Consider the M/M/1 system with a queue capacity of two in which customers arrive at rate 2 = 3 per hour and the server completes service at rate u = 2 per hour. However, the server experiences a breakdown according to a Possion process at rate a=1, which causes the system to shut down. All customers that are in the system depart, and no additional arrivals are allowed to enter until the breakdown is fixed. The time to fix the breakdown is exponentially distributed with with mean of 2/3 hours. a) Give the transition diagram and solve the balance equations. b) Find the average number of customers in the queue and the average amount of time a customer spends in the queue. c) What is the utilization rate of the server? Consider the M/M/1 system with a queue capacity of two in which customers arrive at rate 2 = 3 per hour and the server completes service at rate u = 2 per hour. However, the server experiences a breakdown according to a Possion process at rate a=1, which causes the system to shut down. All customers that are in the system depart, and no additional arrivals are allowed to enter until the breakdown is fixed. The time to fix the breakdown is exponentially distributed with with mean of 2/3 hours. a) Give the transition diagram and solve the balance equations. b) Find the average number of customers in the queue and the average amount of time a customer spends in the queue. c) What is the utilization rate of the server