Analytic, asymptotic and algorithmic properties of the first two moment matrices of the counts during an interval (0,t ] in the Markovian arrival process (MAP) are discussed. These properties are useful in the computation of Palm densities and dispersion functions with arbitrary initial conditions. These descriptors, in turn, are helpful in visualizing the behavior of the point process following the occurrence of special events, such as bursts of arrivals, or in studying the superposition of two independent MAPs.
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Narayana et al. (1992) studied this question.