# Driverless cars plus mathematics could equal the end of traffic jams

Here we go again. Image: Getty.

Being stuck in miles of halted traffic is not a relaxing way to start or finish a summer holiday. And as we crawl along the road, our views blocked by by slow-moving roofboxes and caravans, many of us will fantasise about a future free of traffic jams.

As a mathematician and motorist, I view traffic as a complex system, consisting of many interacting agents including cars, lorries, cyclists and pedestrians. Sometimes these agents interact in a free-flowing way; at other, infuriating, times they simply grind to a halt. All scenarios can be examined – and hopefully improved – using mathematical modelling, a way of describing the world in the language of maths.

Mathematical models tell us for instance that if drivers kept within the variable speed limits sometimes displayed on a motorway, traffic would flow consistently at, say, 50mph. Instead we tend to drive more aggressively, accelerating as soon as the opportunity arises – and being forced to brake moments later. The result is greater fuel consumption and a longer overall journey time.

Cooperative driving seems to go against human nature when we get behind the wheel. But could this change if our roads were taken over by driverless cars?

Incorporating driverless cars into mathematical traffic models will prove key to improving traffic flow and assessing the various conditions in which traffic reaches a traffic jam threshold, or “jamming density”. The chances of reaching this point are affected by changes such as road layout, traffic volume and traffic light systems. And crucially, they are affected by whoever is in control of the vehicles.

In mathematical analysis, dense traffic can be treated as a flow and modelled using differential equations which describe the movement of fluids. Queuing models consider individual vehicles on a network of roads and the expected time they spend both in motion and waiting at junctions.

Another type of model consists of a grid in which cars' positions are updated, according to certain rules, from one grid cell to the next. These rules can be based on their current velocity, acceleration and deceleration due to other vehicles and random events. This random deceleration is included to account for situations caused by something other than other vehicles – a pedestrian crossing the road for example, or a driver distracted by a passenger.

Adaptations to such models can take into account factors such as traffic light synchronisation or road closures, and they will need to be adapted further to take into account the movement of driverless cars.

In theory, autonomous cars will typically drive within the speed limits; have faster reaction times allowing them to drive closer together; and will behave less randomly than humans, who tend to overreact in certain situations. On a tactical level, choosing the optimum route, accounting for obstacles and traffic density, driverless cars will behave in a more rational way, as they can communicate with other cars and quickly change route or driving behaviour.

So driverless cars may well make the mathematician’s job easier. Randomness is often introduced into models in order to incorporate unpredictable human behaviour. A system of driverless cars should be simpler to model than the equivalent human-driven traffic because there is less uncertainty. We could predict exactly how individual vehicles respond to events.

In a world with only driverless cars on the roads, computers would have full control of traffic. But for the time being, to avoid traffic jams we need to understand how autonomous and human-driven vehicles will interact together.

Of course, even with the best modelling, cooperative behaviour from driverless cars is not guaranteed. Different manufacturers might compete to come up with the best traffic-controlling software to ensure their cars get from A to B faster than their rivals. And, like the behaviour of individual human drivers, this could negatively affect everyone’s journey time.

But even supposing we managed to implement rules that optimised traffic flow for everyone, we could still get to the point where there are simply too many cars on the road, and jamming density is reached.

Yet there is still potential for self-driving cars to help in this scenario. Some car makers expect that eventually we will stop viewing cars as possessions and instead simply treat them as a transport service. Again, by applying mathematical techniques and modelling, we could optimise how this shared autonomous vehicle service could operate most efficiently, reducing the overall number of cars on the road.

So while driverless cars alone might not rid us of traffic jams completely by themselves, an injection of mathematics into future policy could help navigate a smoother journey ahead.

Lorna Wilson is commercial research associate at the University of Bath.

# “This is a civic pride for the digital age”: why we should why we should willingly let City Hall have our data

He was the future once: David Cameron discusses smart cities with Angela Merkel and a German technology executive. Image: Getty.

Victorian England. From the shadows of wealth grew poverty. Slums slumped against symbols of civic pride, cowering next to towering town halls funded through rich merchant princes, whose elitist rule was insufficient to deal with too many people in too few houses with too little infrastructure.

Enter municipality. With darkness came electric light; with disease came tunnels to disperse their cause; with time came reform, regulation and the rise of town planning.

It’s over a century since those places which first industrialised became those first urbanised; yet even the wealthiest cities in the world continue to struggle with the complexities of urbanisation. In London, ten thousand die each year from pollution; in New York, six times this amount reside in homeless shelters.On the rush-hour roads of Sydney, cars stand still, and in the ‘burbs or banlieues of Paris slums still stand.

An umbrella bought during a downpour costs more than one bough under blue sky – and the truth is that, for too, long city halls have failed to forecast and so incurred greater costs. It’s a reactive culture summed up by words first head in Jimmy Carter’s budget office: if it ain’t broke, don’t fix it. Disease before sewer, gridlock before investment, collapse before rebuild – visible fix over unseen prevention

But with the world’s urban population growing by 65m every year, this has to change: there is not enough resource to manage cities reactively. Enter technology and the move to smart cities.

From Barcelona to New YorkOxford to Amsterdam, Singapore to Seoul: billions of low-cost devices are being installed into everyday objects to send and receive data: street lights recording pollution, and bridges reporting performance; traffic lights that count, and whose analysis will be counted upon, to ease traffic congestion; health wristbands understanding our heart’s needs, shop ceilings noting our heart’s desires. A web of information woven into the very fabric of cities which, when added to data from sources like mobile phones, is providing a living-breathing picture of how we and our cities operate.

This data is no longer retrospective or historic but live and dynamic. It is of such quantity, and can be analysed at such granular detail, that it can provide certainty where once there was only supposition. It is build-up before the gridlock, illness before epidemic; the crack of an ageing bridge, the first signs of smog. It is diagnostic to preventative. Umbrella under blue sky.

Those promoting the “internet of things”, estimated to be worth \$11.1trn a year by 2025, will declare it a panacea – but it is not, at least not entirely. Sure, challenges regarding data quality, privacy, standardisation, and security will be overcome; 4G will become 5G will become 6G. Devices will communicate intelligently with each other – autonomous vehicle to autonomous vehicle, autonomous vehicle to bridge, drone to home. Data will become as fundamental to cities as infrastructure, and will be referred to as such.

Yet city halls in democracies, whilst infinitely better informed, will continue to make their decisions which are restricted by commercialism, framed by political ideology, and driven by short-term electoral or media pressures.

### People first

From the mid-sixties to the start of this century a UK television programme called Tomorrow’s World showcased future living. For every correct prediction (mobile phones) came countless incorrect ones: the floating-bicycle, say, or paper underwear. My point is that only a small part of understanding the future of cities is about understanding technology. The majority is about understanding people and society, the people from whom the very word “city” is derived: civitas, the collective of citizens.

Gutenberg did not change the world by inventing the printing press in the 13th century – but he did enable the world to change. The technology was the printing press, the outputs were books filled with knowledge, the outcomes were the actions of the many who used that knowledge. Technology is a tool, a process towards an outcome.

In much the same way, the Internet of Things will not change the world – but it will enable the world to change. Sensors are the technology, data the outputs, the analysis of this data and subsequent decisions, the outcome.

It is crucial to avoid the Tomorrow’s World approach. That is, racing to implement technology first without consideration of identified social, economic or environmental needs; introducing more complexity when most citizens seek simplicity. As the writer and urbanist Jane Jacobs once said:“First comes the image of what we want, then the machinery is adapted to turn out that image.”

Start with people. Form the image. Think of technology through the Greek origins of the word, techne and logos – a discourse about the way things are gained – and capitalise on collective intelligence to move towards that image.

Since cities first started to appear some millennia ago, they’ve provided incontrovertible evidence that the wisdom of crowds is far greater than the individual; that collective intelligence gained from that trinity of city institutions – citizen, government, industry – surpasses what can be achieved by any one in isolation. Where would Apple, Uber, or Google be without the government-backed inventions like the world-wide-web, touchscreen technology, WiFi or global positioning systems?

### A new civic pride

Of course, an app on a smart phone that can ask a thousand questions is meaningless if nobody feels motivated to answer. Increasing urbanisation brings increasing interdependency: lives intrinsically linked, services shared. The challenge for city halls is to turn the increase in what people have in common, into an increase in common purpose, through understanding the three benefits that motivate and lead to action.

Extrinsic benefits, of status and reward, caused merchant princes to fund city halls in Victorian England: such benefits today see the ambitious putting in extra hours. Intrinsic benefits, like competitiveness or fun, that once caused business tycoons to compete to build the tallest skyscrapers, now explain why “hackathons” and “city challenges” are such a success. Then there are the pro-social benefits of altruism or benevolence, that cause millions to volunteer their time to give back and feel part of something bigger than themselves.

These motivations are of greater significance, because there are no longer people with clipboards standing on street corners asking permission to collate our views on services: it is happening automatically through the Internet of Things. Our choices online, movements offline; the travel we take, the pollution we make; our actions and interactions. We are data.

City halls can take a click-box-small-print approach to this, like so many apps. But there is opportunity to do the opposite. They can promote the fact that citizens can knowingly provide their data towards making lives better; visualise and enable citizens to see and understand their input, alongside data provided by others.

They can incentivise interaction with data, so that entrepreneurs can work back from outcomes, solve challenges, and re-localise where appropriate (we should not need a multinational to get a taxi). They can be proudly open, enabling citizens, industry and government to receive pro-social benefit by contributing to something bigger than themselves: their life and the lives of others.

This is a civic pride for the digital age. Not just localism or patriotism based on geography but the strength of connection between people and their ability to direct and determine change through data. Not just pride in the buildings and infrastructure that form our physical world, but in the quality of data that will shape our future world and move us from a diagnostic to preventative society – umbrellas under blue sky.

We should take pride in technology, yes; but that should come second to the pride in those who, enabled by that technology, drive progress. Who, through the wisdom of crowds, form an image of the future and strengthen democracy by motivating society to move towards it. Who embrace openness and help overcome the challenges of urbanisation.

Kevin Keith is a writer, researcher, urbanist, and director of the southern hemisphere’s largest open data competition, GovHack. He tweets as@KevKeith.