# Markov-chain alternative (from the perspective of “feedback”)

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?

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Just add even more states. Everything that can happen can be called a state and the only problem is to figure out the correct transition probabilities. –  fedja Apr 24 '10 at 18:27
I don't see how a future event in the chain (like reaching a limit) could alter the behaviour at a previous state (to "fork" a new server). And this seems to go against the definiton of a Markov-chain.. –  Zoltan Apr 24 '10 at 20:06
It is not "a future event". The split is triggered by actually achieving the limit, so you just have a non-trivial transition probability from the state with one long queue to the state with 2 short queues, That's all. –  fedja Apr 24 '10 at 22:00