Green Valley Airport has been in operation for several years and is beginning to experience flight congestion. A study of airport operations revealed that planes arrive at an average rate of 12 per hour, with Poisson distribution. On the single runaway, a plane can land and be cleared every 4 minutes on average, and service times have negative exponential distribution. Planes are processed on an FCFS basis, with takeoffs occuring between landings. Planes waiting to land are asked to circle the airport.
a) What is the expected number of airplanes circling the airport, waiting in queue for clearance to land?
b) A new ground-approach radar system approved by the Federal Aviation Administration is being considered as a means of reducing congestion. Under this system, planes can be processed at a constant rate of 15 per hour (i.e. the variance is zero). What would be the expected number of airplanes circling the airport, waiting in queue for clearance to land, if this system were to be used?
c) Assume that the cost of keeping an airplane in the air is approximately $70 per hour. If the cost of the proposed radar system were $100 per hour, would you recommend its adoption?