Moment properties for certain classes of structured Markovian arrival processes

Abstract

We study moment properties of counting processes for certain subclasses of Markovian arrival processes (MAPs). We focus on the class of Markovian transition counting processes (MTCPs) which counts all the transitions of the background Markov chain. While Markov modulated Poisson processes (MMPPs) are often used to model bursty traffic, MTCPs deliver similar modelling capability and reduce the mathematical and computational complexity. To support the suggested use of MTCPs as alternatives to MMPPs, we establish an equivalence in terms of first and second moments of counts with a sub-class of MMPPs which we refer to as slow MMPPs (SMMPPs). For this we construct matched MTCPs (MMTCPs), where an..