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A state-dependent Markov-modulated mechanism for generating events and stochastic models

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Artalejo, Jesús R. and Gómez-Corral, Antonio (2010) A state-dependent Markov-modulated mechanism for generating events and stochastic models. Mathematical Methods in the Applied Sciences, 33 (11). pp. 1342-1349. ISSN 0170-4214

Official URL: http://onlinelibrary.wiley.com/doi/10.1002/mma.1252/abstract;jsessionid=A5D4725A115991536540A53A7772D452.d01t04




Abstract

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.


Item Type:Article
Uncontrolled Keywords:Stochastic models;Queueing; Epidemics
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:15033
Deposited On:26 Apr 2012 08:11
Last Modified:08 Mar 2016 14:49

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