MS Class Note

MS Class Note - Waiting lines 12 The Peachtree Airport in...

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Waiting lines 12. 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. Planes arrive at the airport at the rate of 4 per hour. 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 want 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? Solution

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13. The First American Bank of Rapid City has one outside drive-up teller. It takes the teller an average of 4 minutes to serve a bank customer. Customers arrive at the drive-up window at the rate of 12 per hour. The bank operations officer is currently analyzing the possibility of adding a second drive-up window at an annual cost of \$20,000. It is assumed that arriving cars would be equally divided between both windows. The operations officer estimates that each minute’s reduction in customer waiting time would increase the bank’s revenue by \$2,000 annually. Should the second drive-up window be installed? Solution 15. All truck traveling on Interstate 40 between Albuquerque and Amarillo are required to stop at a weigh station. Trucks arrive at the weigh station at a rate of 200 per 8-hour day, and the station can weigh, on the average, 220 trucks per day. a. Determine the average number of trucks waiting, the average time spend waiting and being weighed at the weigh station by each truck, and the average waiting time before being weighed for each truck. b. If the truck drivers find out they must remain at the weigh station longer than 15 minutes on the average, the will start taking a different route or traveling at night, thus depriving the state of taxes. The state of New Mexico estimates it loses \$10,000 in taxes per year for each extra minute that trucks must remain at the weigh station. A new set of scales would have the same service capacity as the
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• Spring '14
• Mean, Exponential distribution, Truck, average time

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