Product form distributions from decompositions of Markov chains

Necessary and sufficient conditions are given for the decomposition of a discrete-time, discrete-state Markov chain into two Markov chains, each having an independent state behaviour. The independence means that the equilibrium probabilities of the original Markov chain can be calculated as a product of those of the Markov chains resulting from the decomposition. This can greatly reduce the computation required to calculate such probabilities. The technique has applications in computer and telecommunications performance modelling and other disciplines involving Markovian models