Function File: [r s] = ctmcisir (P)

Check if Q is irreducible, and identify Strongly Connected Components (SCC) in the transition graph of the DTMC with infinitesimal generator matrix Q.

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.

OUTPUTS

r

1 if Q is irreducible, 0 otherwise.

s(i)

strongly connected component (SCC) that state i belongs to. SCCs are numbered 1, 2, …. If the graph is strongly connected, then there is a single SCC and the predicate all(s == 1) evaluates to true.

Package: queueing