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 12 minutes to land and clear the runway (following an exponential distribution). Planes arrive at the airport at the rate of one every 15 minutes. The arrival rate follows a Poisson distribution. A plane is considered to have entered the “system” once it has notified the airport that it is in the vicinity and wants to land. For purposes of this analysis, you can ignore the planes taking off.

a) Determine the average number of planes that will stack up (wait) to land.

b) Find the average time a plane must "wait in line" before it can land.

c) What is the probability that a plane approaching the airport will find at least three other planes already in the “system” waiting to land?

d) Suppose that the cost assigned to a plane while it is waiting to land (in the stack) is $1,000 per hour and the cost per hour for the air traffic control operation is $2,000 per hour. What is the total cost of this operation considering both the waiting time and the air traffic control operation?

e) There is a second airport in the immediate vicinity of the Peachtree airport which is currently closed. The FAA is considering re-opening this one as there would be no cost to do this and it believes it would improve customer service. However the cost per hour for the air traffic control operation is $2,500 per hour at this second airport. It would still take an airplane 12 minutes to land and clear the runway (following an exponential distribution). The Peachtree airport and this second airport would work as a multiple server system. What would be the cost of this multiple server operation?