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The batch Markov-modulated Poisson process (BMMPP) is a subclass of the versatile batch Markovian arrival process (BMAP), 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 BMMPPm(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.
batch markovian arrival process (bmap); correlation structure; identifiability; markov-modulated poisson process (mmpp); markovian arrival process; bayesian-analysis; service queue; nonidentifiability; identifiability; software; chains