Consider the queue: Customer \rightarrow S_1 \rightarrow S_2 \rightarrow leave.

Customers arrive at rate 2; S_1 serves at rate 4; S_2 serves at rate 2.

If a customer comes to an occupied server he leaves the system.

Formulate a markov chain model for this system with state space \{0,1,2,12\} where the states indicate the servers who are busy.

(a)In the long run what proportion of customers enter the system? (If a customer leaves before being served by S_1 he does not enter)
(b)What proportion of customers visit server 2?