Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/73975
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dc.contributor.authorBean, N.-
dc.contributor.authorO'Reilly, M.-
dc.contributor.authorRen, Y.-
dc.date.issued2012-
dc.identifier.citationPerformance Evaluation, 2012; 69(9):440-445-
dc.identifier.issn0166-5316-
dc.identifier.issn1872-745X-
dc.identifier.urihttp://hdl.handle.net/2440/73975-
dc.description.abstractSecond-order reward models are an important class of models for evaluating the performance of real-life systems in which the reward measure fluctuates according to some underlying noise. These models consist of a Markov chain driving the evolution of the system, and a continuous reward variable representing its performance. Thus far, only models with a finite number of states have been studied. We consider second-order reward models driven by Quasi-birth-and-death processes, a class of block-structured Markov chains with infinitely many states. We derive the expressions for the Laplace-Stieltjes transforms of the accumulated reward and demonstrate how they can be efficiently evaluated. We use our results to analyse a simple example and, in doing so, show that the second-order feature can make a significant difference to the accumulated reward. The inclusion of the second-order feature also creates new difficulties which require the development of new conditions in the analysis. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved.-
dc.description.statementofresponsibilityNigel G. Bean, Małgorzata M. O’Reilly, Yong Ren-
dc.language.isoen-
dc.publisherElsevier Science BV-
dc.rightsCrown copyright © 2012-
dc.source.urihttp://dx.doi.org/10.1016/j.peva.2012.05.002-
dc.subjectReward model-
dc.subjectQuasi-birth-and-death (QBD) process-
dc.subjectRG-factorization-
dc.subjectBrownian motion-
dc.titleSecond-order Markov reward models driven by QBD processes-
dc.typeJournal article-
dc.identifier.doi10.1016/j.peva.2012.05.002-
dc.relation.granthttp://purl.org/au-research/grants/arc/DP110101663-
pubs.publication-statusPublished-
dc.identifier.orcidBean, N. [0000-0002-5351-3104]-
Appears in Collections:Aurora harvest
Environment Institute publications
Mathematical Sciences publications

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