Monotonicity and asymptotic queue-length distribution in discrete-time networks
type: Item
instance of: scholarly article
title: Monotonicity and asymptotic queue-length distribution in discrete-time networks
zbMATH Open document ID: 0991.90035
DOI: 10.1023/A:1014715630648
author: R. Smith
published in: Queueing Systems
publication date: 2002-05-28T00:00:00Z
review text: Monotonicity of performance measures for closed, cyclic, discrete-time networks with one server per node and with independent geometric service times in equilibrium is established. It is observed that the joint distribution of queue-length random variables is negatively associated. The queue-length distribution at any node converges in a strong sense to a distribution that is conditionally geometric and the \(r\)-th moment converges to the corresponding moment of the limiting distribution for any positive \(r\). Some consequences are derived.
reviewed by: Václav Koubek
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B15
Mathematics Subject Classification ID: 68M20
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 1746321
zbMATH Keywords: discrete-time network
zbMATH Keywords: cyclic network
zbMATH Keywords: queue-length random variable
zbMATH Keywords: distribution
zbMATH Keywords: monotonicity
zbMATH Keywords: negative association
zbMATH Keywords: asymptotic analysis
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1746321