Octave package for Queueing Networks and Markov chains analysis: dtmcisir

Function Reference: `dtmcisir`

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

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

INPUTS

P(i,j)

transition probability from state $i$ to state $j$ . P must be an $N \times N$ stochastic matrix.

OUTPUTS

r

1 if P is irreducible (i.e., the state transition graph is strongly connected), 0 otherwise (scalar)

s(i)

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

Function Reference: dtmcisir

Function Reference: `dtmcisir`