The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow a Poisson probability distribution, with an arrival rate of 9 boats per hour, and that service times follow an exponential probability distribution, with a service rate of 15 boats per hour. The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Assume that the arrival rate is 5 boats per hour and that the service rate for each server is 10 boats per hour.
A. What is the probability that the boat dock will be idle?
B. What is the average number of boats that will be waiting for service?
C. What is the average time a boat will spend waiting for service?
D. What is the average time a boat will spend at the dock?
E. If you were the manager of Fore and Aft Marina, would you be satisfied with the service level your system will be providing? Why or why not?