4. (30p.) On average 10 customers come to a barber shop in one hour. The service time takes 30 minutes on average. There are only two chairs in the shop: one for the service and the other one for the waiting customer. Fifty per cent of customers do not want to wait at all. If they see that the barber is busy upon their arrival, they do not enter and they leave. One-fourth of customers can only wait by sitting. If they see that both chairs are occupied, they do not enter and they leave. The other one-fourth of customers can wait by sitting or standing. Customers are impatient. If they wait too long, they abandon (exit without receiving service). The mean time to abandon for a customer who waits by sitting is 30 minutes. Customers are more impatient while they are standing. The mean time to abandon for a standing customer is 5 minutes. Assume memoryless property for all the times. a. b. C. Construct a CTMC. Draw the state transition diagram. Find n and m for each n. Write the balance equations. Is this queuing system stable?