Parameter estimation of Markov modulated fluid arrival processes

Markov modulated discrete arrival processes have a wide literature, including parameter estimation methods based on expectation–maximization (EM). In this paper, we investigate the adaptation of these EM based methods to Markov modulated fluid arrival processes (MMFAP), and conclude that only the generator matrix of the modulating Markov chain of MMFAPs can be approximated by EM based method. For the rest of the parameters, the fluid rates and the fluid variances, we investigate the efficiency of numerical likelihood maximization. To reduce the computational complexity of the likelihood computation, we accelerate the numerical inverse Laplace transformation step of the procedure with function fitting.