A Two-Step EM Algorithm for MAP Fitting

摘要

In this paper we propose a two-step expectation-maximization (EM) algorithm to fit parameters of a Markovian arrival process (MAP) according to measured data traces. The first step of the EM algorithm performs fitting of the empirical distribution function to a phase type (PH) distribution, and the second step transforms the PH distribution into a MAP and modifies the MAP matrices to capture the autocovariance of the trace. In the first step of the algorithm a compact presentation of the distribution function is used and in the second step statistical properties of measured data traces are exploited to improve the efficiency of the algorithm. Numerical examples show that even compact MAP models yield relatively good approximations for the distribution function and the autocovariance.