# Traffic jam mystery solved by mathematicians

##### December 19, 2007

Mathematicians from the University of Exeter have solved the mystery of traffic jams by developing a model to show how major delays occur on our roads, with no apparent cause. Many traffic jams leave drivers baffled as they finally reach the end of a tail-back to find no visible cause for their delay.

Now, a team of mathematicians from the Universities of Exeter, Bristol and Budapest, have found the answer and published their findings in leading academic journal Proceedings of the Royal Society.

The team developed a mathematical model to show the impact of unexpected events such as a lorry pulling out of its lane on a dual carriageway. Their model revealed that slowing down below a critical speed when reacting to such an event, a driver would force the car behind to slow down further and the next car back to reduce its speed further still.

The result of this is that several miles back, cars would finally grind to a halt, with drivers oblivious to the reason for their delay. The model predicts that this is a very typical scenario on a busy highway (above 15 vehicles per km). The jam moves backwards through the traffic creating a so-called ‘backward travelling wave’, which drivers may encounter many miles upstream, several minutes after it was triggered.

Dr Gábor Orosz of the University of Exeter said: “As many of us prepare to travel long distances to see family and friends over Christmas, we’re likely to experience the frustration of getting stuck in a traffic jam that seems to have no cause. Our model shows that overreaction of a single driver can have enormous impact on the rest of the traffic, leading to massive delays.”

Drivers and policy-makers have not previously known why jams like this occur, though many have put it down to the sheer volume of traffic. While this clearly plays a part in this new theory, the main issue is around the smoothness of traffic flow. According to the model, heavy traffic will not automatically lead to congestion but can be smooth-flowing. This model takes into account the time-delay in drivers’ reactions, which lead to drivers braking more heavily than would have been necessary had they identified and reacted to a problem ahead a second earlier.

Dr Orosz continued: “When you tap your brake, the traffic may come to a full stand-still several miles behind you. It really matters how hard you brake - a slight braking from a driver who has identified a problem early will allow the traffic flow to remain smooth. Heavier braking, usually caused by a driver reacting late to a problem, can affect traffic flow for many miles.”

The research team now plans to develop a model for cars equipped with new electronic devices, which could cut down on over-braking as a result of slow reactions.

Source: University of Exeter

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##### SurDin
3.5 / 5 (6) Dec 19, 2007
The conclusion from this is that if you keep a better distance from the car ahead, then you won't have to break as hard and will lessen the traffic.
##### mysticfree
4.5 / 5 (4) Dec 19, 2007
New theory? Finally solved? There are several websites by college professors that have been around for a couple of years that should the exact mathematics for this very idea. Take this site for example:
http://www.math.u...pet.html

Looks like the Univ of Exeter experienced their own delays of sort...
##### earls
3.4 / 5 (7) Dec 19, 2007
SurDin said it all. IDIOTS refuse to maintain a buffer between themselves and other cars making it impossible to adapt to changing traffic patterns & conditions - then the whole system collapses. And all it takes to know that is about 20 minutes on any highway.

As mentioned, sensors that prevent drivers from approaching within a certain distance of another vehicle would make a big difference. And with adequate sensor / artificial driver technology, stop lights/signs could be made obsolete by the fact you could have traffic weave between each other at intersections.

Don't even get me started on people who can't figure out how to merge.
3.6 / 5 (5) Dec 19, 2007
Drivers and policy-makers have not previously known why jams like this occur???

This was always obviously a buffer between cars problem.. this is new to people??? What kind of world are we living in? FFS...
##### drknowledge
2.8 / 5 (5) Dec 19, 2007
Excuse me, but the contents of this article, as reported, are findings available (in printed publication) 20 years ago. In addition, the inflated article title is an example of appending a sensationalist "hook" to grab readers.

The content is inaccurate. The title misleading.

A poor showing for a Web site that purports to maintain high scientific standards.
##### Maalstrom
2 / 5 (3) Dec 19, 2007
Automated Driving Systems are the only way to go. Whether controlled by the highway infrastructure or a collaborative GPS solution within the cars themselves, it is clearly time to take the majority of driving responsibilities out of the hands of distracted and fallible Humans. Traffic Trains controlled by the highways would make travel so much quicker and safer. Plus you could sleep/read/do business while you travel.
##### MiddleBassIsland
4 / 5 (2) Dec 19, 2007
There's nothing new in this except perhaps the mathematical proof of a fact known for years.

I remember stop and go driving for miles on a freeway in a 70mph zone, and the discovery that it was all caused by an old pickup traveling 35mph in the left (passing) lane. But I've never seen police enforcement of driving violations that contribute to traffic congestion!

What I'd like to see analyzed next is how rude lane behavior that leads to unnecessary speed changes contributes to lower fuel economy as well as congestion.
##### AJW
3 / 5 (2) Dec 19, 2007
This information was determined and published at least four years ago in Germany.
##### flubber
1.3 / 5 (3) Dec 20, 2007
Obviously these 'researchers' don't drive. I hope I hope they didn't get paid for this.
##### cgr
3 / 5 (1) Dec 20, 2007
Actually, I believe the point being made here is about reaction time. I know it's easy to blow up about leaving sufficient space between yourself and the vehicle in front of you, but that does not actually solve the problem. Regardless of the space in front of you or the space behind you, your reaction time may differ from that of the vehicle behind you. If anyone's reaction time falls out of scope for a sufficient recovery that keeps traffic flowing at an acceptable pace, then a jam is going to occur, regardless of the number of car lengths between vehicles.

Taking that in to account, such jams caused by these stopping "waves" could occur at any time given any number of vehicles on the road. Of course, it's less likely to occur with fewer vehicles and I would assume there is some average reaction time given a certain number of cars on the road.

Additionally, awareness alone will not solve this problem. People are simply too stupid. What interests me is applying this model to on board electronics such as distance sensors and automatic cruise control and GPS.

Now that would be a breakthrough. Of course, nobody will be driving for themselves anymore.

Perhaps we should all take trains :)
##### ElViejo
3 / 5 (1) Dec 20, 2007
Modelling traffic as flow of a compressible fluid in a pipe was done by Honeywell Systems and Research Center (USA) in the early to mid 1970s. AFAIK, this was the first use of this paradigm; I was on the patent review committee at the time (back then, you actually had to invent something to get a patent) for patents on traffic control systems based on the idea and no prior art was found.
##### tao53nyc
2 / 5 (2) Dec 20, 2007
I just see it as "painful elucidation of the obvious."
4 / 5 (2) Dec 20, 2007
as many have implied, and to paraphrase: "Thank you captains obvious..."
##### peeved
3 / 5 (1) Dec 20, 2007
You could be the most attentive driver and still be the cause of a major backup. Your reaction time can be slow due to poor visibility ahead. I drive a light Pickup sitting quite high and leave a large gap and yet I still can't see around large SUV's with tinted windows, box trucks and semi trailers. There may be slowing traffic ahead and I may not know it because of a large vehicle that is not slowing as fast as the traffic in front of him and then suddenly find myself braking hard and very likely causing a traffic jam behind me.

To say people just don't leave enough space is not enough off an answer. Or to say that some people simply react slowly. It's definately a complex combination and electronic traffic control devices will not solve the problem. Never mind the fact that many will be hacked or disabled (and it only takes a single driver to cause such an event), they would not account for many traffic situations such as lateral incidents - a tire blow out causing a vehicle to swerve into another lane. Yes this is an accident and not normal traffic, but consider during an accident how these distance control devices would actually make the situation WORSE potentially bringing traffic to a complete stop.

The likely problem is the design on highway systems especially for large cities where ALL ROADS LEAD IN. Can we say "GRIDLOCK".
##### rja
3 / 5 (2) Dec 20, 2007
Truckers have known this for years and years. Of course we don't know the math formula but we didn't need to come up with one in order to know what causes a traffic jam when seemingly no cause is present.

Truckers drive over 120,000 miles per year compared to the 10,000-15,000 miles per year that autos do. That's a heck of a lot more experience which is where the traffic knowledge comes from.

But hey, if you need a formula to figure it out...
##### SteveB
1 / 5 (2) Dec 21, 2007
I don't know why it took a team of scientists to figure out common sense. Please read my Blog (written a long time ago) which highlights simple rules of driving in order to increase "traffic flow":

If this stuff was taught in school, traffic would be dramatically improved!:

Common Sense Driving Code:
##### SteveB
not rated yet Dec 21, 2007
Sorry... my previous link does not display properly by comment feature:
use this one:

Common Sense Driving Code:
http://www.blogwe...fficguru
##### JanSch
not rated yet Dec 21, 2007
LOL
Way back in 1985, in my second year of CS, a couple of other students and I, created such a model as part of a Simula67 programming course. The conclusions where exactly the same as these Exeter folks.
So what's the big deal? This is really basic stuff. Getting moronic politicians and civil servants to understand this, and act accordingly, is a totally different ballgame though!
##### jawesome
not rated yet Dec 21, 2007
Has anyone considered that the majority of traffic jams are actually caused by inconsiderate drivers who slow down to look at something interesting on the side of the road without realizing that there is a long line of cars behind them trying to get by. Ironically enough, when I see this (which seems to be the cause of the majority of traffic jams I'm in), every single car that drives by slows down to look at the interesting event despite the fact that they were probably cursing the fact that they're in a traffic jam.
##### allyourbase
not rated yet Dec 21, 2007
ARGH. This theory is garbage. The braking driver is but the _second_ part of a traffic jam.

The first part stems froms idiots--especially here in the US--that don't understand the concept of a "passing lane" and use any ol' available lane for travel.

Or, worse still are those that obliviously stagger their cars adjacent vehicles in adjacent lanes so that no passing is possible.

Worse yet are those that drive in the "passing lane." There is absolutely, positively no excuse for driving a continued distance in the passing lane. Ever.

Hop into the passing lane. Pass slower vehicles and get the heck back out.

The worst of all is when you get both someone driving in the passing lane AND another knucklehead in the adjacent lane staggered too closely to the vehicle in the passing lane so that no one can pass.

Finally, when no one can move by the two blocking cars, cars _end up_ having to brake as drivers weave in and out and jockey to try to get around the now massively bunched up cluster of cars, many of which are in incorrect lanes, exacerbating things further.

THIS, my friends, is what *causes* traffic jams!

If only people would realize the effect of their incorrect lane selection, traffic jams would all but evaporate.

Alas, I am not too hopeful of changing the driving habits of millions of people.
##### dsl5000
not rated yet Dec 22, 2007
Alas, driving test is subjective. They teach to signal, to look left and right, but some people only hear and not listen to follow through...hence why there is also a defensive driving course...haha...basically to sum it up, Believe in oneself to drive smart, follow rules and take precaution. Everyone else can be labeled "idiot" when driving, never assume! (e.g. someone flashing left blinker..assumed to go left no? some idiots turn right)
##### Mark3456
5 / 5 (1) Dec 22, 2007
The conclusion from this is that if you keep a better distance from the car ahead, then you won't have to break as hard and will lessen the traffic.

It's amazing that so many are criticising the study, but don't understand traffic themselves. Many are saying that the solution is to increase the distance to the car ahead. However, this will likely bring the traffic to a crawl on congested motorways. How do people not understand this?
##### kcasey415
1 / 5 (1) Dec 24, 2007
a sign on the back on my car states...."it's called cruise control STUPID, use it"....oh and mr. gore don't steal my idea to stop global warming because you are a scam artist but we could save gallons of fuel...someone please figure that savings out
##### hopper
1 / 5 (1) Dec 24, 2007
Someone needs to show the math of this to
people at the fed--and they need to farm this
math to mathematician/economist teams who
can build this into their models.
##### recurr
not rated yet Dec 25, 2007
Drive the speed limit. Don't speed.
##### RuskySoln
not rated yet Dec 27, 2007
The real moral is DONT DRIVE. Yeah, yeah, but, but. Well at least we wont be aware that our great grandchildren are spitting on our graves for using all the petroleum and leaving behind such a mess. All for convenience.
##### Trafflan
not rated yet Dec 27, 2007
Everyone has a theory on traffic because we spend a horrific amount of time in the car. After a while of trying to create a 'bumper stumper' out of the "unpersonalized plate" from the car in front of you, what else are you gonna do?

The short of the long, is "Give them Three, Save a Life" Save a lifetime of stop and go traffic and don't worry about the person dicing in front of you, worry about all the ones behind you as that little bit of space means more to them than it does to you.

If only Transportation Policy included Public Relations and Driver Training and Awareness.
##### Marquette
not rated yet Dec 28, 2007
We need a two-tiered license system - one for street driving, and one for the freeways. The freeway license would have more stringent standards, and require applicants to complete successful tests in a driving simulator. The simulation would not only test their ability to navigate traffic, but simulate their effects on following traffic. Those that pass would get an endorsement on their driver's license, and a special magnetic license for the back of their car with a hologram police could scan with a laser. Unauthorized drivers on the freeways would be stopped and towed, and the drivers fined. How many times have you seen some idiot stop on the on ramp, drive straight across the freeway to the passing lane, then drive 35 mph with the left blinker on? Those idiots need to be kept off the highways.
##### Ashibayai
not rated yet Dec 31, 2007
To those who say a larger following distance wouldn't help. Please consider the problem analogous to Phonon's only with the problem of limited acceleration/deceleration.

http://en.wikiped...i/Phonon

Also, it may take up more space on a freeway, but since the speed of the cars actually ON the freeway would be greatly increased it would probably more than offset the density of cars achieved in stop and go traffic.
##### nilbud
5 / 5 (1) Jan 10, 2008
Get a motorbike and drive everywhere at 100mph . You'll either get where you're going fast or die, either is preferable to being stuck in a cage in a jam.