Reference no: EM132192033

An airport has two runways; one is dedicated to take-offs only, the other to landings. The two runways are run independently of one another. The time it takes an aeroplane to land or take off is an exponential random variable whose mean is 2 minutes. The number of requests per hour for take-offs or landings is each a Poisson random variable whose mean is 25. Consider first the landing runway.

a) On average, how many aeroplanes are “stacked up” (i.e., waiting to land)?

b) On average, how much time elapses between when an aeroplane arrives (i.e., requests permission to land) and the time it completes landing? (Show all calculations)

c) The Aviation Authority requires that on average an air-traffic controller work for a maximum of 45 minutes out of every hour. Currently, there is only one air traffic controller at the airport is responsible for landings during every one-hour period. Should the airport use more controllers in order to meet the standard set by the Aviation Authority? Justify your answer.

d) Suppose now that both runways can be used for both take-offs and landings. Now average service time for both take-offs and landings increases from 2 minutes to 2.16 minutes per aeroplane. Which arrangement — two separate systems or one pooled system — minimizes the average total amount of time it takes an aeroplane to either take off or land (waiting time plus landing or take-off time)? Note that in this case, the average number of aeroplanes waiting (to be given permission to land or take off) turns out to be 7.674.