Counter-examples involving markovian arrival processes

Abstract

By considering simple two-state Markovian arrival processes, a number of examples are given which show the limitations of the information conveyed by the distributions of the counting random variables. Some of these are intended to lay some conjectures on point processes to rest, while others have primarily didactic value. We also prove the (unanticipated) equivalence of the point processes generated by the two-state Markov modulated Poisson process to a two-state Markov switched Poisson process.