Similarity transformations of MAPs

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