Suppose that a single-server queuing system fits all the assumptions of the birth-and-death process except that customers always arrive in pairs. The mean arrival rate is 2 pairs per hour (4 customers per hour), and the mean service (when the server is busy) is 5 customers per hour.
(1) Construct the rate diagram for this queuing system.
(2) Develop the balance equations.
(3) For comparison purposes, display the rate diagram for the corresponding queuing system that completely fits the birth-and-death process, i.e., where customers arrive individually at a mean rate of 4 per hour.