Fed up with being crushed against the window on your way into work? Frustrated by not being able to board the Tube when those minutes wasted could have been spent at home? Annoyed with aggressive attitudes early in the morning?
No-one enjoys the Tube journey, but imagine if there was a strategy to maximise comfort. If you were told there was a method for seeking out those golden little spaces, would you believe it?
The aim: a comfortable, spacious Tube journey to work
Let’s focus on the Central Line Tube journey from Liverpool Street to Chancery Lane station – for selfish reasons as it’s our route. On average, 171,000 people exit or enter Liverpool Street station each day – no wonder the Central Line is one of the busiest in the capital and it is rare to get on the first train arriving at the platform.
Central Line trains comprise 8 carriages each of which can (and each morning do) squeeze in around 150 people. Due to the lazy nature of human beings, most tend to stay around platform entrances to board the Tube (of course, there are also the smart guys who move to the next carriage if they spot that the grass is greener there) resulting in a crowded, sweaty and unequally populated space. Platform entrances are situated in different positions at every station resulting in carriages taking it in turns to feel the pressure of these masses.
So, does an optimal strategy in the Tube game really exist? Only those who have watched Tube after Tube passing by without the chance to board or have wandered along platforms in the hope of finding the best carriage can embrace the importance of this question. Fortunately, the Operational Research toolkit contains the technique of simulation that will lead to the answer.
How can this be achieved?
The idea is to analyse which carriage on a Central Line train gives the best chance of boarding at Liverpool Street to head west towards Chancery Lane.
We look at a train’s progress from Stratford to Liverpool Street by predicting, based on platform entrance locations, the proportion of commuters entering each carriage at the four stops. The carriages will be numbered 1 – 8 starting from the front of the train.
The analysis uses the following simplifications and assumptions:
- When the train arrives at Stratford station there is an equal number of commuters in each carriage
- Everyone thinks the same way
- Separate Tube doors are not taken into consideration, only the carriages
- People leave the Tube in equal numbers from each carriage
The effect of people congregating around the entrances is displayed in the graphs below. The top two represent the number of people standing at each point along the platform at specific stations with the resulting carriage populations after the two stations in the bottom graph.
Simulation reflects the randomness of real life. It adds a behavioural aspect to the model – if a particular carriage is busier than another upon entering the station, those waiting have the option to move to an adjacent one; the larger the difference between two carriages, the more likely a move (provided the person is in the longer queue). Shown below is the route people take from entering the Tube station to boarding their chosen carriage used for the simulation.
So, where is the optimal place to stand?
Results indicate that carriage 8 (the back of the train) is the optimal carriage to choose for the journey.
The table below shows the relative number of extra people on average in each carriage compared with carriage 8 (which had the lowest value). The lower and upper values show the range this number is likely to take. So, for example, if you chose carriage 2 it is likely to contain 7 more people than carriage 8, but this can range from 3 to 9 more (for 95% of the time).
Interestingly, 56% of people changed carriage in the simulation indicating that the rules set for behaviour have had a huge impact on these figures. Hence simulation techniques can achieve more realistic results.
So if you want to win the race for the Tube space, head right to the back of the train. If in reality you find this not to be true, too many people have read this article and followed our advice.
For a blog about the underground, please head to http://london-underground.blogspot.com.
A useful app for knowing which door is closest to the exit at your destination can be found at http://www.tubeexits.co.uk to make your journey that bit easier.
For statistics relating to the tube, visit http://www.tfl.gov.uk/tfl/corporate/modesoftransport/tube/performance/ or http://www.tfl.gov.uk/corporate/modesoftransport/londonunderground/1608.aspx.
Or if you’re really keen, join the London Underground Society at http://www.lurs.org.uk/.