Function File: M = ctmcfpt (Q)

Function File: m = ctmcfpt (Q, i, j)

Compute mean first passage times for an irreducible continuous-time Markov chain.

INPUTS

Q(i,j)

Infinitesimal generator matrix. Q is a N \times N square matrix where Q(i,j) is the transition rate from state i to state j, for 1 ≤ i, j ≤ N, i \neq j. Transition rates must be nonnegative, and \sum_{j=1}^N Q_{i,j} = 0

i

Initial state.

j

Destination state.

OUTPUTS

M(i,j)

average time before state j is visited for the first time, starting from state i. We let M(i,i) = 0.

m

m is the average time before state j is visited for the first time, starting from state i.

See also: ctmcmtta.

Demonstration 1

 Q = [ -1.0  0.9  0.1; ...
        0.1 -1.0  0.9; ...
        0.9  0.1 -1.0 ];
 M = ctmcfpt(Q)
 m = ctmcfpt(Q,1,3)

M =

   0.00000   1.20879   2.08791
   2.08791   0.00000   1.20879
   1.20879   2.08791   0.00000

m =  2.0879

Package: queueing