Structured analysis approaches for large Markov chains

This paper introduces structured analysis approaches for the iterative nume rical analysis of continuous time Markov chains (CTMCs) which are a means t o extend the size of analyzable state spaces significantly compared with co nventional techniques. It is shown how generator matrices of large CTMCs ca n be represented in a very compact form using tensor products/sums, how thi s representation can be exploited in numerical solution techniques and how numerical analysis profits from this exploitation. Additionally, advanced t ensor based analysis techniques including aggregation/disaggregation and pr econditioning techniques are introduced. (C) 1999 Elsevier Science B.V. and IMACS. All rights reserved.