The Markovian arrival process (MAP) is widely used for probabilistic analysis of communication network traffic. An important problem in MAP-based traffic modeling is estimating model parameters to fit observed traffic data. So far, no estimation procedure has been available for estimating group data.

In this paper, Okamura, Dohi, and Trivedi propose two expectation-maximization (EM) algorithms for fitting the MAP and the Markov modulated Poisson process (MMPP) with generalized group data. The proposed EM algorithm can perform the maximum likelihood estimation when exact arrival times are not known. Moreover, in order to deal with the data that consists of many arrival observations in one bin, they propose the approximate EM algorithm for the MMPP special case.

The numerical results point out that the maximum number of arrivals strongly affects the computation time of the EM algorithm with group data and that the length of step size for group data is a significant factor in determining the accuracy and the computation time in both exact and approximate EM algorithms. The authors also present an application of the proposed EM algorithm to real traffic data.

The two methods proposed in this paper should be useful for estimating time series data that arises in a variety of situations, including Internet traffic. However, the size of MAP is limited, due to the computational effort needed. Many phases are necessary to accurately fit the MAP to the trace data with long-range dependence.