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.

It all adds up

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

 
 
 
 

Covid-19 is highlighting cities' unequal access to green space

In the UK, Londoners are most likely to rely on their local park for green space, and have the best access to parks. (Leon Neal/Getty Images)

As coronavirus lockdowns ease, people are flooding back to parks – but not everyone has easy access to green space in their city.

Statistics from Google show that park attendance in countries across the globe has shot up as people have been allowed to move around their cities again.

This is especially true in urban areas, where densely populated neighbourhoods limit the size of private green space – meaning residents have to go to the park to get in touch with nature. Readers from England can use our interactive tool below to find out how much green space people have access to in their area, and how it compares to the rest of the country.

 

Prime Minister Boris Johnson’s announcement Monday that people are allowed to mingle in parks and gardens with groups of up to six people was partially following what people were doing already.

Data from mobile phones show people have been returning to parks across the UK, and also across Europe, as weather improves and lockdown eases.

People have been returning to parks across the world

Stay-at-home requirements were eased in Italy on 4 May, which led to a flood of people returning to parks.

France eased restrictions on 1 May, and the UK eased up slightly on 13 May, allowing people to sit down in public places so long as they remain socially distanced.

Other countries have seen park attendance rise without major easing of lockdown – including Canada, Spain, and the US (although states there have individual rules and some have eased restrictions).

In some countries, people never really stopped going to parks.

Authorities in the Netherlands and Germany were not as strict as other countries about their citizens visiting local parks during lockdown, while Sweden has famously been avoiding placing many restrictions on people’s daily lives.


There is a growing body of evidence to suggest that access to green space has major benefits for public health.

A recent study by researchers at the University of Exeter found that spending time in the garden is linked to similar benefits for health and wellbeing as living in wealthy areas.

People with access to a private garden also had higher psychological wellbeing, and those with an outdoor space such as a yard were more likely to meet physical activity guidelines than those without access to outdoor space. 

Separate UK research has found that living with a regular view of a green space provides health benefits worth £300 per person per year.

Access is not shared equally, however, which has important implications for equality under lockdown, and the spread of disease.

Statistics from the UK show that one in eight households has no garden, making access to parks more important.

There is a geographic inequality here. Londoners, who have the least access to private gardens, are most likely to rely on their local park for green space, and have the best access to parks. 

However the high population in the capital means that on the whole, green space per person is lower – an issue for people living in densely populated cities everywhere.

There is also an occupational inequality.

Those on low pay – including in what are statistically classed as “semi-skilled” and “unskilled” manual occupations, casual workers and those who are unemployed – are almost three times as likely as those in managerial, administrative, professional occupations to be without a garden, meaning they rely more heavily on their local park.

Britain’s parks and fields are also at significant risk of development, according to new research by the Fields in Trust charity, which shows the number of people living further than a 10-minute walk from a public park rising by 5% over the next five years. That loss of green spaces is likely to impact disadvantaged communities the most, the researchers say.

This is borne out by looking at the parts of the country that have private gardens.

The least deprived areas have the largest gardens

Though the relationship is not crystal clear, it shows at the top end: Those living in the least deprived areas have the largest private green space.

Although the risk of catching coronavirus is lower outdoors, spending time in parks among other people is undoubtedly more risky when it comes to transmitting or catching the virus than spending time in your own outdoor space. 

Access to green space is therefore another example – along with the ability to work from home and death rates – of how the burden of the pandemic has not been equally shouldered by all.

Michael Goodier is a data reporter at New Statesman Media Group, and Josh Rayman is a graphics and data visualisation developer at New Statesman Media Group.