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.


“Black cabs are not public transport”: on the most baffling press release we’ve seen in some time

An earlier black cab protest: this one was against congestion and pollution. I'm not making this up. Image: Getty.

You know, I sometimes think that trade unions get a raw deal in this country. Reports of industrial action almost always frame it as a matter of workers’ selfishness and public disruption, rather than one of defending vital labour rights; and when London’s tube grinds to a halt, few people will find out what the dispute is actually about before declaring that the drivers should all be replaced by robots at the earliest possible opportunity or, possibly, shot.

We should be a bit more sympathetic towards trade unions, is what I’m saying here: a bit more understanding about the role they played in improving working life for all of us, and the fact that defending their members’ interests is literally their job.

Anyway, all that said, the RMT seems to have gone completely fucking doolally.

TAXI UNION RMT says that the closure of the pivotal Bank Junction to all vehicles (other than buses and bicycles) exposes Transport for London’s (TfL) symptom-focused decision-making and unwillingness to tackle the cause of the problem.

So begins a press release the union put out on Thursday. It’s referring to a plan to place new restrictions on who can pass one of the City of London’s dirtiest and most dangerous junctions, by banning private vehicles from using it.

The junction in question: busy day. Image: Google.

If at first glance the RMT’s words seem reasonable enough, then consider two pieces of information not included in that paragraph:

1) It’s not a TfL scheme, but a City of London Corporation one (essentially, the local council); and

2) The reason for the press release is that, at 5pm on Thursday, hundreds of black cab drivers descended on Bank Junction to create gridlock, in their time-honoured way of whining about something. Blocking major roads for several hours at a time has always struck me as an odd way of trying to win friends and influence people, if I’m frank, but let’s get back to the press release, the next line of which drops a strong hint that something else is going on here:

TfL’s gutlessness in failing to stand-up to multi-national venture capital-backed raiders such as Uber, has left our streets flooded with minicabs.

That suggests that this is another barrage in the black cabs’ ongoing war against competition from Uber. This conflict is odd in its way – it’s not as if there weren’t minicabs offering a low cost alternative to the classic London taxi before Uber came along, but we’ve not had a lengthy PR war against, say, Gants Hill Cars – but it’s at least familiar territory, so it’d be easy, at this point, to assume we know where we are.

Except then it gets really weird.

With buses stuck in gridlock behind haphazardly driven Uber cars – and with the Tube dangerously overcrowded during peak hours – people are turning out of desperation to commuting by bicycle.

Despite its impracticality, there has been an explosion in the number of people commuting by bike. Astonishingly, 30% of road traffic traversing Bank Junction are now cyclists.

Soooo... the only reason anyone might want to cycle is because public transport is now bad because of Uber? Not because it’s fun or healthy or just nicer than being stuck in a metal box for 45 minutes – because of badly driven Ubers something something?

Other things the cabbies will blame Uber for in upcoming press releases: climate change, Brexit, the outbreak of the Franco-Prussian war in July 1870, the fact they couldn’t get tickets for Hamilton.

It is time that TfL refused to licence Uber, which it acknowledges is unlawfully “plying for hire”.

Okay, maybe, we can talk about that.

It is time that black cabs were recognised and supported as a mode of public transport.


It is time that cuts to the Tube were reversed.

I mean, sure, we can talk about that too, but... can you go back to that last bit, please?

RMT General Secretary, Mick Cash, said:

“RMT agrees with proposals which improve public safety, but it is clear that the driving factor behind the decision is to improve bus journey times under a buckling road network.

“Black cabs are an integral part of the public transport system and as the data shows, one of the safest.”

This is all so very mixed up, it’s hard to know where to begin. Black cabs are not public transport – as lovely as they are, they’re simply too expensive. Even in New York City, where the cabs are much, much cheaper, it’d be silly to class them as public transport. In London, where they’re so over-priced they’re basically the preserve of the rich and those who’ve had enough to drink to mistakenly consider themselves such, it’s just nonsense.

Also – if this decision has been taken for the sake of improving bus journey times, then what’s wrong with that? I haven’t run the numbers, but I’d be amazed if that wasn’t a bigger gain to the city than “improving life for the people who take cabs”. Because – as I may have mentioned – black cabs are not public transport.

Anyway, to sum the RMT’s position up: we should invest in the tube but not the buses, expensive black cabs are public transport but cheaper Ubers are the work of the devil, and the only reason anyone would ever go by bike is because they’ve been left with no choice by all those people in the wrong sort of taxi screwing everything up. Oh, and causing gridlock at peak time is a good way to win friends.

Everyone got that straight?

None of this is to say Uber is perfect – there are many things about it that are terrible, including both the way people have mistaken it for a revolutionary new form of capitalism (as opposed to, say, a minicab firm with an app), and its attitude to workers (ironically, what they could really do with is a union). The way TfL is acting towards the firm is no doubt imperfect too.

But the RMT’s attitude in this press release is just baffling. Of course it has to defends its members interests – taxi drivers just as much as tube drivers. And of course it has to be seen to be doing so, so as to attract new members.

But should it really be trying to do both in the same press release? Because the result is a statement which demands TfL do more for cab drivers, slams it for doing anything for bus users, and casually insults anyone on two wheels in the process.

A union’s job is to look after its members. I’m not sure nonsense like this will achieve anything of the sort.

Jonn Elledge is the editor of CityMetric. He is on Twitter, far too much, as @jonnelledge.

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