This paper presents an EM algorithm for fitting traces with Markovian arrival processes (MAPs). The proposed algorithm operates on a special subclass of MAPs. This special structure enables the efficient implementation of the EM algorithm; it is more orders of magnitudes faster than methods operating on the general MAP class while providing similar or better likelihood values. An other important feature of the algorithm is that it is able to fit multi-class traces with marked Markovian arrival processes as well. Several numerical examples demonstrate the efficiency of the procedure
