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Findings about the BMMPP for modeling dependent and simultaneous data in reliability and queueing systems
Author(s) -
Yera Yoel G.,
Lillo Rosa E.,
RamírezCobo Pepa
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2327
Subject(s) - autocorrelation , identifiability , markov chain , queueing theory , poisson distribution , reliability (semiconductor) , markovian arrival process , markov process , computer science , mathematics , poisson process , markov model , statistics , algorithm , combinatorics , statistical physics , physics , power (physics) , quantum mechanics
The batch Markov‐modulated Poisson process ( B M M P P ) is a subclass of the versatile batch Markovian arrival process ( B M A P ), which has been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures, or risk events). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary B M M P P m ( K ) is proven, where K is the maximum batch size and m is the number of states of the underlying Markov chain. This is a powerful result for inferential issues. On the other hand, some novelties related to the correlation and autocorrelation structures are provided.