A state-dependent Markov-modulated mechanism for generating events and stochastic models
Article first published online: 15 DEC 2009
Copyright © 2009 John Wiley & Sons, Ltd.
Mathematical Methods in the Applied Sciences
Volume 33, Issue 11, pages 1342–1349, 30 July 2010
How to Cite
Artalejo, J. R. and Gómez-Corral, A. (2010), A state-dependent Markov-modulated mechanism for generating events and stochastic models. Math. Meth. Appl. Sci., 33: 1342–1349. doi: 10.1002/mma.1252
- Issue published online: 21 JUN 2010
- Article first published online: 15 DEC 2009
- Manuscript Received: 28 JUL 2009
- Government of Spain (Ministry of Science and Innovation)
- European Commission. Grant Number: MTM 2008-01121
- stochastic models;
In this paper, we introduce a versatile block-structured state-dependent event (BSDE) approach that provides a methodological tool to construct non-homogeneous Markov-modulated stochastic models. Alternatively, the BSDE approach can be used to construct even a part (e.g. the arrival process) of the model. To illustrate the usefulness of the BSDE approach, several arrival patterns as well as queueing and epidemic models are considered. In particular, we deal with a state-dependent quasi-birth-and-death process that gives a constructive generalization of the scalar birth-and-death process and the homogeneous quasi-birth-and-death process. Copyright © 2009 John Wiley & Sons, Ltd.