Mathematical Problems in Engineering
Volume 5 (1999), Issue 4, Pages 349-359

Similarity transformations of MAPs

Allan T. Andersen, V. A. Barker, and Bo Friis Nielsen

Department of Mathematical Modelling, Building 321, Technical University of Denmark, Lyngby DK-2800, Denmark

Received 12 October 1998

Copyright © 1999 Allan T. Andersen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.