Function File: L = dtmcexps (P, n, p0)

Function File: L = dtmcexps (P, p0)

Compute the expected number of visits to each state during the first n transitions, or until abrosption.

INPUTS

P(i,j)

N \times N transition matrix. P(i,j) is the transition probability from state i to state j.

n

Number of steps during which the expected number of visits are computed (n ≥ 0). If n=0, returns p0. If n > 0, returns the expected number of visits after exactly n transitions.

p0(i)

Initial state occupancy probabilities; p0(i) is the probability that the system is in state i at step 0.

OUTPUTS

L(i)

When called with two arguments, L(i) is the expected number of visits to state i before absorption. When called with three arguments, L(i) is the expected number of visits to state i during the first n transitions.

REFERENCES

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

See also: ctmcexps.

Package: queueing