At Charles De Gaulle Airport in Paris, France, it typically takes 6 minutes for a plane to land once it receives clearance, with landing times following an exponential pattern. Although planes have scheduled arrival times, the variability in these times causes them to arrive randomly, averaging 7 planes per hour. This sometimes leads to backups that can be dangerous and costly. Under these conditions, how long, on average, will a pilot spend circling the airport before landing? If the air traffic controller wants to reduce the maximum waiting time in the air to 6 minutes, what would be the best recommendation? After landing, passengers walk on a moving walkway to the Immigration counters for processing. On average, 1.3 passengers arrive at the counters per minute, with arrivals following a Poisson distribution. There are five counters open at Terminal 3, with each officer able to process 18 passengers per hour, and the service times follow an exponential distribution. What is the average waiting time for passengers in line at Immigration? If the goal is to keep the waiting time under 4 minutes, what changes need to be made to the number of counters or the system design? After clearing Immigration, passengers go to the Baggage Claim area. Assuming passengers arrive at Baggage Claim at the same rate as they were processed at Immigration, and that all passengers have checked luggage, with each passenger taking an average of 5 minutes to find and collect their bags from a single moving conveyor (with time following an exponential distribution), how many moving conveyors are needed at Terminal 3 to keep the maximum wait time under 10 minutes? Considering the optimal number of conveyors, use the overall service rate at Baggage Claim to redesign the Customs and Quarantine area. After Baggage Claim, 25% of passengers have nothing to declare at Customs and exit through the green channel to the Taxi stand at Terminal 3. The remaining 75% go to the Quarantine area, where three X-Ray machines and inspectors are available. On average, it takes 8 minutes for a passenger to complete the X-Ray and inspection process before heading to the Taxi stand. If you were one of the passengers, what would you recommend as the optimal number of X-Ray machines and inspectors? Comment on the current facility design.