On compact solution vectors in Kronecker-based Markovian analysis

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dc.citation.epage149en_US
dc.citation.spage132en_US
dc.citation.volumeNumber115en_US
dc.contributor.authorBuchholz, P.en_US
dc.contributor.authorDayar T.en_US
dc.contributor.authorKriege, J.en_US
dc.contributor.authorOrhan, M. C.en_US
dc.date.accessioned2018-04-12T11:10:44Z
dc.date.available2018-04-12T11:10:44Z
dc.date.issued2017en_US
dc.departmentDepartment of Computer Engineeringen_US
dc.description.abstractState based analysis of stochastic models for performance and dependability often requires the computation of the stationary distribution of a multidimensional continuous-time Markov chain (CTMC). The infinitesimal generator underlying a multidimensional CTMC with a large reachable state space can be represented compactly in the form of a block matrix in which each nonzero block is expressed as a sum of Kronecker products of smaller matrices. However, solution vectors used in the analysis of such Kronecker-based Markovian representations require memory proportional to the size of the reachable state space. This implies that memory allocated to solution vectors becomes a bottleneck as the size of the reachable state space increases. Here, it is shown that the hierarchical Tucker decomposition (HTD) can be used with adaptive truncation strategies to store the solution vectors during Kronecker-based Markovian analysis compactly and still carry out the basic operations including vector–matrix multiplication in Kronecker form within Power, Jacobi, and Generalized Minimal Residual methods. Numerical experiments on multidimensional problems of varying sizes indicate that larger memory savings are obtained with the HTD approach as the number of dimensions increases. © 2017 Elsevier B.V.en_US
dc.embargo.release2019-10-01en_US
dc.identifier.doi10.1016/j.peva.2017.08.002en_US
dc.identifier.issn0166-5316
dc.identifier.urihttp://hdl.handle.net/11693/37344
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.peva.2017.08.002en_US
dc.source.titlePerformance Evaluationen_US
dc.subjectCompact vectoren_US
dc.subjectHierarchical tucker decompositionen_US
dc.subjectKronecker producten_US
dc.subjectMarkov chainen_US
dc.subjectReachable state spaceen_US
dc.subjectChainsen_US
dc.subjectContinuous time systemsen_US
dc.subjectJacobian matricesen_US
dc.subjectMarkov processesen_US
dc.subjectMatrix algebraen_US
dc.subjectStochastic modelsen_US
dc.subjectStochastic systemsen_US
dc.subjectVectorsen_US
dc.subjectContinuous time Markov chainen_US
dc.subjectGeneralized minimal residual methodsen_US
dc.subjectInfinitesimal generatoren_US
dc.subjectMarkovian representationen_US
dc.subjectMultidimensional problemsen_US
dc.subjectTucker decompositionsen_US
dc.subjectVector-matrix multiplicationsen_US
dc.subjectVector spacesen_US
dc.titleOn compact solution vectors in Kronecker-based Markovian analysisen_US
dc.typeArticleen_US
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