Reflecting diffusions and queueing networks
type: Item
instance of: scholarly article
title: Reflecting diffusions and queueing networks
zbMATH Open document ID: 0933.60102
published in: Documenta Mathematica
publication date: 1998-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/224170
full work available at URL: Williams.MAN.html
review text: Let \(Z(t)\) be the \(K\)-vector of numbers of customers at time \(t\) in an open queueing network with \(J\) stations and \(K\) customer classes and \(W(t)\) be the \(J\)-vector of workloads at the \(J\) stations. This paper surveys recent progress on a classical problem, when these processes after appropriate scaling have multidimensional reflected Brownian motion in an orthant as their heavy-traffic limit. The conditions involve multiplicative state space collapse as discussed by Bramson in the paper reviewed above.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1184371
zbMATH Keywords: Brownian motion
zbMATH Keywords: customer class
zbMATH Keywords: fluid limit
zbMATH Keywords: heavy traffic
zbMATH Keywords: multiclass networks
zbMATH Keywords: semimartingale
zbMATH Keywords: state space collapse
author: R. J. Williams
reviewed by: Søren Asmussen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184371