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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.

Distribution (Probability theory). --- Kronecker products. --- Markov processes. --- Mathematics. --- Numerical analysis. --- Kronecker products --- Markov processes --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematical Statistics --- Number theory. --- Number study --- Numbers, Theory of --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Mathematical statistics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Numerical Analysis. --- Probability and Statistics in Computer Science. --- Stochastic processes --- Distribution (Probability theory. --- Computer science. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Informatics --- Science --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical methods

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Operational research. Game theory --- Numerical analysis --- stochastische analyse --- informatietechnologie --- kansrekening --- numerieke analyse