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.

 
 
 
 

This fun map allows you to see what a nuclear detonation would do to any city on Earth

A 1971 nuclear test at Mururoa atoll. Image: Getty.

In 1984, the BBC broadcast Threads, a documentary-style drama in which a young Sheffield couple rush to get married because of an unplanned pregnancy, but never quite get round to it because half way through the film the Soviets drop a nuclear bomb on Sheffield. Jimmy, we assume, is killed in the blast (he just disappears, never to be seen again); Ruth survives, but dies of old age 10 years later, while still in her early 30s, leaving her daughter to find for herself in a post-apocalyptic wasteland.

It’s horrifying. It’s so horrifying I’ve never seen the whole thing, even though it’s an incredibly good film which is freely available online, because I once watched the 10 minutes from the middle of the film which show the bomb actually going off and it genuinely gave me nightmares for a month.

In my mind, I suppose, I’d always imagined that being nuked would be a reasonably clean way to go – a bright light, a rushing noise and then whatever happened next wasn’t your problem. Threads taught me that maybe I had a rose-tinted view of nuclear holocaust.

Anyway. In the event you’d like to check what a nuke would do to the real Sheffield, the helpful NukeMap website has the answer.

It shows that dropping a bomb of the same size as the one the US used on Hiroshima in 1945 – a relatively diddly 15kt – would probably kill around 76,500 people:

Those within the central yellow and red circles would be likely to die instantly, due to fireball or air pressure. In the green circle, the radiation would kill at least half the population over a period of hours, days or weeks. In the grey, the thing most likely to kill you would be the collapse of your house, thanks to the air blast, while those in the outer, orange circle would most likely to get away with third degree burns.

Other than that, it’d be quite a nice day.

“Little boy”, the bomb dropped on Hiroshima, was tiny, by the standards of the bombs out there in the world today, of course – but don’t worry, because NukeMap lets you try bigger bombs on for size, too.

The largest bomb in the US arsenal at present is the B-83 which, weighing in at 1.2Mt, is about 80 times the size of Little Boy. Detonate that, and the map has to zoom out, quite a lot.

That’s an estimated 303,000 dead, around a quarter of the population of South Yorkshire. Another 400,000 are injured.

The biggest bomb of all in this fictional arsenal is the USSRS’s 100Mt Tsar Bomba, which was designed but never tested. (The smaller 50MT variety was tested in 1951.) Here’s what that would do:

Around 1.5m dead; 4.7m injured. Bloody hell.

We don’t have to stick to Sheffield, of course. Here’s what the same bomb would do to London:

(Near universal fatalities in zones 1 & 2. Widespread death as far as St Albans and Sevenoaks. Third degree burns in Brighton and Milton Keynes. Over 5.9m dead; another 6m injured.)

Everyone in this orange circle is definitely dead.

Or New York:

(More than 8m dead; another 6.7m injured. Fatalities effectively universal in Lower Manhattan, Downtown Brooklyn, Williamsburg, and Hoboken.)

Or, since it’s the biggest city in the world, Tokyo:

(Nearly 14m dead. Another 14.5m injured. By way of comparison, the estimated death toll of the Hiroshima bombing was somewhere between 90,000 and 146,000.)

I’m going to stop there. But if you’re feeling morbid, you can drop a bomb of any size on any area of earth, just to see what happens.


And whatever you do though: do not watch Threads. Just trust me on this.

Jonn Elledge is the editor of CityMetric. He is on Twitter as @jonnelledge and also has a Facebook page now for some reason. 

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