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Expected number of airplanes circling the airport

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1. 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 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 are processed on an FCFS basis, with takeoffs occurring 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. What is the expected number of airplanes waiting in the system?

c. What is the average time for airplanes waiting in queue for clearance to land?

d. What is the average waiting time airplanes need to spend in the system?

e. What is the probability that airplanes land immediately upon arrival? (no waiting time for airplanes to land)

f. What is the probability of more than 3 airplanes in the system?

2. 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 served at a constant rate of 15 per hour. As a channel is added,, the arrival rate will be 6 per hour. If this two-channel system were to be used:

a. What would be the expected number of airplanes circling the airport, waiting in queue for clearance to land?

b. What is the expected number of airplanes waiting in the system?

c. What is the average time for airplanes waiting in queue for clearance to land?

d. What is the average waiting time airplanes need to spend in the system?

Reference no: EM132203587

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