Function File: M = dtmcfpt (P)

Compute mean first passage times and mean recurrence times for an irreducible discrete-time Markov chain over the state space {1, …, N}.

INPUTS

P(i,j)

transition probability from state i to state j. P must be an irreducible stochastic matrix, which means that the sum of each row must be 1 (\sum_{j=1}^N P_{i j} = 1), and the rank of P must be N.

OUTPUTS

M(i,j)

For all 1 ≤ i, j ≤ N, i \neq j, M(i,j) is the average number of transitions before state j is entered for the first time, starting from state i. M(i,i) is the mean recurrence time of state i, and represents the average time needed to return to state i.

REFERENCES

• Grinstead, Charles M.; Snell, J. Laurie (July 1997). Introduction to Probability, Ch. 11: Markov Chains. American Mathematical Society. ISBN 978-0821807491.

See also: ctmcfpt.

Package: queueing