Instability of nonhomogeneous queueing networks
type: Item
instance of: scholarly article
title: Instability of nonhomogeneous queueing networks
zbMATH Open document ID: 1022.60084
DOI: 10.1023/A:1020272405385
published in: Journal of Mathematical Sciences (New York)
publication date: 2003-10-27T00:00:00Z
review text: The author studies strong and weak instability for an open queueing network with multi-server nonhomogeneous stations. The traffic intensity \(\rho\) of the network is defined to be the maximum of the traffic intensities of the stations. Let \(\Omega (t)\) and \(\nu_t\) be the total workload and the number of customers in the system at time \(t\), respectively. It is shown that \(\rho > 1\) implies that \(\liminf_{t\to \infty} \Omega(t)/t > 0\) and \(\liminf_{t\to \infty} \nu_t/t > 0\). For \(\rho = 1\) the main results are that the network has infinite expected regeneration time and that \(\Omega(t) \to \infty\) stochastically. Analogous results are proved for corresponding networks with several classes of customers and Markovian switching between these classes.
reviewed by: Wolfgang Stadje
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 1848093
zbMATH Keywords: queueing network
zbMATH Keywords: nonhomogeneous
zbMATH Keywords: multiclass
zbMATH Keywords: traffic intensity
zbMATH Keywords: strong instability
zbMATH Keywords: weak instability
author: Evsei Morozov
MaRDI profile type: Publication
full work available at URL: a:1020272405385
OpenAlex ID: W177056171
description: scientific article; zbMATH DE number 1848093