Buchholz, P.Dayar, TuğrulKriege, J.Orhan, M. Can2018-04-122018-04-122016-080302-9743http://hdl.handle.net/11693/37502Date of Conference: 23-25 August, 2016Conference name: QEST: International Conference on Quantitative Evaluation of Systems - 13th International Conference, QEST 2016It is well known that the infinitesimal generator underlying a multi-dimensional Markov chain with a relatively large reachable state space can be represented compactly on a computer in the form of a block matrix in which each nonzero block is expressed as a sum of Kronecker products of smaller matrices. Nevertheless, solution vectors used in the analysis of such Kronecker-based Markovian representations still require memory proportional to the size of the reachable state space, and this becomes a bigger problem as the number of dimensions increases. The current paper shows that it is possible to use the hierarchical Tucker decomposition (HTD) to store the solution vectors during Kroneckerbased Markovian analysis relatively compactly and still carry out the basic operation of vector-matrix multiplication in Kronecker form relatively efficiently. Numerical experiments on two different problems of varying sizes indicate that larger memory savings are obtained with the HTD approach as the number of dimensions increases. © Springer International Publishing Switzerland 2016.EnglishCompact vectorsHierarchical Tucker decompositionKronecker productsMarkov chainsReachable state spaceChainsMarkov processesMatrix algebraVectorsCompact representationInfinitesimal generatorKronecker productMarkovian representationMulti-dimensional Markov chainsNumerical experimentsTucker decompositionsVector-matrix multiplicationsVector spacesConference Paper10.1007/978-3-319-43425-4_18