Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 36

The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests, and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hotel and the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. It takes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel (exponentially distributed).
a. What is the average time a cab must wait for a fare
b. What is the probability that the line will be full when a cab drives by, causing it to drive on