Solve question 1 - 4

I will post again for 5 to 8.

Problem 3. A service facility consists of one server who can serve an average of 2 customers per hour service times are exponential). An average of 3 customers per hour arrive at the facility (interarrival times are assumed esponential). The system capacity is three customers. Complete the following items listed below: 1. Define the states 2. Define the events and the rates associated with the events. 3. Construct the state transition diagram for this model. 4. Set up flow balance equations using your state transition diagram. 5. Solve for the steady state probabilities. 6. On average, how many potential customers enter the system each hous? 7. What is the probability that the server will be busy? 8. How do we know a steady state probability distribution exists for a queueing system? If the arrival rate is bigger than the service cate what does this imply