Equilibrium distribution of finite-state Markov processes

Very simple methods are presented for computing equilibrium distributions of finite-state Markov processes in continuous time and in discrete time, namely Markov chains. These use the APL domino function which takes a least-squares approach which is efficient with systems of up to 50 states and probably more. This approach can also be used to solve for mean interval occupancies. It is not suggested that the least-squares solution be implemented in traditional languages like Fortran simply for the purpose of finding equilibrium distributions, for which the state reduction method is simpler. However, if APL is available the methods described provide accurate and extremely simple solutions for discrete or continuous-time models. More importantly, the APL domino function leads to a powerful and simple computation of mean interval occupancies and, hence, availabilities