@TECHREPORT\{IMM2007-05554,
    author       = "N. G. Bean and B. F. Nielsen",
    title        = "Quasi-Birth-and-Death Processes with Rational Arrival Process Components",
    year         = "2007",
    keywords     = "Matrix Exponential Distribution, Phase-Type Distribution, Rational Arrival Process, Markovian Arrival Process, Quasi-Birth-and-Death Process",
    number       = "",
    series       = "IMM-Technical Report-2007-20",
    institution  = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5554-full.html",
    abstract     = "In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional {QBD}. We demonstrate the analysis by considering a queue where the arrival process and the sequence of service times are derived from two different RAPs that are not just Markovian Arrival processes. We also introduce an element of correlation between the arrival process and the sequence of service times."
}