Question

WAITING LINES

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 10 minutes to land and clear the runway, but planes arrive at the rate of 4 per hour.

Set up the waiting lines problem and be prepared to answer questions from the output

WAITINGLINES(Airport)

__________8a. What is the average number of planes that will stack up waiting to land?

__________8b. What is the average time a plane must wait in line before it can land?

__________8c. What is the probability that no planes are in the area and the traffic controller

can actually take a breather?
__________8d. What is 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?

__________8e. If the FAA requires 15 minutes of idle time every hour for their Air Traffic

Controllers (75% utilization), will the airport have to hire an extra one?

Answer 1

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 10 minutes to land and clear the runway, but planes arrive at the rate of 4 per hour.

That is arrival rate () = 4 per hour. and service rate () = 10 minutes = 60/10 per hour = 6 per hour

8a. The average number of planes that will stack up waiting to land is

8b. The average time a plane must wait in line before it can land is

8c. The probability that no planes are in the area and the traffic controller can actually take a breather is

8d. 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 is

8e.

If the FAA requires 15 minutes of idle time every hour for their Air Traffic Controllers, then airport have to hire an extra one when given utilization factor is exceed 0.75. So,

We see that no requirement to hire an extra one.