03299nam 22005295 450 991030013800332120200704082817.03-319-97129-810.1007/978-3-319-97129-2(CKB)4100000006674883(MiAaPQ)EBC5521384(DE-He213)978-3-319-97129-2(PPN)230539440(EXLCZ)99410000000667488320180921d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierKronecker Modeling and Analysis of Multidimensional Markovian Systems /by Tuğrul Dayar1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (284 pages)Springer Series in Operations Research and Financial Engineering,1431-85983-319-97128-X Introduction -- Modeling with Kronecker Products -- Avoiding Unreachable States -- Preprocessing -- Vector-Kronecker Product Multiplication -- Steady-State Analysis -- Transient Analysis -- Conclusion.This work considers Kronecker-based models with finite as well as countably infinite state spaces for multidimensional Markovian systems by paying particular attention to those whose reachable state spaces are smaller than their product state spaces. Numerical methods for steady-state and transient analysis of Kronecker-based multidimensional Markovian models are discussed in detail together with implementation issues. Case studies are provided to explain concepts and motivate use of methods. Having grown out of research from the past twenty years, this book expands upon the author’s previously published book Analyzing Markov Chains using Kronecker Products (Springer, 2012). The subject matter is interdisciplinary and at the intersection of applied mathematics and computer science. The book will be of use to researchers and graduate students with an understanding of basic linear algebra, probability, and discrete mathematics.Springer Series in Operations Research and Financial Engineering,1431-8598ProbabilitiesComputer scienceMathematicsComputer system failuresProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Computational Mathematics and Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M1400XSystem Performance and Evaluationhttps://scigraph.springernature.com/ontologies/product-market-codes/I13049Probabilities.Computer scienceMathematics.Computer system failures.Probability Theory and Stochastic Processes.Computational Mathematics and Numerical Analysis.System Performance and Evaluation.512.9434Dayar Tuğrulauthttp://id.loc.gov/vocabulary/relators/aut767834BOOK9910300138003321Kronecker Modeling and Analysis of Multidimensional Markovian Systems1923100UNINA