An airport runway has a capacity of 60 operations (ie landing and take-offs) per

Question

An airport runway has a capacity of 60 operations (ie landing and take-offs) per hour. In a particular hour, there are 30 landings evenly spaced over the hour. During that same hour, 20 departing aircraft uniformly arrive at the runway within a 20-minute period. Assume no other departing aircraft arrive at the runway during the hour.

a) What is the maximum number of aircraft waiting during the hour?

b) Assume that landing aircraft have priority over departing aircraft.
Also assume each aircraft carriers 200 passengers. What is the total delay to the passengers in the 20 departing aircraft?

Explanation / Answer

The capacity is 60 operations per hour, so 1 per minute. A plane lands every 2 minutes. That leaves one slot every other minute for a plane to take off. A plane arrives once a minute to take off. In the first 10 minutes, 10 try to take off, but only 5 can, thus 5 wait. At 15 minutes, 15 try to take off, but only 7 can, 8 wait. At 20 minutes, 20 try, but only 10 can take off, 10 wait. At 21 minutes, 11 have taken off, only 9 wait. To calculate the delay time per passenger draw a table

Minute - In - Out - Arrive time - Wait time
1 - 1
2 -0- 1- 1- 1 minute
3- 1
4 -0-1-2- 2 minutes
5- 1
6-0- 1 -3- 3 minutes
7- 1
8-0-1- 4- 4 minutes

keep going until all 20 planes have taken off. You can sum up the waiting time multiply by 200 passengers per plane and get the total passenger waiting time.

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