Ferry boats and customers arrive at a ferry station in accordance with two independent homogeneous Poisson processes with intensities λ and μ, respectively. If there are k customers at the ferry...

Ferry boats and customers arrive at a ferry station in accordance with two independent homogeneous Poisson processes with intensities λ and μ, 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 ≥ 0} and draw the transition graph.