Large deviations ordering of point processes in some queueing networks
type: Item
instance of: scholarly article
title: Large deviations ordering of point processes in some queueing networks
zbMATH Open document ID: 0918.60083
DOI: 10.1023/A:1019159408810
author: Laurent Massoulié
published in: Queueing Systems
publication date: 1999-08-17T00:00:00Z
review text: Authors's abstract: Given a stochastic ordering between point processes (p.p.), say that a p.p. \(N\) is smooth if it is less than the Poisson process with the same average intensity for this ordering. We investigate whether initially smooth processes retain their smoothness as they cross a network of FIFO \(\cdot/\text{D}/1\) queues along fixed routes. For the so-called strong variability ordering we show that point processes remain smooth as they proceed through a tandem of quasi-saturated (i.e., loaded to 1) \(\text{M}+\cdot/\text{D}/1\) queues. We then introduce the large deviations ordering, which involves comparison of the rate functions associated with large deviations principles satisfied by the point processes. For this ordering, we show that smoothness is retained when the processes cross a feed-forward network of unsaturated \(\cdot /\text{D}/1\) queues. We also examine the LD characteristics of a deterministic p.p. at the output of an \(\text{M}+ \cdot/\text{D}/1\) queue.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 1241121
zbMATH Keywords: stochastic ordering
zbMATH Keywords: point processes
zbMATH Keywords: large deviations ordering
zbMATH Keywords: sample path large deviations
reviewed by: Erik A. van Doorn
MaRDI profile type: Publication
full work available at URL: a:1019159408810
OpenAlex ID: W2031922390
description: scientific article; zbMATH DE number 1241121