Ferry boats and customers arrive at a ferry station in accordance with two independent homogeneous Poisson processes with intensities \(\lambda\) and \(\mu\), respectively. If there are \(k\) customers at the ferry station, when a boat arrives, then it departs with \(\min (k, n)\) passengers ( \(n\) is the capacity of each boat). If \(k>n\), then the remaining \(k-n\) customers wait for the next boat. The sojourn times of the boats at the station are assumed to be negligibly small.

Model the situation by a suitable homogeneous Markov chain \(\{X(t), t \geq 0\}\) and draw the transition graph.