Topic: Queueing Theory Case Narrative: 1. An air charter company catering to tourists is planning to fly to a remotely located but very popular Philippine tourist destination in Palawan serviced by a smal airport with only one runway. As a result, chartered airplanes landing in this airport are accommodated for landing during specific hours of the day (7 AM to 12 NN only for safety considerations) on a First Come First Served basis by the air traffic controller. Other arriving airplanes that have not been given clearance will have to fly on a holding pattern until each airplane is given clearance to land Based on the records of the air traffic controller, requests from airplane pilots to land at the airport from 7 AM to 12 NN is received every 12 minutes (on average) and is assumed to follow a Poisson Distribution. If an airplane that has been given landing clearance can complete the landing and proper parking of the airplane on the tarmac (to allow the next airplane to be given landing clearance) in 6 minutes, on average, (assumed to follow an exponential distribution): 1.1. Without consideration for airport capacity, what would be the probability that there would be 8 airplanes arriving in one hour? Express in percentage to the nearest tenths. 1.2. Without consideration for airport capacity, what would be the probability that there would be at least 3 airplanes arriving in one hour? Express in percentage to the nearest tenths. 1.3. What is the probability that the air charter company's plane will be instructed to be in the holding pattern when its pilot requests for clearance to land? Express in percentage to the nearest tenths. ( percentage to the nearest tenths. in the holding pattern, landing or parking), how much is the average cost of waiting (for fuel 1.4. What is the probability that there will be three airplanes in the holding pattern? Express in 1.5. If the airline charter company's airplane consumes 40 liters/hour (regardless of whether it is alone) for clearance to land if the cost of aviation gasoline is PhP60/liter? 1.6. What would be the average fuel cost for being in the holding pattern up to the point where it is able to land and park on the tarmac?
