Consider a single-server queuing system that serves two types of customers (A and B) on a first-in-first-out basis, with unlimited capacity to store waiting customers. Types A and B have independent Poisson arrival processes with average arrival rates of 2 per hour and 4 per hour, respectively. Because the two arrival streams are independent, the overall arrival process is also a Poisson process, with an average arrival rate of 6 customers per hour, and the probability that a new arrival is of type A is 212+4)=1/3. Service of each type A customer takes exactly 15 minutes, and service of each type B customer takes exactly 6 minutes.
What is the expected time in system for a type A customer (including waiting and service time)?