I'm trying to sketch the Markov chain for a Random Early Discard queueing policy where customers arrive to the queue of infinite size according to a Poisson process with rate $\lambda$. Customers that arrive are entered into the queue with probability $\alpha_{n} = \frac{1}{n+1}$ and are blocked from the queue with rate $1-\alpha_{n}$. The service time is exponentially distributed with mean $\frac{1}{\mu}$.
I think the jumps from state 0 -> 1 -> 2 -> ... -> n -> n+1 should be $\alpha_{n}\lambda$ and arrows going to the same state, say 0 to 0, should be $(1-\alpha_{n})\lambda$, and arrows going successively backward between states would be $\mu$. Is this correct or am I misunderstanding how this works? I learned some introductory stuff about Markov chains in probability, but the arrows were always labeled as probabilities that added to 1 instead of rates of arrivals per second.