The first two moment matrices of the counts for the Markovian arrival process

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. There properties are useful in the computation of Palm densities and disperson 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 super-position of two independent MAPs.