date: 1993-02-22T00:00:00Z
review text: Consider a stable single-server queue in which the arrivals occur at the epochs of a stationary point process that is not necessarily a renewal process and the service times are i.i.d. random variables \(\{S_ n\}\). Let \(W\) be a random variable distributed as the stationary customer waiting time. A classical result shows that when the arrival process is renewal, for \(\gamma>0\), \(EW^ \gamma<\infty\) if and only if \(ES_ 1^{\gamma+1}<\infty\). Analogues of this result for the case when the arrivals no longer form a renewal process are developed. Two special cases are considered in detail: when the arrivals are generated by a Cox process and when the sequence of interarrival times contains an embedded regenerative phenomenon.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 120363
zbMATH Keywords: stable single-server queue
zbMATH Keywords: renewal process
zbMATH Keywords: stationary customer waiting time
zbMATH Keywords: Cox process
zbMATH Keywords: embedded regenerative phenomenon
reviewed by: D. P. Kennedy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177005585
OpenAlex ID: W2088103816
DOI: 10.1214/AOAP/1177005585
description: scientific article; zbMATH DE number 120363