  The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the
versatile Batch Markovian Arrival process (BMAP) which has been proposed for
the modeling of dependent events occurring in batches (as group arrivals,
failures or risk events). This paper focuses on exploring the possibilities of
the BMMPP for the modeling of real phenomena involving point processes with
group arrivals. The first result in this sense is the characterization of the
two-state BMMPP with maximum batch size equal to K, the BMMPP2(K), by a set of
moments related to the inter-event time and batch size distributions. This
characterization leads to a sequential fitting approach via a moments matching
method. The performance of the novel fitting approach is illustrated on both
simulated and a real teletraffic data set, and compared to that of the EM
algorithm. In addition, as an extension of the inference approach, the queue
length distributions at departures in the queueing system BMMPP/M/1 is also
estimated.
