Question

Safety regulations require that the time between airplane takeoffs (on the same runway) will be at least 2 minutes. When taking off, the run time of an airplane on the runway is 48 seconds. Planes are on average waiting 5 minutes and 30 seconds for take-off. On average there are 16 planes taking off per hour. How many planes are either on the runway or waiting to take off?

Answer 1

This problem will be solved using Little’s law which states :

Rate of flow in the system x Throughput time = System Inventory

In the given problem ,

Rate of flow = Frequency of take off = 16 planes / hour = 16/60 Planes per minute

Throughput time

= Total time taken for take off ( Waiting time on the runway + Run time on the runway)

= 5.5 minutes ( i.e. 5 minutes 30 seconds ) + 48 seconds ( 0.8 minutes )

= 6.3 minutes

Hence,

Number of planes on the runway or waiting to take off ( i.e.) System Inventory)

= Rate of flow x Throughput time

= 16/60 x 6.3

= 1.6799 ( 1.68 rounded to 2 decimal places)

NUMBER OF PLANES EITHER ON THE RUNWAY OR WAITING TO TAKE OFF = 1.68