An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 19

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 5 boats per hour, and that service times follow an exponential probability distribution, with a service rate of 10 boats per hour. Answer the following questions:
a. What is the probability that no boats are in the system?
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?