โ Scribed by Tuฤrul Dayar (auth.)
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Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively.
Front Matter....Pages i-ix
Introduction....Pages 1-7
Preliminaries....Pages 9-19
Iterative Methods....Pages 21-35
Decompositional Methods....Pages 37-56
Matrix-Analytic Methods....Pages 57-73
Conclusion....Pages 75-75
Back Matter....Pages 77-86
Probability Theory and Stochastic Processes; Numerical Analysis; Probability and Statistics in Computer Science
๐ SIMILAR VOLUMES
Introduction -- Preliminaries -- Iterative Methods -- Decompositional Methods -- Matrix-Analytic Methods -- Conclusion.653Computer science
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