Oita airport has been in operation for several years and it is beginning to experience flight congestions. A study of airport operations revealed that planes arrive at an average rate of 12 per hour with a poisson distribution. On the single runway a plane can land and be cleared every 4 minutes on average, and service times have a negative exponential distribution. Planes waiting to land are asked to circle the airport and can land on a first come first serve basis.
a) What is the expected number of airplanes circling the airport, waiting in queue for clearance to land?
b) A new radar system is being considered as a means to reducing congestion. Under the new system planes can be processed at a rate of 17 per hour. Under the leasing contract, the new system cost the airport 100$ per hour. Assume that the cost of keeping an airplane in the air is $70 per hour, is the leasing of the new radar system recommended?
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