Consider this old exam question. By denoting $\lambda_A = \frac{1}{2}, \lambda_A = \frac{1}{6}$ as the customer arrival intensities for terminals A and B respective, and by $\mu_{S_{A, B}} = \frac{1}{12}, \mu_{S_{A}} = \frac{1}{8}, \mu_{S_{B}} = \frac{1}{10}$ the shuttle's return intensity from tours A&B, A and B I sketched the following chain. In my opinion that chain is wrong, as it allows the possibility of a customer 1 heading to terminal A arriving before a customer 2 that heads to terminal B such that the shuttle would head to terminal B instead of both A and B. Therefore I think that this chain encapsulates the situation better, but the chain has four states when the problem asked for a chain with three states.
So is the question flawed, or is it possible to describe the situation with only three states?