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

Quasi-Birth-and-Death Processes with Rational Arrival Process Components
Nigel G. Bean, Bo Friis Nielsen
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.
Keywords	Matrix Exponential Distribution, Phase-Type Distribution, Rational Arrival Process, Markovian Arrival Process, Quasi-Birth-and-Death Process
Type	Technical report
Year	2007
Publisher	Informatics and Mathematical Modelling, Technical University of Denmark, DTU
Address	Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby
Series	IMM-Technical Report-2007-20
Electronic version(s)	[pdf]
BibTeX data	[bibtex]
IMM Group(s)	Mathematical Statistics