Structured analysis approaches for large Markov chains Original Research Article

This paper introduces structured analysis approaches for the iterative numerical analysis of continuous time Markov chains (CTMCs) which are a means to extend the size of analyzable state spaces significantly compared with conventional techniques. It is shown how generator matrices of large CTMCs can be represented in a very compact form using tensor products/sums, how this representation can be exploited in numerical solution techniques and how numerical analysis profits from this exploitation. Additionally, advanced tensor based analysis techniques including aggregation/disaggregation and preconditioning techniques are introduced.