I'm trying to understand the arrival rate of a queue model having a limited population size of $M$. Now the notes given to us from our lecturer state that the arrival rate is:
$$\lambda_n = \begin{cases} (M-n)\lambda,& 0\leqslant n<M\\ 0,& n\geqslant M\end{cases} $$
- $M$ = Total number of customers.
- $n$ = State number
Can someone please give me a formal or intuitive definition of this? Because I don't really understand how this holds. I searched online but haven't found any concrete definition about this, also I do not own any books regarding this study unit. Thanks.