1. Cachon and Terweisch 8.5: Atlantic Video, a small video rental store in Philadelphia, is open 24 hours a day and experiences customers arriving around the clock. A recent analysis done by the store manager indicates that there are 30 customers arriving every hour, with a standard deviation of interarrival times of 2 minutes. This arrival pattern is consistent throughout the day. The checkout is currently operated by one employee, who needs on average 1.7 minutes to check out a customer. The standard deviation of this checkout time is 3 minutes.
(a) If you assume that every customer rents at least one video, what is the average time a customer has to wait in line before getting served by the checkout employee, not including the actual checkout time?
(b) If there are no customers requiring checkout, the employee is sorting returned videos, of which there are always plenty waiting to be sorted. How many videos can the employee sort over an 8 hour shift (assume no breaks) if it takes exactly 1.5 minutes to sort a single video?