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https://hdl.handle.net/2440/73975
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dc.contributor.author | Bean, N. | - |
dc.contributor.author | O'Reilly, M. | - |
dc.contributor.author | Ren, Y. | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | Performance Evaluation, 2012; 69(9):440-445 | - |
dc.identifier.issn | 0166-5316 | - |
dc.identifier.issn | 1872-745X | - |
dc.identifier.uri | http://hdl.handle.net/2440/73975 | - |
dc.description.abstract | Second-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.statementofresponsibility | Nigel G. Bean, Małgorzata M. O’Reilly, Yong Ren | - |
dc.language.iso | en | - |
dc.publisher | Elsevier Science BV | - |
dc.rights | Crown copyright © 2012 | - |
dc.source.uri | http://dx.doi.org/10.1016/j.peva.2012.05.002 | - |
dc.subject | Reward model | - |
dc.subject | Quasi-birth-and-death (QBD) process | - |
dc.subject | RG-factorization | - |
dc.subject | Brownian motion | - |
dc.title | Second-order Markov reward models driven by QBD processes | - |
dc.type | Journal article | - |
dc.identifier.doi | 10.1016/j.peva.2012.05.002 | - |
dc.relation.grant | http://purl.org/au-research/grants/arc/DP110101663 | - |
pubs.publication-status | Published | - |
dc.identifier.orcid | Bean, N. [0000-0002-5351-3104] | - |
Appears in Collections: | Aurora harvest Environment Institute publications Mathematical Sciences publications |
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