Conditional mean first passage time in a Markov chain

摘要

Kemeny and Snell (Markov Chains, Van Nostrand, 1960) developed a computational procedure for calculating the conditional mean time to absorption in a designated absorbing state in an absorbing Markov chain which has multiple absorbing states plus a set of transient states, given that the chain will ultimately end up in the designated absorbing state. This paper extends the computational procedure developed by Kemeny and Snell so that it can be applied to a multichain which has at least one closed communicating class of non-absorbing recurrent states. The paper derives a formula for calculating the conditional mean first passage time from a transient state to a designated recurrent state in a multichain, when it is hypothesized that the multichain will eventually reach the recurrent closed class to which the designated recurrent state belongs. The procedure devised by Kemeny and Snell, augmented by the formula contributed by this paper, is applied to a simplified multichain chain model of a production process.