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Type: Journal article
Title: Quasi-birth-and-death processes with rational arrival process components
Author: Bean, N.
Nielsen, B.
Citation: Stochastic Models, 2010; 26(3):309-334
Publisher: Taylor & Francis Inc.
Issue Date: 2010
ISSN: 1532-6349
Statement of
N. G. Bean and B. F. Nielsen
Abstract: 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.
Keywords: Markovian arrival process
Matrix–exponential distribution
Phase-type distribution
Quasi-birth-and-death process
Rational arrival process.
Rights: Copyright © Taylor & Francis Group, LLC
DOI: 10.1080/15326349.2010.498311
Grant ID:
Appears in Collections:Aurora harvest
Environment Institute publications
Mathematical Sciences publications

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