# [Solution]The Queuing Problem

ABC airport has two runways, one for take offs and one for landings. For a particular day, arrival times of aircrafts are provided. These arrival…

ABC airport has two runways, one for take offs and one for landings. For a particular day, arrival times of aircrafts are provided. These arrival times denote the time when airplanes are requesting to land (measured in minutes past Midnight of February 22, 2021). Data on receiving clearance and time required to land is also provided. A plane must be cleared for landing and then actually land before clearance can be given to another plane to land. Awaiting airplanes must circle the airport until they are cleared to begin their descent.

The Airport Safety Manager has decided upon two criteria to maintain the safety regulations for landing and prevent congestion: (1) the average # airplanes waiting to receive clearance should not exceed 1.75 planes;(2) average waiting time before landing clearance should be less than 4 minutes.

State which queuing model you are using and why it is reasonable to use it.
Evaluate the queueing model and how well are these criteria are being satisfied (or not).
Airport management is thinking of adding the second or third runway as well for landings. If the service rate remains about the same, will they achieve their goals?  In which scenario?
Each runway will cost about \$150 million. If landing fees for each plane is about \$250 what will the increase in arrivals to the airport have to be in order to pay for 1 new runway in 5 years? 2 new runways? If traffic remains the same even after adding one or two runways, how much will they have to increase their landing fees to pay for the new runways (1 or 2) in 5 years?

Question 2
Consider a fast-food restaurant drive through. You as a Manager decide to look at the past data of arrival times and service times and want to analyze the queueing system. Following criteria are decided by the company to make sure that queueing system is up to the mark:

Wait time for a customer before getting the chance to order should be less than 2 minutes; and, utilization of server should be at least 50%.

Due to COVID, drive throughs are gaining more attention than dine in. Answer these questions:

State which queuing model you are using and why it is reasonable to use it.
Given this historic data, are you currently meeting standards?
It is forecasted that the arrival rate might increase by 25%. Can you meet these criteria given how this system is currently operating? Explain why or why not.
Your manager thinks he may have to hire another person but doesn’t want to. He thinks that if the servers can serve 10% faster then they can avoid hiring someone. Is he right? Explain why or why not. Does he have a good idea? How much faster (by %) will the servers have to serve in order to meet the criteria (if it is indeed possible to meet the criteria by simply going faster).

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