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.

 
 
 
 

A nation that doesn’t officially exist: on Somaliland’s campaign to build a national library in Hargeisa

The Somaliland National Library, Hargeisa. Image: Ahmed Elmi.

For seven years now, there’s been a fundraising campaign underway to build a new national library in a nation that doesn’t officially exist. 

Since 2010, the Somali diaspora have been sending money, to pay for construction of the new building in the capital, Hargeisa. In a video promoting the project, the British journalist Rageeh Omar, who was born in Mogadishu to a Hargeisa family, said it would be... 

“...one of the most important institutions and reference points for all Somalilanders. I hope it sets a benchmark in terms of when a country decides to do something for itself, for the greater good, for learning and for progress – that anything can be achieved.”

Now the first storey of the Somaliland National Library is largely complete. The next step is to fill it with books. The diaspora has been sending those, too.

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Some background is necessary here to explain the “country that doesn’t exist” part. During the Scramble for Africa of the 1880s, at the height of European imperialism, several different empires established protectorates in the Somali territories on the Horn of Africa. In 1883, the French took the port of Djibouti; the following year, the British grabbed the north coast, which looks out onto the Gulf of Aden. Five years after that, the Italians took the east coast, which faces the Indian Ocean.

And, excepting some uproar during World War II, so things remained for the next 70 years or so.

The Somali territories in 1890. Image: Ingoman/Wikimedia Commons.

When the winds of change arrived in 1960, the British and Italian portions agreed to unite as the Somali Republic: a hair-pin shaped territory, hugging the coast and surrounding Ethiopia on two sides. But British Somaliland gained its independence first: for just five days, at the end of June 1960, it was effectively an independent country. This will become important later.

(In case you are wondering what happened to the French bit, it voted to remain with France in a distinctly dodgy referendum. It later became independent as Djibouti in 1977.)

The new country, informally known as Somalia, had a difficult history: nine years of democracy ended in a coup, and were followed by the 22 year military dictatorship under the presidency of General Siad Barre. In 1991, under pressure from rebel groups including the Hargeisa-based Somali National Movement (SNM), Barre fled, and his government finally collapsed. So, in effect, did the country.

For one thing, it split in two, along the old colonial boundaries: the local authorities in the British portion, backed by the SNM, made a unilateral declaration of independence. In the formerly Italian south, though, things collapsed in a rather more literal sense: the territory centred on Mogadishu was devastated by the Somali civil war, which has killed around 500,000, displaced more than twice that, and is still officially going on.

Somalia (blue) and Somaliland (yellow) in 2016. Image: Nicolay Sidorov/Wikimedia Commons.

The north, meanwhile, got off relatively lightly: today it’s the democratic and moderately prosperous Republic of Somaliland. It claims to be the successor to the independent state of Somaliland, which existed for those five days in June 1960.

This hasn’t persuaded anybody, though, and today it’s the only de facto sovereign state that has never been recognised by a single UN member. Reading about it, one gets the distinct sense that this is because it’s basically doing okay, so its lack of diplomatic recognition has never risen up anyone’s priority list.

Neither has its library.

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Rageeh Omar described the site of the new library in his fundraising video. It occupies 6,000m2 in the middle of Hargeisa, two minutes from the city’s main hospital, 10 from the presidential palace. In one sequence he stands on the half-completed building’s roof and points out the neighbours: the city’s main high street, with the country’s largest shopping mall; the Ministry of Telecoms that lies right next door.

This spiel, in a video produced by the project’s promoters, suggests something about the new library: that part of its job is to be another in this list of landmarks, more evidence that Hargeisa, a city of 1.5m, should be recognised as the proper capital of a real country.

But it isn’t just that: the description of the library’s function, in the government’s Strategic Plan 2013-2023, makes clear it’s also meant to be a real educational facility. NGOS, the report notes, have focused their resources on primary schools first, secondary schools second and other educational facilities not at all. (This makes sense, given that they want most bang for their buck.)

And so, the new building will provide “the normal functions of public library, but also... additional services that are intentionally aimed at solving the unique education problems of a post conflict society”. It’ll provide books for a network of library trucks, providing “book services” to the regions outside Hargeisa, and a “book dispersal and exchange system”, to provide books for schools and other educational facilities. There’ll even be a “Camel Library Caravan that will specifically aim at accessing the nomadic pastoralists in remote areas”.

All this, it’s hoped, will raise literacy levels, in English as well as the local languages of Arabic and Somali, and so boost the economy too.

As described. Image courtesy of Nimko Ali.

Ahmed Elmi, the London-based Somali who’s founder and director of the library campaign, says that the Somaliland government has invested $192,000 in the library. A further $97,000 came from individual and business donors in both Hargeisa and in the disaspora. “We had higher ambitions,” Elmi tells me, “but we had to humble our approach, since the last three years the country has been suffering from a large drought.”

Now the scheme is moving to its second phase: books, computers and printers, plus landscaping the gardens. This will cost another $175,000. “We are also open to donations of books, furniture and technology,” Emli says. “Or even someone with technical expertise who can help up set-up the librarian system instead of a contemporary donation of a cash sum.” The Czech government, in fact, has helped with the latter: it’s not offered financial support, but has offered to spend four weeks training two librarians.  

Inside the library.

On internet forums frequented by the Somali diaspora, a number of people have left comments about the best way to do this. One said he’d “donated all my old science and maths schoolbooks last year”. And then there’s this:

“At least 16 thousand landers get back to home every year, if everyone bring one book our children will have plenty of books to read. But we should make sure to not bring useless books such celebrity biography books or romantic novels. the kids should have plenty of science,maths and vocational books.”

Which is good advice for all of us, really.


Perhaps the pithiest description of the project comes from its Facebook page: “Africa always suffers food shortage, diseases, civil wars, corruption etc. – but the Somaliland people need a modern library to build a better place for the generations to come.”

The building doesn’t look like much: a squat concrete block, one storey-high. But there’s something about the idea of a country coming together like this to build something that’s rather moving. Books are better than sovereignty anyway.

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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