Note on functional iteration technique for \(M/G/1\) type Markov chains
type: Item
instance of: scholarly article
title: Note on functional iteration technique for \(M/G/1\) type Markov chains
zbMATH Open document ID: 1190.65014
author: N. H. Rhee
published in: Linear Algebra and its Applications
publication date: 2010-02-09T00:00:00Z
review text: The mean convergence rate of the iterative approximation of the nonnegative solution \(G\) of the following matrix equation \( X= \sum^{\infty}_{i=0}X^iA_i \), which comes from the M/G/1 queuing system and studied completely by \textit{B. Meini} [Numer. Math. 78, No.~1, 39--58 (1997; Zbl 0889.65145)], is shown related to the second eigenvalue of \(G\) .
reviewed by: Gong Guanglu
Mathematics Subject Classification ID: 65C40
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 15B51
zbMATH DE Number: 5667906
zbMATH Keywords: stochastic matrices
zbMATH Keywords: minimal nonnegative solution
zbMATH Keywords: Markov chains
zbMATH Keywords: iterative methods
zbMATH Keywords: mean asymptotic convergence rate
zbMATH Keywords: matrix equation
MaRDI profile type: Publication
full work available at URL: j.laa.2009.10.017
OpenAlex ID: W2011201786
cites work: Numerical Methods for Structured Markov Chains
cites work: New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains
cites work: Q4039989
cites work: Q5342712
DOI: 10.1016/J.LAA.2009.10.017
description: scientific article; zbMATH DE number 5667906