First of all, I'm not quiet sure the "feedback" word is used in this context. Let's say we have a simple M/M/1 queue. Markov-chains are used to describe such entities, for example taking the number of people in the queue as a state.

What if we introduce feedback into the picture? What if there's a chance at each state that if the number of people in the queue are larger than a fixed number, then we add an other queue to the picture - essentially transforming the underlying structure?

The same question arises if we say that at state $k$, there's an $A_{k}$ chance that $f(k)$ number of people arrive - we don't know the exact number of states.

Is there a way to describe this kind of situation?