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5.6. 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.

5.6. 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.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter7: Applying Fractions
Section7.5: Percents
Problem 57WE
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5.6. 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.
Transcribed Image Text:5.6. 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 ten- sion. Will this airport have to hire an extra air traffic controller?
Transcribed Image Text:There must be 15 minutes of idle time available to relieve the ten- sion. Will this airport have to hire an extra air traffic controller?
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