Similarity transformations of MAPs

Abstract

We introduce the notion of similar Markovian Arrival Processes (MAPs) and show that the event stationary point processes related to two similar MAPs are stochastically equivalent. This holds true for the time stationary point processes too. We show that several well known stochastical equivalences as e.g. that between the H2 renewal process and the Interrupted Poisson Process (IPP) can be expressed by the similarity transformations of MAPs. In the appendix the valid region of similarity transformations for two-state MAPs is characterized.