Function Reference: ctmcmtta

Function File: t = ctmcmtta (Q, p)

Compute the Mean-Time to Absorption (MTTA) of the CTMC described by the infinitesimal generator matrix Q, starting from initial occupancy probabilities p. If there are no absorbing states, this function fails with an error.

INPUTS

Q(i,j)

N \times N infinitesimal generator matrix. Q(i,j) is the transition rate from state i to state j, i \neq j. The matrix Q must satisfy the condition \sum_j=1^N Q_i,j = 0

p(i)

probability that the system is in state i at time 0, for each i=1, …, N

OUTPUTS

t

Mean time to absorption of the process represented by matrix Q. If there are no absorbing states, this function fails.

REFERENCES

  • G. Bolch, S. Greiner, H. de Meer and K. Trivedi, Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998.

See also: ctmcexps

Example: 1

  

 mu = 0.01;
 death = [ 3 4 5 ] * mu;
 birth = 0*death;
 Q = ctmcbd(birth,death);
 t = ctmcmtta(Q,[0 0 0 1])

t = 78.333

Example: 2

  

 N = 50;
 birth = death = ones(1,N-1); birth(1) = death(N-1) = 0;
 Q = diag(birth,1)+diag(death,-1);
 Q -= diag(sum(Q,2));
 t = zeros(1,N/2);
 initial_state = 1:(N/2);
 for i=initial_state
   p = zeros(1,N); p(i) = 1;
   t(i) = ctmcmtta(Q,p);
 endfor
 plot(initial_state,t,"+");
 title(sprintf("Birth-Death process, %d states, absorbing states=1,%d",N,N));
 xlabel("Initial state");
 ylabel("MTTA");
plotted figure