There is some probability of starting in i and being absorbed in j for any value of n from 1 on up, because there is some probability of remaining in the transient states at each value of n. In this case, we have scalars rather than matrices, and the algebra is simple. So, when we have an absorbing Markov Chain, we can analyze it in several ways. First, we can find the probability of absorption on the n th transition. Finally, we can find the delay in the transient states prior to absorption.
Examples Let's consider a machine that fails.
Now let's look at the gambler's ruin problem. Say we have a game which we win with probability 0.6 and lose with probability 0.4. If we are just playing for fun, we might be interested in how long the game will last. As with any modeling and analysis approach, part of success lies in understanding the meaning of what we can compute. Problems Consider a production system with 5 stations.