Question 2 (50 points) A marina operates with two machines that put boats into the water. Boat owners arrive according to a Poisson process. After the boat owners arrive, they form a single common line, and the service is provided on a first-come-first-serve basis. Each machine operates as follows. Boat owners reverse their trailers into the machine, which operates like a large sling and lowers the boat into the water. The time to serve a customer at a machine follows an exponential distribution. Historical data show that, on average, it takes 18 minutes from the arrival of a boat owner till the time his/her boat is put into water. The average waiting time in line is 8 minutes. On average, there are 2.4 boats in the entire system, including those waiting in line and those being served by the machines.

a) (10 points) What is the average service rate of each machine? Give your answer in number of boats per hour.

b) (10 points) What is the average rate of customer arrival to the marina? Give your answer in number of customers per hour.

c) (5 points) What is the probability that a customer can be served immediately upon his/her arrival, without waiting?