Consider a call center in which calls arrive according to a Poisson pro- cess with rate 20 per hour. Assume that there are two operators handling three phone lines. However, the second operator only works when all three lines are busy. Assume that the service times for both operators are independent ex- ponential random variables with rate 12 per hour. (Please define the random variables you use and explain your results.)

(a) (10) Describe a continuous time Markov chain to model the system and give the transition rate diagram.

(b) (10) What's the long-run average probability that both operators are busy?