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https://hdl.handle.net/2440/94262
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dc.contributor.author | Latouche, G. | - |
dc.contributor.author | Nguyen, G. | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Queueing Systems: Theory and Applications, 2015; 80(1-2):105-125 | - |
dc.identifier.issn | 0257-0130 | - |
dc.identifier.issn | 1572-9443 | - |
dc.identifier.uri | http://hdl.handle.net/2440/94262 | - |
dc.description.abstract | We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has been shown recently that MMBM may be expressed as the limit of a parameterized family of Markov-modulated fluid models. We prove that the weak convergence also holds for systems with two reflecting boundaries, one at zero and one at b > 0, and that the stationary distributions of the approximating fluid models converge to the stationary distribution of the two-sided reflected MMBM. In so doing, we obtain a new representation for the stationary distribution. It is factorised into a vector determined by the phase behaviour when the fluid is either at the level 0 or the level b, and a matrix expression characteristic of the process when the fluid is in the open interval (0, b). | - |
dc.description.statementofresponsibility | Guy Latouche, Giang Nguyen | - |
dc.language.iso | en | - |
dc.publisher | Springer | - |
dc.rights | © Springer Science+Business Media New York 2015 | - |
dc.source.uri | http://dx.doi.org/10.1007/s11134-014-9432-8 | - |
dc.subject | Markov-modulated linear fluid models; reflected two-sided Markov-modulated Brownian motion; weak convergence; stationary distribution | - |
dc.title | Fluid approach to two-sided reflected Markov-modulated Brownian motion | - |
dc.type | Journal article | - |
dc.identifier.doi | 10.1007/s11134-014-9432-8 | - |
dc.relation.grant | http://purl.org/au-research/grants/arc/DP110101663 | - |
pubs.publication-status | Published | - |
Appears in Collections: | Aurora harvest 7 Mathematical Sciences publications |
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