Consider a machine repairmen problem with $20$ machines and $2$ repairmen. Each machine remains operational for an exponential duration with mean $40$ minutes. When a failure occurs, repair activity starts immediately if a repair person is available. Otherwise, the machine has to wait until a repair person becomes free. Repair times also last for an exponential period with mean $20$ minutes. Once the machine is repaired, it is back in operation governed by the same lifetime distribution. a$)$ State the characteristics of this system and describe the relevant model using Kendall$$s notation. b$)$ Draw the state transition diagram specifying the states and the transition rates.