Security line simulation

For some reason the Pittsburgh airport is extremely crowded in the mornings. When I was there a week or so ago it was no exception: I watched as many people who were loudly claiming they arrived around 1.5 hours early miss their flights. The only real bottleneck is the security line. The strange thing is, I have never seen it crowded at any other time of day except the very early morning, which leads me to believe that they simply don't have enough people working to put people through. Today I overhead that they only had one crew ("again!") so I suppose that even though the total number of people here is not very large compared to other times of day, they have a proportionally smaller security crew.

Here's the thing that bugged me though. When people on the security line freaked out about not making their flights after the line didn't budge for 10 minutes, the woman in charge of preventing riots advised them to have shown up earlier. Now, I'm all for punishing the ill-prepared over the prepared, but it got me to thinking: what IF people only showed up between 2 and 3 hours? Does that actually solve the problem?

I made a simple simulation of the airport lines to find out. Here are some details about it:

  • I used the same flight times on the day I was there.
  • The number of people on each flight had a mean of 60 and variance of 5.
  • There were 6 airlines total, and people had to wait at their individual airlines for check-in before they all had to wait at the same security line together.
  • The mean checking in time was 15 seconds per person (there are multiple self-check counters open) with a minimum time of 5 seconds (while they ask you for your ID, print boarding pass, etc).
  • The mean security line time was 7 seconds per person, with a minimum time of 2 seconds (takes at least 2 seconds to walk through the naked machine).
  • There was no transportation time - people walk from the check counter to the end of the security line at insanely fast speeds.
  • Even though the security lines are open 24 hours, the check-in counters open at 4am (this is TRUE).

There are other little assumptions, too, and if you must know here's the code.

So, let's say I arrive 2 hours early, which seems totally reasonable. First I'll compare two situations:

  1. Everyone, including me, arrives around 2 hours in advance of their flights, give or take 5 minutes.
  2. People arrive between 1:55 and 3 hours before their flights. I arrive 2 hours before my flight

There are many sources of randomness in this simulation, so I ran 1000 simulations and here I show how many minutes before takeoff I arrived at my gate (checked in, got through security, walked at infinite speed to my gate).

According to the simulation, if people get to the airport between 2 and 3 hours before their flights, I miss my plane about half the time, even though I've arrived 2 hours beforehand. If people arrive about 2 hours before their flight instead, I am never late. Here's how the actual line wait times contribute to gate arrival times:

So what's happening here? Think about the lines - if you arrive 2 hours before your departure time, and you have to wait on lines with people who have arrived up to 3 hours before their flights (some of which take off after your flight), those lines are going to be a lot longer. So the airport is telling people to arrive earlier without actually telling their own employees to start earlier. Airline customers are unwittingly participating in a prisoner's dilemma scenario - if they arrive earlier they are virtually guaranteed a seat while simultaneously increasing the lines unnecessarily for people who are a bit later. If everyone agrees to come with the same time buffer (let's say 2 hours), the line waits are actually shorter for everyone (given the same security scanning resources). In any case, the airport has two basic options for solving this problem - they can actually run more than one scanning station in the mornings so that they can handle the increased "early" crowd that they've caused by telling people to come earlier and earlier (costs money they don't have), OR they can encourage people to come EXACTLY 2 hours beforehand, not earlier.

But more likely we'll be told to arrive 4-5 hours before our flights in a few more years.