Approximate Product Form Solutions for MarkovChainsJohann Christoph

An approximation technique for nite state Markov chains is proposed. The solutions are in product form 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. Accurate approximations are obtained, and moreover, the accuracy can be innuenced: 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. In this paper, we discuss steady state probabilities.