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.

 
 
 
 

Two east London boroughs are planning to tax nightlife to fund the clean up. Will it work?

A Shoreditch rave, 2013. Image: Getty.

No-one likes cleaning up after a party, but someone’s got to do it. On a city-wide scale, that job falls to the local authority. But that still leaves the question: who pays?

In east London, the number of bars and clubs has increased dramatically in recent years. The thriving club scene has come with benefits – but also a price tag for the morning clean-up and cost of policing. The boroughs of Hackney and Tower Hamlets are now looking to nightlife venues to cover these costs.

Back in 2012, councils were given powers to introduce ‘late night levies’: essentially a tax on all the licensed venues that open between midnight and 6am. The amount venues are expected to pay is based on the premises’ rateable value. Seventy per cent of any money raised goes to the police and the council keeps the rest.

Few councils took up the offer. Four years after the legislation was introduced, only eight local authorities had introduced a levy, including Southampton, Nottingham, and Cheltenham. Three of the levies were in the capital, including Camden and Islington. The most lucrative was in the City of London, where £420,000 was raised in the 2015-16 financial year.

Even in places where levies have been introduced, they haven’t always had the desired effect. Nottingham adopted a late night levy in November 2014. Last year, it emerged that the tax had raised £150,000 less than expected in its first year. Only a few months before, Cheltenham scrapped its levy after it similarly failed to meet expectations.


Last year, the House of Lords committee published its review of the 2003 Licensing Act. The committee found that “hardly any respondents believed that late night levies were currently working as they should be” – and councils reported that the obligation to pass revenues from the levy to the police had made the tax unappealing. Concluding its findings on the late night levy, the committee said: “We believe on balance that it has failed to achieve its objectives, and should be abolished.”

As might be expected of a nightlife tax, late night levies are also vociferously opposed by the hospitality industry. Commenting on the proposed levy in Tower Hamlets, Brigid Simmonds, chief executive at the British Beer and Pub Association, said: “A levy would represent a damaging new tax – it is the wrong approach. The focus should be on partnership working, with the police and local business, to address any issues in the night time economy.”

Nevertheless, boroughs in east London are pressing ahead with their plans. Tower Hamlets was recently forced to restart a consultation on its late night levy after a first attempt was the subject of a successful legal challenge by the Association of Licensed Multiple Retailers (ALMR). Kate Nicholls, chief executive at the ALMR, said:

“We will continue to oppose these measures wherever they are considered in any part of the UK and will urge local authorities’ to work with businesses, not against them, to find solutions to any issues they may have.”

Meanwhile, Hackney council intends to introduce a levy after a consultation which revealed 52 per cents of respondents were in favour of the plans. Announcing the consultation in February, licensing chair Emma Plouviez said:

“With ever-shrinking budgets, we need to find a way to ensure the our nightlife can continue to operate safely, so we’re considering looking to these businesses for a contribution towards making sure their customers can enjoy a safe night out and their neighbours and surrounding community doesn’t suffer.”

With budgets stretched, it’s inevitable that councils will seek to take advantage of any source of income they can. Nevertheless, earlier examples of the late night levy suggest this nightlife tax is unlikely to prove as lucrative as is hoped. Even if it does, should we expect nightlife venues to plug the gap left by public sector cuts?