Escalator Action

Epistemic Status: Slow ride. Take it easy.

You Memba Elevator Action? I memba.

A recent study (link is to NY Times) came out saying that we should not walk on escalators, because not walking is faster.
From the article:
The train pulls into Pennsylvania Station during the morning rush, the doors open and you make a beeline for the escalators.
You stick to the left and walk up the stairs, figuring you can save precious seconds and get a bit of exercise.
But the experts are united in this: You’re doing it wrong, seizing an advantage at the expense and safety of other commuters. Boarding an escalator two by two and standing side by side is the better approach.
We will ignore the talk about which method is better for the escalator, which seems downright silly, and focus on the main event: They are explicitly saying that when you choose to walk up the stairs, you are doing it wrong.
Since walking is trivially and obviously better than walking, this result is a little suspicious. And by a little suspicious, I mean almost certainly either wrong, highly misleading or both.
Certainly individually, on the margin, for yourself you are quite obviously doing it right.
Consider a largely empty escalator. If Alice gets on the escalator and sits there, it takes her 40 seconds. If she walks up the left side, and no one is in her way, it takes her 26 (numbers from article). Given everyone else’s actions, if she wants to get from Point A to Point B quickly, and I strongly suspect that she does, she should walk up the escalator.
Consider an escalator in the standard style. On the left people walk up, on the right people stand. If there is enough space for all, then nothing Alice does impacts anyone else unless she blocks the left side, so assume there is not enough room. In that situation, demand for the right side almost always exceeds demand for the left side, so Alice is almost certainly going to not only get to the top faster by walking, she is helping everyone else get there faster too. Yay Alice.
Consider an escalator where people are already standing on both sides without walking, Alice will hit a wall of people if she tries to walk. She now is faced with either asking people to let her through, and paying that social cost, or not doing so. If she does ask, if she gets turned down no one moves any slower or faster. If people agree to move, then she gets to walk, and since no one is going backwards, no one gets there any slower. So worst case is someone else is a little irritated, but nothing is slowed down.
This seems to cover all cases, so the bailey of ‘don’t ever walk on escalators’ is nonsense, Q.E.D. However, we also want to deal with the motte, and see how to deal with that. Should people stand two by two on the escalator with no one walking at all?
During a non-peak period, meaning any period where reserving the left side for walking would not result in anyone waiting to get on the escalator, clearly people should walk, and the win is substantial. This means that we would need people to vary their behavior depending on the situation, or else accept a big loss in the default case, in order to get a no-walk equilibrium to hold when we want it. Tough crowd.
During the peak period, what matters is throughput. We need to get as many people from Point A to Point B as possible, to reduce the wait to get on the escalator, or even more pressing, to prevent a permanent and ever-increasing line waiting for the escalator, which is a disaster (a disaster I tell you!). The throughput of the right side is fixed, as is its speed, so what matters is the throughput of the left side. How do we maximize that?
There are many ways to analyze this in theory. I think the easiest is to consider multiple possible systems:
System #1 (ideal standing): Everyone stands, no one walks, we use every step. We get one person per step to the top (e.g. one person per 40 seconds per step)..
System #2 (ideal walking): Everyone looks at the step above them. If it is free, they walk onto that step. If it is not free, they stand until it is. Is this faster?
If every step is occupied anyway this is just System #1, and we get equal performance.
Let’s now consider the marginal case: One of the steps is empty. Thus, Instead of 100 people on the escalator (let’s say), there are 99, but that 99th is currently walking up a step. In exchange, the 100th person is waiting at the bottom. So we win if and only if that one person is going twice as fast as they would otherwise. On a sufficiently slow escalator, this could happen, but in the base case (40 vs. 26) it is not the case, and the missing step is clearly costing time even in the perfect case. If they really only use every third step that is a disaster.
Plus, walking sounds like work.
Thus, we conclude that the basic idea that we should put someone on every step is correct, given people are not generally comfortable moving until the following step is clear. No, in general, when demand exceeds supply, the first best case is for people to not walk on escalators.
Looked at another way, this is even more obvious. Suppose you have a full escalator, or just an escalator with someone on step 2. You can choose to get on that escalator at step 1, or you can chose to wait and then get on step 0 (when it becomes step 1), and then walk to step 1. That seems obviously stupid, so why should there ever be a gap on the left side? Why doesn’t the whole thing fill up quickly? How does anyone get the ability to walk in the first place?
They gain that ability because people, in some places, adopt a norm that standing on the left side is not acceptable even when the right side is full. It is worth noting that New Yorkers are too smart for this. If things are busy the entire escalator will be packed. People act the way ‘the experts’ want them to. How do we get this outcome? We get it because people are willing to enter the escalator on the left side without waiting for three steps of room, and/or without intending to walk, and if even a small number of people do this, the result is the standing equilibrium. In fact, it takes a strong norm against standing on the left side to avoid that outcome.
Here’s the thing. A lot of people do not want to walk. When they get to the escalator they choose the right side. Given this fact, and that the right side is packed, all you have to do is make them feel all right about standing on the left side. You do not need, as the article implies, “altruism.” Appealing to altruism can be the right thing to do, but often it’s an unworkable solution and the appeal to it does more to make people feel bad than to accomplish anything, whereas a more simple solution would work great.
So when “experts” say in the article things such as: “Overall I am not too optimistic that people’s sense of altruism can override their sense of urgency and immediacy in a major metro area where the demands for speed and expediency are high” and “In the U.S., self-interest dominates our behavior on the road, on escalators and anywhere there is a capacity problem, I don’t believe Americans, any longer (if they ever did), have a rational button.” I don’t exactly want to claim that they do have a rational button, since I certainly have not seen such a thing, but locally they seem fully capable of reaching the correct collective solution, and also you don’t need some sort of altruism or collective action or superrationality. You don’t even need rationality.
It’s actually even worse than that. The altruistic action is the people refusing to go on the left side and not walk. The altruists are almost all of us and they are ruining it for everyone. All you need is not to have an actively bad social norm where people act altruistic to coordinate against the right answer. Because some people, neigh, most people, are lazy and don’t want to walk. Alternatively, people are in enough of a hurry (around these parts, anyway) not to get attached to ludicrous amounts of personal space, and that quickly leads to the same outcome (everyone starts moving in starts and stops, and quickly things slow to a crawl).  Talk about your Ineffective Altruism! How irrational!
On the plus side, as Robin Hanson puts it, Hail Most Humans for keeping to the cultural norms even when they have no real personal incentive to do so. Good job, everyone!
There is a counterargument to all this, which attempts to rehabilitate people’s altruism and irrationality, which is that actually people probably should walk on some escalators after all. Let’s do some math:
When 40 percent of the people walked, the average time for standers was 138 seconds and 46 seconds for walkers, according to their calculations. When everyone stood, the average time fell to 59 seconds. For walkers, that meant losing 13 seconds but for standers, it was a 79-second improvement. Researchers also found the length of the line to reach and step onto an escalator dropped to 24 people from 73.
This seems like an extreme case, where we have a very large bottleneck at the escalator even in the good case, but let’s go with it.
Are we sure that the 59 second outcome is worse? Some people have places to go and people to see. Others, not so much. Let us not become too attached to equality. People are self-selecting into the walking group and the standing group. Isn’t that interesting? The walkers take 46 seconds, the standards 138 seconds. That’s a minute and a half (plus two seconds) lost to not walking. So 60 percent of people are choosing, as determined by a time market, to not be willing to walk for a few seconds on an escalator in order to save more than twice that amount of time. Walking must be really averse to them. A few of them will have actual physical issues, but I have a hard time believing walking up some stairs is an issue for anything like this many people.
Alternate framing of that same thing: 138 seconds and 46 seconds with walkers, 59 seconds for both otherwise. The standers have been delayed by 92 seconds. Those 92 seconds represent time spent waiting for the escalator, or else I am deeply confused. So there is a 92 second line to wait in, in order to stand. Whereas the walkers do their entire path in 46 seconds. Their line is very short. And yet, this is the equilibrium. This is what people chose to do. I know we hate walking, but do we really hate walking that much?
Instead, one could reasonably claim that those who choose to walk at any given moment value their time a lot more than people who are content to stand. Six times as much? Doesn’t that seem like a stretch? Perhaps, but you don’t choose in advance. You choose at the time. Everyone has been on that trip where they absolutely, positively cannot be late. Everyone has also been in the situation where they are transferring to another train that won’t come for ten minutes, so the time does not matter almost at all. A difference of a factor of six seems more than reasonable for the same person on different days. So by using willingness to walk as a form of price discrimination, we have managed to (at a cost to those who cannot physically walk up at a reasonable pace) give people who need the time, either right now or in general, the chance to save a little time when they need it most.
Do I think the math works in this situation? No, but the math is highly suspect. Let’s walk through it. If we are talking about a factor of six, given the people for whom walking is a large cost, this seems definitely worse, but that required not only a general time advantage but a colossal time advantage. It required a backup by a factor of more than two. In order to have a factor of more than two, you need a semi-permanent backup of flow. If a train empties, and everyone takes the escalator before the next train can arrive, then a split escalator must have a throughput of at least 50% of the non-split case (since two split escalators contain a non-split one as a subset), which means that double the time is a strict upper bound. If we use the 26:40 ratio and put someone in every third step, we would get about half the throughput from a walking line than a non-walking line, so the upper bound would be about 33% additional time rather than 100%. If we used the 40% number for the people who walked, since how did they get that experimental result exactly if that wasn’t the throughput ratio (4:6) then we get almost the same answer. We violated even the 100% bound, which means that we have a continuous pile-up here: Before train #1 can finish getting its passengers out of the station, train #2 arrives and more people get in line behind them, slowly getting worse throughout rush hour. Alternatively, we have a similar case entering the station, and the escalator is not capable of handling all the passengers in its slow throughput state (so this would then be a limiting factor and actively reduce ridership, which I have seen actual never anywhere, but maybe?). Otherwise this case does not seem possible.
If we assume you can get train #1 through before train #2, slash we in general have enough throughput on average, we can cap the loss at 33% (since that represents maximum clumping, and less clumping will mean less lost time). At this point, the factor of six above drops dramatically, and we are looking at what is likely a factor of less than two. At that point, I have no trouble believing that the half who care more value their time more than twice as much as the half that care less. Everyone chooses which path to take, so mostly this seems fair, and you have to fall back on a “walking sounds like work and has large disutility” argument to rescue the non-walking argument, even in the case where things are pretty busy.
I conclude four things.
One, that the media and social scientists will do everything they can to spin altruism and acting “rationally” as the solution, and lack of altruism and people acting “irrationally” as the solution, no matter what the data says.
Two, that we should consider having a norm where it is acceptable to stand on the left side of escalators when there is a substantial line to use that escalator, but that unless there is a long-term bottleneck such that the escalator’s throughput is a limiting factor for large time periods and/or across multiple clumping events, it is far from clear that this is a win, especially given the win in other cases from having a walking lane.
Three, score another win for New York Culture and norms, versus other major cities. You gonna be efficient bout this or what?
Four, that London Underground and Washington D.C. Metro need to stop being such cheapskates and put in more escalators.
Advertisements
This entry was posted in Impractical Optimization and tagged , . Bookmark the permalink.

4 Responses to Escalator Action

  1. Sam says:

    One more point on the big disparity between the walker/stander times: if you’re travelling in a group, one non-walker means no-one in your group gains anything from walking, assuming that there’s no spare elevator capacity. Though this probably isn’t a *big* contributor, because the biggest peaks are due to commuters, who travel singly; tourists, families and the like can avoid the crush.

    • TheZvi says:

      Makes sense. Certainly this can help explain people’s choices a bit, similar to the physical disability exception, but as you note, most of the people at the busiest times will (almost?) always be commuters or otherwise travelling alone.

  2. Daniel Speyer says:

    Where is this drop in throughput coming from?
    So long as every time a new stair becomes available, two people step onto it, the escalator is at full throughput. If the people then accelerate, it will not be a full density, but throughput won’t decrease. And if the walkers are fast (usually not, but sometimes) you can get multiple people entering on the left side of the same stair, increasing throughput.

    • TheZvi says:

      This was odd to me too, and I went through exactly that logic. Perhaps I did not spell this out explicitly enough. From the article I gathered two sources.

      Source one is that people choose to stand rather than walk, even when it means they have to stand in line in order to stand, thus the walking side loses throughput. If people do in fact do this, this seems right, although I have never actually seen this case that I can remember (there being an actual line to use one side, and those people not just using the other side). However, it seems clearly implied by the wait times, as my analysis shows.

      Source two is that the article claims that people will only join a walking side every three steps, invalidating the inequality that whenever someone sees an empty step, they walk onto it. Again this defies my observations/memories but again it is required to make their observations make any sense.

      Both of these things may stem from studies being done in a somehow ‘unnatural’ world in which people are not used to using the escalator in the form they are using it, since I have to believe that behaviors would adjust and evolve with repeated use to get to a better place.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s