Originally Posted by
wetrat0
Example: Consider a small checkpoint where 150 passengers arrive per hour, and there is screening capacity for 165 passengers per hour. Then the expected waiting time is 4 minutes (1/15 hour). Now, assume that the screening capacity is cut by 8% to 151.8 per hour. Then the expected waiting time will be 33.3 minutes (1/1.8 hour), which is over 700% increase. The key point is that depending on the arrival and service rates, an 8% cut could result in a waiting time increase that is much larger than 8%.
- Congestion caused by variability will result in exponentially longer waits as the service rate approaches the arrival rate.
- Passengers should be prepared for the very real possibility that TSA lines will get much longer due to sequestration.
Thanks for the analysis; this is a good discussion.
My queuing theory is very rusty and quite old, but I think I see a potential issue with the example. There is a knee in the curve of expected wait time vs service utilization (occupancy) somewhere around a occupancy of 70%. If utilization gets above that knee, small increases in arrival or decrease in service rate causes very large changes in expected wait time. My memory is that a stable well-behaved system needs to operate well below that knee to deal with variability.
A quick graph of expected wait time, 1 / (service rate - arrival rate), vs ratios of arrival rate to service rate varying between 0 and 1 gives:
The wait times (units irrelevant) are very sensitive to occupancy for occupancy values greater than 0.8 or so.
Your example starts with an occupancy of 150/165 = 91% which is very much beyond the knee of the wait-time curve and then increases the occupancy to over 99%. If TSA checkpoints typically operated in this region, wouldn't they be prone to extreme spikes in wait time due to small changes in arrivals and service? As bad as TSA is, over the last few years they seem to have greatly reduced such spikes, which suggests to me they are operating well below 60% occupancy or so and that someone at TSA has a decent grasp on this math. A small change in service rate at that part of the curve shouldn't cause a huge spike in wait time.
Changing your example a bit, if the checkpoint has a capacity to screen 300 pax per hour with 150 pax arriving per hour (occupancy of 50%), wait times would be fairly stable and expected to be 0.40 minutes (computed by 1/(300-150) * 60). If you cut the capacity 8% to 276 pax per hour, occupancy becomes 54% and expected wait time becomes 0.47 minutes (1/(276-150) * 60). That's a nearly 20% increase in wait time, but it's fairly insubstantial because the wait time is so small to begin with.
The question then becomes how close to that knee is a typical TSA checkpoint?