EAN: 9781461441892

SPRINGERBRIEFS IN MATHEMATICS ANALYZING MARKO...

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.

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