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.

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The ATM is 50. Here’s how a hole in the wall changed the world

The olden days. Image Lloyds Banking Group Archives & Museum.

Next time you withdraw money from a hole in the wall, consider singing a rendition of happy birthday. For today, the Automated Teller Machine (or ATM) celebrates its half century.

Fifty years ago, the first cash machine was put to work at the Enfield branch of Barclays Bank in London. Two days later, a Swedish device known as the Bankomat was in operation in Uppsala. And a couple of weeks after that, another one built by Chubb and Smith Industries was inaugurated in London by Westminster Bank (today part of RBS Group).

These events fired the starting gun for today’s self-service banking culture – long before the widespread acceptance of debit and credit cards. The success of the cash machine enabled people to make impromptu purchases, spend more money on weekend and evening leisure, and demand banking services when and where they wanted them. The infrastructure, systems and knowledge they spawned also enabled bankers to offer their customers point of sale terminals, and telephone and internet banking.

There was substantial media attention when these “robot cashiers” were launched. Banks promised their customers that the cash machine would liberate them from the shackles of business hours and banking at a single branch. But customers had to learn how to use – and remember – a PIN, perform a self-service transaction and trust a machine with their money.

People take these things for granted today, but when cash machines first appeared many had never before been in contact with advanced electronics.

And the system was far from perfect. Despite widespread demand, only bank customers considered to have “better credit” were offered the service. The early machines were also clunky, heavy (and dangerous) to move, insecure, unreliable, and seldom conveniently located.

Indeed, unlike today’s machines, the first ATMs could do only one thing: dispense a fixed amount of cash when activated by a paper token or bespoke plastic card issued to customers at retail branches during business hours. Once used, tokens would be stored by the machine so that branch staff could retrieve them and debit the appropriate accounts. The plastic cards, meanwhile, would have to be sent back to the customer by post. Needless to say, it took banks and technology companies years to agree common standards and finally deliver on their promise of 24/7 access to cash.

The globalisation effect

Estimates by RBR London concur with my research, suggesting that by 1970, there were still fewer than 1,500 of the machines around the world, concentrated in Europe, North America and Japan. But there were 40,000 by 1980 and a million by 2000.

A number of factors made this ATM explosion possible. First, sharing locations created more transaction volume at individual ATMs. This gave incentives for small and medium-sized financial institutions to invest in this technology. At one point, for instance, there were some 200 shared ATM networks in the US and 80 shared networks in Japan.

They also became more popular once banks digitised their records, allowing the machines to perform a host of other tasks, such as bank transfers, balance requests and bill payments. Over the last five decades, a huge number of people have made the shift away from the cash economy and into the banking system. Consequently, ATMs became a key way of avoiding congestion at branches.

ATM design began to accommodate people with visual and mobility disabilities, too. And in recent decades, many countries have allowed non-bank companies, known as Independent ATM Deployers (IAD) to operate machines. The IAD were key to populating non-bank locations such as corner shops, petrol stations and casinos.

Indeed, while a large bank in the UK might own 4,000 devices and one in the US as many as 12,000, Cardtronics, the largest IAD, manages a fleet of 230,000 ATMs in 11 countries.


Bank to the future

The ATM has remained a relevant and convenient self-service channel for the last half century – and its history is one of invention and re-invention, evolution rather than revolution.

Self-service banking and ATMs continue to evolve. Instead of PIN authentication, some ATMS now use “tap and go” contactless payment technology using bank cards and mobile phones. Meanwhile, ATMs in Poland and Japan have used biometric recognition, which can identify a customer’s iris, fingerprint or voice, for some time, while banks in other countries are considering them.

So it’s a good time to consider what the history of cash dispensers can teach us. The ATM was not the result of a eureka moment of a single middle-aged man in a bath or garage, but from active collaboration between various groups of bankers and engineers to solve the significant challenges of a changing world. It took two decades for the ATM to mature and gain widespread, worldwide acceptance, but today there are 3.5m ATMs with another 500,000 expected by 2020.

Research I am currently undertaking suggests that ATMs may have reached saturation point in some Western countries. However, research by the ATM Industry Association suggests there is strong demand for them in China, India and the Middle East. In fact, while in the West people tend to use them for three self-service functions (cash withdrawal, balance enquiries, and purchasing mobile phone airtime), Chinese customers consumers regularly use them for as many as 100 different tasks.

Taken for granted?

Interestingly, people in most urban areas around the world tend to interact with the same five ATMs. But they shouldn’t be taken for granted. In many countries in Africa, Asia and South America, they offer services to millions of people otherwise excluded from the banking sector.

In most developed counties, meanwhile, the retail branch and the ATM are the only two channels over which financial institutions have 100 per cent control. This is important when you need to verify the authenticity of your customer. Banks do not control the make and model of their customers’ smart phones, tablets or personal computers, which are vulnerable to hacking and fraud. While ATMs are targeted by thieves, mass cybernetic attacks on them have yet to materialise.

The ConversationI am often asked whether the advent of a cashless, digital economy heralds the end of the ATM. My response is that while the world might do away with cash and call ATMs something else, the revolution of automated self-service banking that began 50 years ago is here to stay.

Bernardo Batiz-Lazo is professor of business history and bank management at Bangor University.

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