This thesis presents the time-stopping method. The time-stopping method is a topological version of the state-partitioning method. The method modifies a markov diagram by stopping the time when the state of the system belongs to some sets. Its purpose is to reduce the markov diagram to a new markov diagram composed of the specific state.
By using the time-stopping method, this thesis derives the steady-state probability and characteristics of the cyclic process. And it also derives algorithms for computing the steady-state probability of the markov processes that have the special structures, which are composed of cycle chains that are connected at one or two states.
