Problem: At Changi airport in Singapore it takes on the average 5 minutes to land an aero-plane, once it is given the signal to land. The landing time is exponentially distributed. Although incoming planes have scheduled arrival times, the wide variability in arrival times produces an effect which makes the incoming planes appear to arrive in a Poisson fashion at an average rate of 6 per hour. This produces occasional stack-ups at the airport which can be dangerous and very costly. Under these circumstances, how much time will a pilot expect to spend circling the field waiting to land? If the aviation controller wants to reduce the maximum time spent circling the field waiting to land to 5 minutes, what is the optimal recommendation? After landing at the airport, passengers walk on a travellator to arrive at the Immigration counters for immigration clearance. The average arrival rate of the passengers at the immigration counters is 1.3 per minute and the arrival process is assumed to be Poisson distributed. There are five immigration service counters open at any given time at Terminal 4 of the airport and each officer can serve 20 passengers per hour with service time exponentially distributed. Determine the average queue length waiting time of the passengers in the queue in front of the immigration. If the expected waiting time is required to be less than or equal to 5 minutes, what changes are needed in terms of number of immigration counters and the design. Following the immigration clearance, passengers are directed to Baggage Claim area of the airport. Assuming the arrival rate of the passengers at the Baggage Claim to be equal to overall service rate at the immigration counters and all the passengers have checked-in baggage to claim, and average time to search and collect the baggage from the single moving conveyor to be 6 minutes which is exponentially distributed. Determine the optimal number of moving conveyors required at Terminal 4 if the maximum waiting time should not exceed 12 minutes at the Baggage Claim conveyors. Consider the redesigned optimal number of moving conveyors at Terminal 4 and use the overall service rate at the Baggage Claim for further calculations and redesigning the Customs and Quarantine area facility as described below. After the baggage claim the passengers are directed to Customs and Quarantine area of the airport. Suppose 20 per cent of the passengers who claim their baggage do not have any item to declare at the Customs and Quarantine inspection and exit through the green signal channel and proceed to Taxi stand of Terminal 4 of the airport. The remaining 80% of the arriving passengers at the baggage Claim exit are directed to Quarantine area equipped with three X-Ray machines and inspectors. On the average passengers spend 10 minutes at the X-Ray machines and baggage inspection before they leave for Taxi stand. If you happen to be one of passengers, give your recommendation for the optimal number of X-Ray machines and inspectors. Comment on the existing facility design.