Two queues in series. Consider a two station queueing network in which arrivals only occur at the first server and do so at rate 2. If a customer finds server 1 free he enters the system; otherwise he goes away. When a customer is at the first server he moves on to the second server if it is free the system if it is not. Suppose that server 1 serves at rate 4 while server 2 serves at rate 2. Formulate a Markov chain model for this system with state space 10, 1,2,12} where the state indicates the servers who are busy. In the long run

(a) what proportion of customers enter the system?
(b) What proportion of the customers visit server 2?