Analyzing Markov chains using Kronecker products: theory and applications

Kronecker products are used to define the underlying Markov chain (MC) invarious 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, systemsthat 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 networksand stochastic chemical kinetics are provided to motivate decompositional andmatrix analytic methods, respectively. INDICE: Introduction.- Background.- Kronecker representation.- Preprocessing.- Block iterative methods for Kronecker products.- Preconditioned projection methods.- Multilevel methods.- Decompositional methods.- Matrix analytic methods.

• ISBN: 978-1-4614-4189-2
• Editorial: Springer
• Encuadernacion: Rústica
• Fecha Publicación: 31/08/2012
• Nº Volúmenes: 1
• Idioma: Inglés