Quasi-Birth-and-Death Processes with Rational Arrival Process Components

This paper introduces the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process (RAP) components. We use the physical interpretation of the prediction process of the RAP, developed by Asmussen and Bladt, and develop an analysis that parallels the analysis of a traditional QBD.

Further, we present an algorithm for the numerical evaluation of the matrix G. As an example, we consider two queues where the arrival process and the sequence of service times are taken from two dependent RAPs, that are not Markovian Arrival Processes