The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 8 minutes to land and clear the runway (exponentially distributed). Planes arrive at the airport at the rate of 5 per hour (Poisson distributed).
a. Determine the average number of planes that will stack up waiting to land.
b. Find the average time a plane must wait in line before it can land.
c. Calculate the average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land.
d. The FAA has a rule that an air traffic controller can, on the average, land planes a maximum of 45 minutes out of every hour. There must be 15 minutes of idle time available to relieve the tension. Will this airport have to hire an extra air traffic controller?