Estimating Markov-modulated compound Poisson processes

This paper addresses a parameter estimation problem for Markov-modulated compound Poisson process (MMCPP) and compound Markovian arrival process (CMAP). MMCPP and CMAP are extended from Markov-modulated Poisson process (MMPP) and Markovian arrival process (MAP) by combining compound Poisson process (CPP). The EM (expectation-maximization) algorithm is well known as an effective method in order to perform the statistical estimation for the family of MAPs. In this paper, we develop the EM algorithm for MMCPP and CMAP by using the similar technique to the forward-backward algorithm of hidden Markov model (HMM). In particular, we derive concrete estimation algorithms for MMCPP and CMAP whose outputs are given by exponential distributions or multivariate normal distributions.

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