18 An average of 10 people per hour arrive (interarrival times are exponential) intending to swim laps at the local YMCA. Each intends to swim an average of 30 minutes.
The YMCA has three lanes open for lap swimming. If one swimmer is in a lane, he or she swims up and down the right side of the lane. If two swimmers are in a lane, each swims up and down one side of the lane. Swimmers always join the lane with the fewest number of swimmers. If all three lanes are occupied by two swimmers, a prospective swimmer becomes disgusted and goes running.
a What fraction of the time will 3 people be swimming laps?
b On the average, how many people are swimming laps in the pool?
c How many lanes does the YMCA need to allot to lap swimming to ensure that at most 5% of all prospective swimmers will become disgusted and go running?