Approximate product form solutions for Markov chains

An approximation technique for finite state Markov chains is proposed. The solutions are in product from and can be calculated iteratively. This iteration is equivalent to disaggregating macro probabilities, multiplying with transition probabilities, and aggregating the obtained state probabilities — we call it DA iteration. Large Markov chains with many states can be solved, so large that the state probabilities could neither be stored nor calculated in any computer. te approximations are obtained, and moreover, the accuracy can be influenced: The more aggregates are considered, the better the approximations are, if the aggregates are chosen suitably. Practical experience is encouraging: The obtained accuracy compares favourably with other approximation methods and with exact solutions. s paper, we discuss steady state probabilities, but time-dependent solutions are also obtainable.