Question

The traffic volume in the year 2018 at an airport (number of take-offs and landings) during peak hour of each day is a described as a log-normal random variable with a mean of 200 planes and a standard deviation of 60 planes. a. If the present runway capacity (for landings and take-offs) is 350 planes per hour, what is the current probability of congestion? [2 marks] b. If the mean traffic volume is increasing linearly at the annual rate of 10% of the volume in 2018 with the coefficient of variation remaining constant what would be the probability of congestion at the airport in year 2028? [2 marks] c. Assuming the same projected growth rate of traffic volume as part (b), and that the maximum acceptable probability of congestion is 10% what year will the airport need to increase their runway capacity? [4 marks] d. Assuming the same projected growth rate of traffic volume as part (b) when the airport upgrades their runway capacity in part (c) what new runaway capacity will they need to ensure the probability of congestion does not exceed the max acceptable probability of congestion of 10% until year 2038? [2 marks]

Answer 1

Answer:

The traffic intensity is given by T. Calculate the probability of traffic congestion when run way capacity is 350 planes. P(T 350 1-D Here, probability of traffic congestion when the run way capacity is 350 planes is P(T>350) sample mean is x, mean is 11 an standard deviation is ơ Substitute 350 for x, 200 for fl , and 60 for ơ P(T 350)-1-D 350-200 60 -1-D(2.5

From the table of"Standard normal probabilities", write the value of Ф(25) as 0.99379 P(T 350)-1-0.99379 0.00621

The mean traffic rate increases linearly at the annual rate of 10% Calculate the mean traffic volume after 10 years. Ao current volume + current volume 1 0% x years Here, mean traffic volume after 10 years is The current volume is 200 o- 200+200x0.1x10 -400

Calculate the current coefficient of variation Here, coefficient of variation is δ Substitute 200 for μ and 60 for σ 60 200 0.3

Calculate the standard deviation after 10 years. Here, standard deviation after 10 years is ơ10 Substitute 0.3 for δ and 400 for 140 ,,-0.3x 400 - 120

Calculate the probability of traffic congestion at airport. P(T >350)-1-Mo. Here, probability of traffic congestion after 10 years is P(T,>350) Substitute 350 for x, 400 for tho , and 120 for ơio PT 301- 3502400 1-(0.416)

From the table of"Standard normal probabilities", write the value of Ф (0.416) as 0.99379. P(T 350)-1-(1-0.655) -0.662

Therefore, the probability of congestion at the airport in 2028 is 0.0662.

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