Local poissonification of the markovian arrival process

In a novel approach to quantifying the burstiness of a stationary point process, the points in successive intervals of length a are uniformly and independently redistributed over those intervals. As the window size a is increased, we obtain new point processes which increasingly mimic the local behavior of the Poisson process. For the Markovian arrival process, a number of mathematical descriptors of the resulting processes, such as the dispersion function, the distribution of the interval length and the exponential peakedness function are expressed in computationally implementable matrix formulas.