Reflections on the Numerical Solution of Markov Chains

It has been 45 years since Vic Wallace introduced RQA1, the first software system to generate and then compute the stationary distribution of Markov chains. RQA1 proved successful for a period of time but eventually hit upon a type of problem that it just could not solve, namely a nearly-completely-decomposable (NCD) Markov chain. In the intervening years our understanding of NCD systems has grown immensely which in turn has lead to the development of numerical techniques specifically designed for, and very effective at, solving such problems.