Analyzing Markov Chains using Kronecker Products: Theory and by Tugrul Dayar

By Tugrul Dayar

Kronecker items are used to outline the underlying Markov chain (MC) in a variety of modeling formalisms, together with compositional Markovian types, hierarchical Markovian types, and stochastic strategy algebras. the incentive at the back of utilizing a Kronecker established illustration instead of a flat one is to relieve the garage necessities linked to the MC. With this technique, structures which are an order of significance greater may be analyzed at the related platform. The advancements within the answer of such MCs are reviewed from an algebraic standpoint and attainable components for extra learn are indicated with an emphasis on preprocessing utilizing reordering, grouping, and lumping and numerical research utilizing block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic equipment. Case experiences from closed queueing networks and stochastic chemical kinetics are supplied to inspire decompositional and matrix analytic tools, respectively.

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