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A state‐dependent Markov‐modulated mechanism for generating events and stochastic models
Author(s) -
Artalejo Jesus R.,
GómezCorral A.
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1252
Subject(s) - queueing theory , birth–death process , generalization , markov process , mathematics , construct (python library) , markovian arrival process , homogeneous , scalar (mathematics) , constructive , state (computer science) , stochastic modelling , process (computing) , mathematical optimization , computer science , algorithm , combinatorics , statistics , mathematical analysis , population , demography , geometry , sociology , programming language , operating system
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.