Returns the transition probability matrix P for a discrete
birth-death process over state space {1, …, N}.
For each i=1, …, (N-1),
b(i) is the transition probability from state
i to (i+1), and d(i) is the transition
probability from state (i+1) to i.
Matrix \bf P is defined as:
/ \ |1-b(1) b(1) | | d(1) (1-d(1)-b(2)) b(2) | | d(2) (1-d(2)-b(3)) b(3) | | | | ... ... ... | | | | d(N-2) (1-d(N-2)-b(N-1)) b(N-1) | | d(N-1) 1-d(N-1) | \ /
where \lambda_i and \mu_i are the birth and death probabilities, respectively.
See also: ctmcbd.
The following code
birth = [ .2 .3 .4 ]; death = [ .1 .2 .3 ]; P = dtmcbd( birth, death ); disp(P)
Produces the following output
0.80000 0.20000 0.00000 0.00000 0.10000 0.60000 0.30000 0.00000 0.00000 0.20000 0.40000 0.40000 0.00000 0.00000 0.30000 0.70000
Package: queueing