Moments based matrix representation of Markov and rational arrival processes with reduced rank marginal

Abstract

The moments based matrix representation of Markovian and rational arrival processes (MAP/RAPs) with full rank marginal (FRM) is provided in [14]. MAP/RAPs with reduced rank marginal (RRM) differ in essential properties from the ones with FRM [13]. The main difficulty of the moments based matrix representation of MAP/RAPs with RRM comes from the fact that the moments needed to characterize a MAP/RAPs with RRM depends on the internal structure of the MAP/RAP. In this work, we propose a general procedure for moments based matrix representation that is applicable to MAP/RAPs with both FRM and RRM, independent of their internal structures. We also show that the procedure terminates in a finite number of steps which is proportional to the order of the MAP/RAP.