Application of Deterministic Annealing EM Algorithm to Markovian Arrival Process Parameter Estimation

This paper proposes a variant of EM (expectation-maximization) algorithm for Markovian arrival process (MAP) parameter estimation. Especially, we derive the deterministic annealing EM (DAEM) algorithm for MAP parameter estimation. The DAEM algorithm is one of the methods to overcome a local maxima problem associated with the conventional EM algorithm. This paper derives concrete E- and M-step formulas for MAP parameter estimation from inter-arrival time data in the framework of DAEM algorithm. Numerical examples demonstrate the DAEM algorithm for Markov-modulated Poisson process (MMPP), and we show that the DAEM algorithm is superior to the conventional EM algorithm in terms of avoiding the convergence to local maxima.