Model Fitting for Homogeneous BMAPs

Abstract

Although the concept of BMAPs has gained widespread use in stochastic modelling of communication systems and other application areas, there are few statistical methods of parameter estimation proposed yet. A survey of estimation methods is given in Asmussen [4]. His emphasis is on maximum likelihood estimation and its implementation via the EM algorithm. For the Markov Modulated Poisson Process (MMPP), an EM algorithm has been developed by Ryden [114, 115, 116, 117], whereas Asmussen et al. [7] derived a fitting procedure for phase-type distributions via the EM algorithm. An in?teresting different approach is given by Botta et al. [20] and Chauveau et al. [37]. They introduce the class of generalized hyperexponential distributions and derive statistical fitting methods by means of inversion of transforms.