Iterative Method for Steady State Reliability Analysis of Complex Markov Systems

An iterative procedure for evaluating steady-state probabilities of complex Markov systems is proposed; it is based upon a generalization of Seidel´s method for solving systems of linear algebraic equations. The probabilities are evaluated with desired accuracy by sequentially solving equation sets of much lower order than this of the entire system. For the systems with states transmitting only to states of higher and (or) lower probability magnitude orders, simple, easily composable recurrent formulas for state probabilities are obtained. An illustrative example is included.