Octave package for Queueing Networks and Markov chains analysis: ctmcisir

Function Reference: `ctmcisir`

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.

Function Reference: ctmcisir

Function Reference: `ctmcisir`