There is currently a single clerk at the cafeteria in a business school building. Each average customer spends 3.125 minutes in total in the cafeteria, although 1.875 minutes of that time is spent waiting in line. On average, there are 1.875 customers in total in the cafeteria (either waiting in line or being rung up by the clerk).
a. What fraction of the time is the clerk busy?
b. The manager is considering adding a second clerk to the cafeteria. One of the Ops professors suggests that this new clerk be dedicated to serving faculty and staff (who make up one third of the customers). He promises that this will make the students better off, since they will no longer be stuck waiting behind faculty or staff. Everyone arrives randomly and unexpectedly to the cafeteria line, and the inter-arrival times are exponentially distributed. Further, the checkout time is the same for everyone. If the professor’s suggestion is implemented, how much time, on average, will a student spend in line?
c. And how much time would a faculty or staff member spend in line?
d. Should the manager accept the suggestion of the Ops professor, or is there a better alternative?