Consider the landing service at the Safe City Airport, which has two identical r

Question

Consider the landing service at the Safe City Airport, which has two identical runways. Runway IR serves only large jets such as the 747, while Runway 1L serves only smaller jets like 727 Large jets wish to use Runway 1R for landing every 3 minutes, while smaller jets wish to use Runway 1L every 2 minutes. The coefficient of variation for both large jets and small jets arrival is 1. Each of the two runways can serve 40 jets per hour, The coefficient of the variation far both the runway services is also 1. With probability _____ there are at least 4 jets waiting for landing (including the ones waiting in the air and the one being landed) at Runway 1L Please show your calculation below: The airport would like to reduce the average waiting time for all jets (both large and small) without any investment or any change to the flight schedules. Please provide a least one suggestion.

Explanation / Answer

Given: Coefficient of Variation of large jets and small jets=1, ie,

standard deviation / mean =1 ie, sd = mean

We consider here the waiting time distribution to be Poisson which is approximated to be exponential distribution

Thus large airlines follows exp(3)

small airlines follows exp(2)

Thus sd of large airlines=3 and small airlines=2

g) Now in runway 1L, small airlines lands with distribution of exp(2):

Thus we can easily calculate the probabilty by putting 4 as the parameter in the distribution.

thus probability is 0.5 * e^-2 = 0.06766

h) the coefficient of variation should be reduced by the airport authority in order to reduce the average waiting time. It can be done by implementing a proper queing theory application to the above problem.

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