The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
An EM algorithm for estimation in Markov-modulated Poisson processes
Computational Statistics & Data Analysis
Continuous-time hidden Markov models for network performance evaluation
Performance Evaluation
Modeling IP traffic using the batch Markovian arrival process
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
An EM algorithm for Markov modulated Markov processes
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
An EM Algorithm for Ion-Channel Current Estimation
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
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We study properties and parameter estimation of a finite-state, homogeneous, continuous-time, bivariate Markov chain. Only one of the two processes of the bivariate Markov chain is assumed observable. The general form of the bivariate Markov chain studied here makes no assumptions on the structure of the generator of the chain. Consequently, simultaneous jumps of the observable and underlying processes are possible, neither process is necessarily Markov, and the time between jumps of each of the two processes has a phase-type distribution. Examples of bivariate Markov chains include the Markov modulated Poisson process and the batch Markovian arrival process when appropriate modulo counts are used in each case. We develop an expectation-maximization (EM) procedure for estimating the generator of a bivariate Markov chain, and we demonstrate its performance. The procedure does not rely on any numerical integration or sampling scheme of the continuous-time bivariate Markov chain. The proposed EM algorithm is equally applicable to multivariate Markov chains.