Project: San Francisco International Airport Security
Airports are increasingly concerned with t he time required for airline passengers to clear security, particularly as the TSA adds more and more screening protocols. At the same time, it is expensive (in terms of staff costs) to keep more security channels open than necessary.
TSA is considering making a change that will cause passengers to have to pass more of their belongs through x-ray screening. This will lengthen the time it takes passengers to drop off their items before they pass through the metal detector, and also the time required to x-ray the items themselves. Your job is to provide SFO’s Terminal 1 with a chart that they can use to decide how many security lanes to open as a function of the passenger load they expect in passengers/hour (TSA has access to airline booking data, so they can forecast the passenger load they will encounter).
Each lane of security consists of a conveyor on which personal items are placed before x-ray, an x-ray scanner for personal items and a metal detector for passengers. Passengers first place their personal items on the conveyor; then they proceed through metal detection while their personal items go separately through x-ray; once both the passenger and the personal items pass security, they are reunited on the other side. Thus, passengers cannot continue beyond security until both x-ray and metal detection are complete.
For security reasons, passengers are not allowed to move ahead of other passengers (no preemption). In addition, 10% of passengers are selected for an individual screening after they collect their personal items. Because TSA directs passengers to security channels, it is fair to assume that if there are C channels open, then each one receives 1/C of the passenger load.
Data are available on the time currently required for each phase of security; the time to unload and place items on the conveyor belt; the time to x-ray a passenger’s items; the time for the passenger to pass through metal detection; and the time to complete through screening (all times are in minutes). The typical passenger currently has three personal items that require x-ray screening; the new rules are expected to push that number to four, on average, a 33% increase.
TSA would like to have an answer to a question, how many security channels to open as a function of an arrival rate so that the average time to pass through security is no more than 15 minutes for passengers who do not receive an individual screening, and 20 minutes for those who do. You can compute a maximum arrival rate that each channel can handle without increasing its queue infinitely. However, if we want the passengers to spend <= 15 minutes (for the non-screened) / 20 minutes (for the screened), the appropriate arrival rate for each channel may be less than the maximum arrival rate. TSA will investigate following system-wise arrival rate cases; 0.7, 1.1, 1.7, 2.1, 2.7, 3.1, 3.7, 4.1, 4.7, 5.1, 5.7, and 6.0 passengers / min.
There are only 10 possible channels to open, so the number of channels does not need to go beyond 10.
Approximation: Sketch a flow diagram that illustrates how passengers and their personal items pass through security. Approximate the maximum load (passengers/hour) that a single security channel can handle (Hint: The average service time of a channel must be smaller than average time between arrivals for the channel to keep up, so approximate the mean service time of a security channel to see what load it can handle. Note that arrival rate = 1/mean time between arrivals).
Project: Simulate the system to produce the answer table.
- TSA can change the number of channels every 3 hours, so make your simulation length 3 hours.
- Make 20 replications.