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Queue Buildup
All passengers landing at Luton airport need to go through Border Control. The first four flights on Monday morning land at 6am, 6:20am, 6:50am and 7:15am. For simplicity, assume that each plane landing between 6am and 8am carries 240 passengers, 75% EU and 25% non-EU citizens. Passengers from each flight continuously join (at a constant rate) the corresponding single queue (EU and non-EU) between 15 and 45 min after the flight landing time. EU passengers need 0.5min of face time with a Border Control Officer, while non-EU need 3min. There are 3 Border Control Officers serving the EU queue and 5 serving the non-EU queue. Ignoring any unpredictable variability in both arrivals and processing times, construct a build-up diagram to answer the following questions:
Q 3.1 - How much time would you expect to wait to clear Border Control if you are the very first passenger from the 6:50am flight on the queue? Please note that the waiting time depends on your passport issue country.
Q 3.2 - If 6-7:30am on Monday is the busiest time at Luton airport, what is the size of the waiting area required to fit all arriving passengers, both EU and non-EU?
Q 3.3 - How many passengers wait for 30 min or more to clear Border Control?
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