Escalators are back in the news! A little over a year ago, Transport for London (i.e., the London Tube) got some press for an experiment they ran essentially prohibiting people from walking up the escalators at one of their stations. (We posted about that here.) Now the New York Times has seen fit to revisit the topic (Why You Shouldn’t Walk on Escalators, Apr 4). The Times’ definitive stance has not gone unchallenged. Indeed, Gizmodo has an essay taking the opposite side (Why You Should Always Walk on Escalators, Apr 4).
The source of controversy here is that Transport for London found that escalators moved more people per hour and delays to get on the escalators were shorter when people were kept from walking up the stairs. This is obviously a paradox. From an individual point of view, walking up the stairs has to be faster. If each individual can move faster, how can the overall wait be worse?
The Times article sites a blog post from Capgemini that provides some interesting numbers based on timing themselves on an actual Tube escalator (Would standing on the left get you through Tube stations quicker?, April 15, 2016):
Walking up the escalator took 26 seconds
Standing on the escalator took 40 seconds
Fewer people can fit on the ‘walking side’ of the escalator – around 70% as many as those standing. This is because a ‘walker’ occupies more steps than a ‘stander’.
More specifically on the last point they estimate that a stander takes two steps while a walker needs three steps.
Now we can do a bit of math. With 3,600 seconds in an hour, an escalator dedicated to standers could move 3,600/40 = 90 customers per hour for every two steps. For walkers we get 138.46 customers per hour for every three steps. (Technically, this for one side of an escalator since if the standers stay on the right, we can devote half of our capacity to each group.)
Consider an escalator with 60 exposed steps (i.e., steps available for use). We would get that in a world of walkers we can lift 2,769 customers per hour. If we serve only standers, capacity drops down to 2,700 customers per hour. So walking has an advantage but it ain’t huge. The absolute advantage grows as the number of steps increases, but on a percentage basis it remains just 2.6%.
Of course, the size of the gain from walking depends on the assumption we make. If walking and standing require the same number of steps per customers, walking increases capacity by over 50%. If you believe that 2.5 steps per walker is a better estimate of the space required for easy walking, walking still delivers a 23% gain.
So what is the problem with letting people walk? This is really about the lumpy nature of capacity. We can’t really mix walkers and standers on the same side of the escalator. If we have just one escalator, do we really want to allocate half our capacity to walkers? Take the numbers above. 2,769 customers per hour translates to around 46.2 per minute. 2,700 per hour gives 45 per minute. Suppose we have 100 customers that need to go upstairs. If we give each group half the of capacity, we can move 96.2 customers per minute — assuming that arrive in the right proportion. Specifically, we need 50.6% ( = 46.2/(46.2 + 45)) to opt for walking. If we get 50.6% to walk, we can get all customers out of the station in 1.09 minutes. However, if less than 50.6% are willing to walk, standers will wait longer — potentially a lot longer. For example, suppose only 40% are willing to walk, it will take 1.33 minutes to serve the last stander while walkers are done in 0.867 minutes. In contrast, if we used both sides for standing, everyone is upstairs in 1.11 minutes. That is, splitting capacity evenly between the segments when the segments are not of equal size boosts the delay of standing customers by 20%. If the walkers make up a smaller portion of users, then the impact on standing customers is even more severe. For example, if walkers are only 30% of users, then the delay of standing customers is 40% higher than when everyone stands.
A couple of points before closing this post. First, this issue is going to be more relevant at deeper stations that have longer escalators (assuming that people are more likely to be dissuaded from walking when facing a long escalator). Second, this should be less of an issue in Chicago. Why? Because our train service is primarily elevated. What hammers a subway system is that you get batch arrival every time a train comes in. The exercise above of how fast can we get 100 people out of the station is in many ways the relevant problem. With an elevated train, you generally don’t have batch arrivals needing the up escalator (the Addison stop after a Cubs game may be an exception).