Aggregation Technique for the Transient Analysis of Stiff Markov Chains

摘要

An approximation algorithm for systematically converting a stiff Markov chain into a nonstiff chain with a smaller state space is discussed in this paper. After classifying the set of all states into fast and slow states, the algorithm proceeds by further classifying fast states into fast recurrent subsets and a fast transient subset. A separate analysis of each of these flat subsets is done and each fast recurrent subset is replaced by a single slow state while the fast recurrent subset is replaced by a probabilistic switch. After this reduction, the remaining small and nonstiff Markov chain is analyzed by a conventional technique. The algorithm produces asymptotically exact results with respect to the aggregation of fast transient states, while for fast recurrent subsets the asymptotic accuracy depends on the degree of coupling between the fast subset and the remaining states. The algorithm is illustrated using two examples.