Translator Disclaimer
December 2012 Kronecker-based infinite level-dependent QBD processes
TuǦrul Dayar, M. Can Orhan
Author Affiliations +
J. Appl. Probab. 49(4): 1166-1187 (December 2012). DOI: 10.1239/jap/1354716665

Abstract

Markovian systems with multiple interacting subsystems under the influence of a control unit are considered. The state spaces of the subsystems are countably infinite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death model for such systems is extended by facilitating the automatic representation and generation of the nonzero blocks in its underlying infinitesimal generator matrix with sums of Kronecker products. Experiments are performed on systems of stochastic chemical kinetics having two or more countably infinite state space subsystems. Results indicate that, even though more memory is consumed, there are many cases where a matrix-analytic solution coupled with Lyapunov theory yields a faster and more accurate steady-state measure compared to that obtained with simulation.

Citation

Download Citation

TuǦrul Dayar. M. Can Orhan. "Kronecker-based infinite level-dependent QBD processes." J. Appl. Probab. 49 (4) 1166 - 1187, December 2012. https://doi.org/10.1239/jap/1354716665

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1268.60099
MathSciNet: MR3058996
Digital Object Identifier: 10.1239/jap/1354716665

Subjects:
Primary: 60J22
Secondary: 60J28, 92C45, 92D25

Rights: Copyright © 2012 Applied Probability Trust

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 4 • December 2012
Back to Top