How many colours would you need to make London’s bus network more comprehensible?

Any colour you want as long as its red. Image: Getty.

Looking at Transport for London’s colour-coded bus trial in Barkingside, CityMetric editor Jonn Elledge found an interesting problem:

Even thinking about the maths does my head in – but it seems unlikely to me that every bus in London can be given a colour different from that of every bus it ever shares a stop with. At some bus stops, there’ll be two buses in violet.

So let’s have a go at this: given the current bus routes in London, how many colours would you need to so that no bus stop has two buses using the same colour?

TfL have their bus stop locations and routes available as open data so we can quickly get a feel for how hard a problem is actually is. The way I processed the file I ended up with 20,028 bus stops and 729 routes (we can probably have arguments about exact numbers, but go with me). A lot of those bus stops serve exactly the same routes as others – so there are only 4,129 unique nodes in this problem. Which is still lots, but feels more manageable.

While there probably an elegant mathematical approach, the boring brute force technique goes like this. Starting out with all bus routes sharing a single colour (let’s say blue), you get the computer to go through every bus stop and change routes to other colours to make sure that bus stop has only unique colours. You then repeat this until all bus stops have no duplicate colours.

You get different results for this depending what order you tackle the bus stops, so you run it with a few different orders to get a feel of about how many colours are needed. Running the program 1,000 times, the lowest number I get using this technique is 44. Lower numbers are probably possible through trying many more orders, but let’s say for the moment this is roughly right – you’d need 44 colours to apply this approach strictly to the entire London bus system. This is really too many colours to be able to usefully distinguish lines, so is probably a no-go.

We get more manageable numbers if we try a less strict version of the rule. If we let bus stops served by five or more routes have two routes of the same colour, the total number of colours required drops to 14. This is approaching a workable colour scheme in terms of actually being able to distinguish between all varieties.

When your number is up

But let’s move on from colours and think about what TfL is actually trying to do here: it wants to make it easier for people who don’t currently use buses to use buses.

It’s worth thinking about where bus route numbers currently come from:

When we introduce a new route – or make alterations to an existing route by splitting it – the last digit or digits of the historic ‘parent’ route are used wherever possible, so that passengers might associate the incoming route with its predecessor. This was the case in 2003, for instance, when route 414 was chosen as the number for the new route between Maida Hill and Putney Bridge, which was intended to augment route historic route 14 south of Hyde Park Corner.

In other words, bus routes numbers are path dependent on old naming decisions because of the desire to keep existing users happy. While this is probably a good idea, it can also end up in results that are very un-good for new users.

So if you ignored the past and the need to keep the millions of current users not confused, what could do if you just scrapped all the current route numbers and started from scratch? Specifically let’s look at two problems:

  • Ambiguous bus routes at the same stop that appear similar;

  • Hard to remember bus numbers.

If you don’t see why these things are problems, imagine yourself as a user for whom the concept of numbers is a bit fuzzier: for instance, dyslexic users for whom the number rearrange (where 365 and 635 might be similar), or those for whom the numbers are literally fuzzy because they’re less able to read the signs.


There are two key areas of ambiguity: digits that are visually similar to each other (66 and 68) and route numbers that are conceptually similar like 114 and 14.

For real world examples of conceptually confusing bus stops, there are 1,601 stops served by routes whose numbers wholly contain the number of another route at the same bus stop. While this is sometimes suggestive of similarity of route, in many instances it isn’t. If you’re at Church Lane the 71 and 671 share 88 per cent of stops in common – but if you’re at Southall Broadway, the 95 and 195 share just 0.1 per cent of their stops. Looking at all the stops with this problem, the average similarity is only 38 per cent.

As most journeys are short, differences at the far end of the route are probably not a problem for most users – but the point is, that vague, warm feeling that similar number routes at the same location should be similar is not backed up by the data.

There are also 205 stops that have routes which are anagrams of each other. The St Nicholas Center has the 407 and the 470, at Brooke Road you have the 76 and 67, and Lytton Grove has the 39 and the 93. This isn’t many in the grand scheme of things – but it’s not ideal.

While we’re thinking about which numbers are nicer than other, let’s look at research which numbers are easier to remember correctly than others. Milikowski & Elshout found that:

The order of memorability was

(1) Single digit numbers;

(2) Teen numbers (10-19);

(3) Doubled numbers (e.g. 44, 77, 22);

(4) Large tabled numbers (numbers which factor and therefore appear in the multiplication tables, such as 49, 36, 60, 84, 27); and

(5) Other numbers that do not fall into any of these categories.

While memorability for Single digit numbers was above 80 percent, that for Other numbers (no subcategory) was only around 40 percent.

This should inform our thinking about route numbers. The first thing our colour system lets you do is dump bus numbers above 100 and use colours as a replacement for the first digit. This immediately makes numbers easier to remember because we’re reducing the number of concepts you need to remember. Route 127 requires you to remember three things (one two seven) while Blue-27 requires you to remember two (Blue twenty-seven). This is more true with smaller numbers, but every little helps.

The next thing we need to do is jettison every number that is a reverse of another (we don’t want both 46 and 64). This gets rid of most numbers above fifty (while retaining doubles). The end result is each colour can now be followed by 62 numbers – which means 62 bus routes.

Ideally you’d also reduce ambiguous symbols such as (1 and 7) or (6 and 8) – but this really cuts down the number of usable numbers. Instead what we’ll do try and make sure ambiguous numbers like this do not appear at the same stop.

Seeing clearly

So here are our new constraints:

  • A colour can only have 62 routes;

  • There are 15 colours (up from 14, because the original solution required some colours to have more than 62 routes);

  • Bus stops with four or fewer buses can’t have multiple routes with the same colour, stops with more can have two;

  • One bus stop cannot have routes of different colours with the same number. You also can’t have both 21 and 27, or 46 and 48.

Is such an arrangement possible? It turns out it is.

To solve this one you randomise which routes get which numbers and score them according to how well they pass the above. Then you create random variations on the best performing plan, and so on, until it narrows in on a version that passes all the rules. This returned a viable arrangement of route colours and names after a few hours (and 161,663 attempts).

Can something like this be done in reality? Confusing all current users seems a bad idea – but maybe this kind of approach should affect how new bus routes are named. Rather than blindly following the history of a route, select rules you want to be true of your naming scheme (they might be different from mine) and get a computer to suggest the minimally confusing approach. It turns out it doesn’t take long to get answers to quite fiddly problems.

But the real point here is I don’t want to wear my glasses to wait for a bus, and changing the naming convention for every single bus route in London is a proportionate response to this problem.

Want more of this stuff? Follow CityMetric on Twitter or Facebook

 
 
 
 

A voice for the city: how should mayors respond to terror attacks?

Andy Burnham speaking in Manchester yesterday. Image: Getty.

When Andy Burnham, a former British government minister, won the election to be Greater Manchester’s Metro Mayor recently he was probably focused on plans for the region’s transport, policing and housing – and, of course, all the behind the scenes political work that goes on when a new role is created. The Conversation

And yet just a few weeks after taking on the role, terrorism has proved to be his first major challenge. Following the horrific bomb attack following a concert at one of Manchester’s most popular venues, he quickly has had to rise to the challenge.

It is a sad fact of life that as a senior politician, you will soon have to face – and deal with – a shocking incident of this kind.

These incidents arrive regardless of your long term plans and whatever you are doing. Gordon Brown’s early tenure as UK prime minister, for example, saw the Glasgow terror incident – which involved an attempted car bombing of the city’s airport in June 2007. Just four days into his premiership, Brown was dealing with the worst terrorist incident in Britain since the attacks on London in July 2005. Andy Burnham now finds himself in a similar situation.


Giving Manchester a voice

For Burnham, as the mayor and messenger of Manchester, an attack of this scale needs a response at several levels.

There is the immediately practical – dealing with casualties. There is the short term logistical – dealing with things like transport and closures. And there is the investigation and (hopefully) prevention of any follow ups.

But he will also need a “voice”. People look to particular figures to give a voice to their outrage, to talk about the need for calm, to provide reassurance, and to offer unity and express the sadness overwhelming many.

Part of the thinking behind the UK government’s enthusiasm for elected mayors was a perceived need to provide strong, local leaders. And a strong, local leader’s voice is exactly what is needed in Manchester now.

There is a certain choreography to the response to these events. It tends to go: a brief initial reaction, a visit to the scene, then a longer statement or speech. This is then usually followed by a press conference and interviews, along with visits to those affected. I say this not to be callous, but to highlight the huge demand the news media places on leading political figures when tragedy strikes.

‘We are strong’

As expected, Burnham made a speech on the morning after the attack. It is probably better described as a statement, in that it was short and to the point. But despite its brevity, in nine paragraphs, he summed up just about every possible line of thought.

The speech covered evil, the shared grieving and the need for the city to carry on. He also praised the work of the emergency services, and highlighted the need for unity and the very human reaction of the local people who provided help to those affected.

Andy Burnham on Sky News. Image: screenshot.

Burnham now has the task of bringing people together while there is still doubt about many aspects of what happened. A vigil in the centre of Manchester was rapidly planned for Tuesday evening, and there will be many other potential initiatives to follow.

Incidents like this tend to leave a large and long-lasting footprint. The effects of the bomb will last for years, whether in concrete reality or in people’s awareness and memories. And Burnham must now lead the effort to ensure Manchester emerges from this shocking incident with cohesion and strength.

Paula Keaveney is senior lecturer in public relations & politics at Edge Hill University.

This article was originally published on The Conversation. Read the original article.