On matrix-geometric solution of nested QBD chains
type: Item
instance of: scholarly article
title: On matrix-geometric solution of nested QBD chains
zbMATH Open document ID: 1042.60055
DOI: 10.1023/A:1021884213344
author: Sung Ho Choi
author: Bara Kim
author: Khosrow Sohraby
author: Bong Dae Choi
published in: Queueing Systems
publication date: 2003-04-10T00:00:00Z
review text: The authors study a nested quasi-birth-and-death (QBD) process, which is a three-dimensional generalization of a QBD process. It is shown that the stationary distribution of the process may be expressed in terms of the fundamental matrices of certain submatrices of the generator of the process, while these fundamental matrices themselves may be expressed in terms of the minimal nonnegative solutions of sets of quadratic matrix equations. An application is given to overload control in communication networks.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 1896715
zbMATH Keywords: nested QBD chains
zbMATH Keywords: level dependent QBD chains
zbMATH Keywords: overload control
zbMATH Keywords: fundamental matrix
zbMATH Keywords: matrix-geometric solution
reviewed by: Erik A. van Doorn
MaRDI profile type: Publication
full work available at URL: a:1021884213344
OpenAlex ID: W26471643
description: scientific article; zbMATH DE number 1896715