Consider a queueing system with two classes of customers, type A and type B. Type A customers arrive according to a Poisson process of rate λA and customers of type B arrive according to an independent Poisson process of rate λB. The queue has a FCFS server with exponential IID service times of rate μ > λA + λB. Characterize the departure process of class A customers; explain carefully. Hint: Consider the combined arrival process and be judicious about how to select between A and B types of customers.
Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.