The chief engineer of an airport is planning to rehabilitate runway pavements ov

Question

The chief engineer of an airport is planning to rehabilitate runway pavements over the next several months. You ask him what impact this would have on delays and queues, but he does not know. Being a smart Georgia Tech student in CEE 3000, you realize immediately that this phenomenon could be modeled using a simple queue analysis. You figure out that airplanes arrive at the airport an average rate of 1 plane per 10 minutes, and that the arrival pattern could be assumed to follow the Poisson distribution. The airport control tower processes airplanes in their order of arrival. You also figure out that the service time could be assumed to follow the exponential distribution. If the service rate is 10 landings per hour, calculate the following parameters. Please use units of minutes for time-containing answers.
A) The average number of airplanes in the system (i.e. in the system and in the queue).
B) The average number of airplanes awaiting clearance to land.
C) The average time an airplane spends in the system.
D) The average time an airplane spends in the queue.
E) The probability that there is no airplane in the system.

Explanation / Answer

arrival rate=1 plane/10 min=6 planes/hour service rate=10/hour utilization=arrival rate/service rate=6/10=3/5..let it be p p=3/5 a)The average number of airplanes in the system=p/(1-p)=1.5 b)The average number of airplanes awaiting clearance to land.=p^2/(I-p) =0.9 d)The average time an airplane spends in the queue= arrival rate/(service rate*(service rate-arrival rate)) =9 min e)The probability that there is no airplane in the system=Probability of 0 planes in the queue=1-p=0.4 c past answer i am posting in few minutes,rest all is well explained.

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