Please explain thoroughly! Thanks so much!

Problem 2: You are in charge of a small medical clinic. People arrive 24/7 for care at a rate of 3 people per hour. Arrivals follow a Poisson process which means that the inter- arrival times are exponentially distributed. There are always two doctors on duty. Service times are exponentially distributed with a mean service time of 30 minutes. To do this problem, you can either use the (rather messy) equations for this type of queue or you can use the non-normalized probability method. If you use the non- normalized probability method, be sure to let the states go from 0 to 1000 or more). a) Find the average number of patients in the system b) Find the average time a patient spends in the system c) Find the average time a patient spends waiting to see a doctor d) Find the average number of people in the waiting room. e) What is the probability that there is no one in the system? f) What do you think would happen to these performance metrics if the service times had a smaller coefficient of variation (standard deviation divided by the mean) than does the exponential distribution which has a coefficient of variation of 1. For example, an Erlang-4 distribution with the same mean as the exponential distribution would have a coefficient of variation of 0.5 g) Suppose the clinic decides that it needs to limit the number of people in the waiting room to 2 people at most. Anyone who arrives when there are already 2 people in the waiting room will be told that they need to seek care somewhere else. It will be as if these patients had not arrived at all. What do you think would happen to the metrics you computed in parts (a) through (d)? h) If you did the first four parts correctly, you would have found that the average waiting time before seeing a doctor exceeded half an hour. How many doctors does the clinic need to ensure that the average waiting time is less than half an hour? Give the number of doctors needed and the new performance metrics (the values of parts (a) through (d)) with this many doctors