4. Consider a two station queueing network (each station has one server) in which arrivals only occur at the rst server and do so at rate 2. If a customer nds server 1 free he enters the system; otherwise he goes away. When a customer is done at the rst server he moves on to the second server if it is free and leaves the system if it is not. Suppose that server 1 serves at rate 4 while server 2 serves at rate 2. All the interarrival time distributions and service time distributions are exponential. (a) In the long run, what proportion of customers enter the system? (b) In the long run, what proportion of the customers visit server 2? (c) Suppose now the system has one customer with server 1 and no customer with server 2. What is the expected time it takes for the system to be idle (i.e., no customer in the network)