Firstly, consider a Markov chain in your mind. Probability of each state of the Markov chain can be obtained by following Chapman–Kolmogorov equation.
$$ P(n\Delta t) = M^{n}P(0) $$
where P is the probability vector, P(0) is initial probability vector and M is transition matrix of Markov chain.
Secondly and now, my problem is about Interactive Markov Chain (IMC). For example, consider following IMC model.
As can be seen, this model has a similarity to Petri Nets. However, I need to know how I can one achieve the probability of each state of this model? In the literature, always authors use software tool but I need a solution by hand on paper not through software tool.
Thanks a lot.