Airport Management

Dino-ville International Airport has two runways, one used exclusively for takeoffs and the other exclusively for landings. Airplanes arrive randomly in Dino-ville air space to request landing instructions at a mean rate of 10 per hour. The interarrival times are exponentially distributed. The time required for an airplane to land after receiving clearance to land has an exponential distribution with a mean of three minutes, and this process must be completed before giving clearance to land to another airplane. Airplanes awaiting clearance must circle the airport.

The Federal Aviation Administration has a number of criteria regarding the safe level of congestion of airplanes waiting to land. These criteria depend on a number of factors regarding the airport involved, such as the number of runways available for landing. For Dino-ville, the criteria are as follows:

1. The average number of airplanes waiting to receive clearance to land should not exceed 1

2. 95% of the time, the actual number of airplanes waiting to receive clearance to land should not exceed 4

3. For 99% of the airplanes, the amount of time spend circling the airport before receiving clearance to land exceed 30 minutes

In this problem, you are asked to analyze the queueing system in Dino-ville International Airport.

a) Explain the queueing system at Dino-ville Airport by defining the customers, arrival rate, server, service rate and use Kendall's notation to define the queueing system.

b) Evaluate if criteria 1-3 are currently satisfied.

c) A major airline is considering adding this airport as one of its hubs. This would increase the mean arrival rate to 15 airplanes per hour. Evaluate if criteria 1-3 would be satisfied if this happens.

d) Airport management is now considering a second runway for landings. It is estimated that this eventually would increase the mean arrival rate to 25 airplanes per hour as more airlines will become active at the airport. Evaluate if criteria 1-3 would be satisfied if this happens.