**The Holborn stand-only escalator trial**

In 2016, Transport for London (TFL) launched a four month trial preventing commuters from walking up the escalators during peak times outgoing from Holborn underground station on the Central line, where traditionally TFL advises customers to stand on the right and walk on the left. The results showed a throughput increase from 115 to 151 commuters per minute across two escalators, cutting congestion by 30%. On average only ~25% of commuters chose to walk up the escalator causing an imbalance of the demand for each side. Preventing commuters from walking balances the demand and fully utilizes both sides of the escalator. How likely someone is willing to walk up an escalator scales with its height, with less people willing to stand as they get taller, so this would imply that what worked for Holborn would also work for similar and larger sized escalators.

The trial was initially planned to be six months long but was cancelled after only four months. This could have been for many reasons, though the main one was definitely the logistical challenge of getting people to follow the trial rules. There’s a conception that it’s important to have a section for walking for those that need to get up faster, even if it comes at the expense of the *standers*, however it might not always be the case that this will be faster.

**When standing is faster than walking**

There’s no doubt that the stand-only system is faster for the average commuter, but what if you want to go as fast as you possibly can? It is possible to create an analytical model of the platform-escalator system to determine a point where the increased time spent in the queue to the escalator outweighs the speed benefit from walking up the escalator. First some assumptions:

- Everyone boards the escalator allowing for at least one step between each person
- The potential input rate onto the escalator is greater than the service rate of the escalator (so the escalator is at full load)
- The offloading rate of the escalator is greater than the service rate of the escalator (so the escalator is the bottleneck)
- You want to get to the top as fast as possible and have a faster maximum climbing speed than everyone else
- When someone steps onto an escalator they randomly pick a lane in the walk/stand system with some probability
- The queue to the escalator is single file without any queue jumping. While not true at the bottom of the escalator, this is generally true for the journey on the platform. For example, Holborn has outgoing escalators at the back of the platform, so for someone getting out at the front of the train this is a good approximation.

When applying these assumptions to the Holborn trial it appears each escalator is capable of carrying 75 people per minute; two people every other step at a rate of 75 steps per minute. It’s safe to estimate the escalator has roughly 120 steps as it is 24m tall and each step is 0.2m high. This means it takes 96 seconds to travel from the bottom to the top when only standing.

Calculating the travel time for walking up the escalator is a bit trickier. The speed that you climb at isn’t as simple as your climb speed plus the speed of the escalator. A high cadence climber on a stair-stepper in the gym will climb at 100 steps per minute, so a good estimate for the max walking speed for the fastest commuter is around 90 steps per minute. However, it’s only possible to move as fast as the slowest person directly in front of you, so even if you’re willing to sprint up the stairs it won’t matter if you catch up to someone that’s half your speed. Phantom traffic jams can arise as people stand and wait to alight at the top of the escalator. When considering both factors, your speed becomes a function of the percentage of people willing to walk. At ~0% you can walk at max speed, but interestingly as the percentage tends to 50% the escalator converges to a stand-only system as phantom traffic jams propagate across the length of the escalator. Assuming an average walking speed of 60 steps per minute with a variability of 30 and a walking percentage of 25%, the real average speed when sampling for the slowest person within 10 spaces in front of you is only 50 steps per minute. On average it will take 56 seconds to climb the escalator when combined with its base speed.

Figuring out how long you’ll spend queuing is simple, it’s just the the number of people in front of you divided by the throughput. For example if there are 300 people in front of you and you’re moving at a rate of 150 people a minute, in the case of the stand-only trial, then you’ll spend 120 seconds in the queue. A similar scenario with a throughput of 115 people a minute yields a different queue time of 160 seconds. In this model of Holborn, it suggests that having 300 people in front of you is the break even point where the trade off for walking speed begins to get outweighed by the additional time spent queuing. So in both situations it would take 120 + 96 = 160 + 56 = 216 seconds to get to the top. More importantly, anyone willing to walk is in the queue behind you will be getting to the top slower than if the system was stand-only.

**How often is it faster?**

Commuters offloading onto the platform is bursty in the sense that they alight all at once from a train rather than at a constant continuous rate. Central line trains have a capacity of 800 passengers and Holborn is a popular destination, so it is not uncommon for a single train to offload 200 people at a time during rush hour. At peak times trains usually run once every 2 minutes and from both directions, so it isn’t uncommon for alighting passengers to join into preexisting queues from previous trains.

An alternative case to consider is when an escalator is suspended for maintenance. This brings the break even point from 300 to 150; doubling the queue time as the throughput is halved. In the scenario where only one escalator is working and 300 people are queuing in front, a walk/stand system would be 40 seconds slower for you than a stand-only system as you would spend an extra 80 seconds queuing for the same 40 second speed benefit from climbing the escalator.

**Does the queue actually start at the platform?**

The queue analyzed so far has started at the base of the platform, but this might not be the full reach of the escalators’ effects. Assuming the incoming trains can offload people at a higher rate than they can leave, the actual rate will match the throughput of the escalator once the platform becomes full. Let’s see how each of the two models compare when assuming:

- An empty platform
- A constant incoming rate of 160 people per minute
- A safe capacity for 1000 people

Walk/stand: 1000/(160-115) = 22 minutes at full throughput, then throttled to 115/m

Stand-only: 1000/(160-150) = 100 minutes at full throughput, then throttled to 150/m

The duration that a station runs at full throughput is important, especially in the context of peak times. The moment a single train is delayed by a low throughput platform, all trains behind it will also run slower as the delay propagates throughout the line. If that station is truly the bottleneck, then all the incoming trains will only be able to run as fast as the station until the platform starts to empty.

Unlike the platform-escalator system, it’s harder to model how much of an effect standing on both sides of the escalator has on ascension time when extending it to include trains, but by now the link between average service time and throughput should be clear. This is why most busier stations usually have 2 up escalators and/or a high platform capacity. In cases where one of the escalators requires maintenance, the down escalator will be converted so that the whole line isn’t slowed down.

**A practical suggestion**

To conclude, there is evidence to suggest that stand-only systems are faster than walk/stand systems for busy platforms with tall escalators during peak times. The Holborn station trial is an example of such evidence despite the difficulty implementing the stand-only system. By exploring the analysis further, I believe there is a solution that satisfies those that wish to walk without the need for a time/station dependent system, while not compromising heavily on the system throughput.

Firstly, it’s important to view each pair of escalators collectively as 4 independent lanes of traffic. In the Holborn case, and somewhat generally for large escalators, the percentage of people willing to walk rarely exceeds 25%. As only one quarter of the traffic wishes to walk it makes sense to only dedicate one out of the four lanes for walking; a hybrid between the other two systems which dedicated 2 and 0 lanes for walking respectively. This will theoretically match the stand-only throughput through load balancing without violating the will of the British public to stand on the right and walk on the left, as there will just be a little bit *more *standing on the right. The walking lane still may not be a walking lane during peak times due to the increased utilization, though at least the possibility of walking will prevent riots on the Central line.