I think this occurs more for airports with the backscatter machines than MMWs....

I have a very non-scientific queue theory. It's called the "government worker queue theory". It goes something like this:
"Government workers will keep the backlog at a steady state size in order to ensure their job security."
My interaction with government agencies includes filing immigration petitiions (I was the sponsor) with INS (before it was USCIS or Homeland Security), getting passports renewed, getting a driver license and its renewals, etc. The backlog is always defined up front, for example, "it will take 9 months to process your immigration petition for person X". Since the actual time to process the petition is probably 4 hours, they sit on a 9 month backlog, always processing the ones that are 9 months old, taking 4 hours each. I've often wondered, why don't they hire some temps or do overtime and "catch up" so that it only takes mailing time + 4 hours? Job security!!! With the 9 month backlog, they won't ever get fired. The longer the backlog, the more secure they are. If the numbers of processors was doubled, they would work slower until the backlog was at the highest tolerated level.

I think the same applies to the TSA people. They are not business people in a free enterprise world. They are government workers. They are not paid X dollars for each person they process correctly. They are paid X dollars an hour, no matter how efficient or inefficient they are.

Bolding mine: God, I hope not!

Losing Pre-Check would be disastrous

Thanks-- the motivation for writing this post was that quite a few folks have claimed or strongly implied that the only way lines are going to become excessively long is if there is a deliberate effort by TSA to make lines longer. I would contend that the queueing analysis shows this is simply not the case. If TSA has to cut its capacity, but does not make any managerial attempt to expedite the screening process, lines could get very long on their own due to inherent variability in screening times. In other words, it does not require any "active" work slowdown: simply a "passive" reaction of continuing to do the same thing after capacity is cut will cause long lines.

The debate over whether TSA ought to try to compensate for cuts in staffing rather than maintaining their current procedures is, in my humble opinion, perfectly legitimate, and should be confined to the appropriate forum.

It's not even that longer queuing times will be that much of a bother. It's that the TSA is a poster-child for the embarrassing state of affairs that US airports have generally become.

Now, put me on a line of the same length at a Japanese airport, and I'm much more relaxed. Polite, non-chatty, they make sure that no one else takes your stuff (sometimes by putting another tray/something else over yours). Admittedly, it's not even guaranteed that the TSA will be the nuisance, as there are plenty of passengers out there doing who knows what while waiting on the security line (this includes elite customers who need to take out their two computers/iPads/multitude of electronics but at least they are wearing loafers).

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?

Wetrat, your model appears to assume that the capacity of a checkpoint (passengers per hour) is constant. As many of us know, it is not. At many airports, if there is a line developing, the TSA will switch to a faster machine (MMW to WTMD) in order to reduce the backlog. They may also "randomly" check less bags. How would these factors affect the results of your analysis?

That's not "non-scientific". You've made observations and formed a theory based on those observations, which is a time-honored scientific method.

I have no idea, but the last time I experienced a wait time of <1 minute at TSA was a while ago at a very small outstation. Such low utilization would also correspond to a high probability that the system is empty, which is also not something I have observed.

This is a good observation. I discussed this above briefly, but did not give any technical reply because the model would have to get a lot more complicated. One way you could model this is at every point in time, the server can choose to work slowly or quickly, but working quickly has a higher cost. The server then chooses to work slowly or quickly at each time point based on minimizing the long run average cost (to the server and to the customers for waiting). The structure of the solution would be such that when the line exceeds N customers, the server would work quickly, but when the line is at most N, it would work slowly. Figuring out N would really require knowing a lot more about the real parameters (arrival rate, various possible service rates, costs, etc.) so it doesn't lend itself to an easy example.

I'll add support to that earlier theory with 16 years of varied personal experiences directly in the thick of low- to mid-level, daily governmental activities. Does that help?

Sounds quite a bit like Parkinson's Law.

I'm not sure that would be a fair assumption. It doesn't cost the worker any more to process a higher number of passengers per hour, because they are doing less screening per passenger. For example, if there are 50 passengers and 6% of them get a bag check, then when there are 100 passengers only 3% of them get a bag check. The cost to the worker is the same.

My theory is that the workers adjust the rate of screening in order to keep the line at a certain length. This is similar to a nightclub, where they want there to be a line outside to make the club look popular, but not long enough to discourage people from coming in.

EWR Checkpoint B-1 (Delta) does not do this anymore. Even if the lines are over 40 minutes long, the TSA "management" refuses to use WTMDs to help decrease the line wait. And TSOs still stand around and don't open another line.

I've seen less and less examples of TSA opening up the WTMDs over past year than I'd seen previously. I chalk it up to TSA just telling us to "suck it up and take it just because they can dish it out to us."