## December 21, 2007

### A matter of Prior Art - traffic waves

Headline News from Exeter University:
Exeter mathematician solves traffic jam mystery
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 10–15 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’s School of Engineering, Computing and Mathematics, 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' staff website is here, personal website here. Related article in Science Daily. One slight problem... Nine years ago, Bill Beaty, Seattle scientist and Geek Extraordinaire published this article on his website analyzing the problem of traffic waves, showing the reason for their formation and showing an incredibly simple cure for them:
TRAFFIC WAVES
SOMETIMES ONE DRIVER CAN VASTLY IMPROVE TRAFFIC.

I live in Seattle and my two daily commutes last about 45 minutes. (That's when I'm lucky; sometimes it's more like two hours each.) This has given me an immense amount of time for watching the interesting patterns in the cars. Boredom led me to fantasize about the traffic being like a flowing liquid, with cars acting as giant water molecules. Over many months I slowly realized that this was not just a fantasy. Why had I never noticed all the "traffic fluid dynamics" out there? Once my brain became sensitized to it, I started seeing quite a variety of interesting things occurring. Eventually I started using my car to poke at the flowing traffic. Observation eventually leads to experimentation, no? There are amazing things you can do as an "amateur traffic dynamicist." You can drive like an "anti-rubbernecker" and erase slowdowns created by other drivers. But first, some basic phenomena.
A bit more directly addressing the spontaneous formation of these waves.
NOT CAUSED BY ACCIDENTS
These sorts of travelling waves are common during heavy traffic conditions. An accident isn't needed to create them, sometimes they are caused by near-misses, by people cutting each other off, by merging lanes at a construction site, or simply by extra cars entering from an on-ramp. In traffic engineering lingo, they can be caused by "incidents" on the highway. A single "rubbernecker" could cause one by momentarily stopping to look at something interesting. Whenever you slow way down in order to merge across a lane to get to your upcoming exit, YOU could create one.

Sometimes the traffic waves have have no real cause at all. They appear because tiny random motions can trigger large results. They are like sand ripples and sand dunes, and they just build up for no clear reason. They are like ocean waves caused by the steady breeze, or like the waves which move along a flapping flag. They just "emerge" spontaneously from the writheing lines of traffic. In the science of Nonlinear Dynamics this is called an EMERGENT PHENOMENON."
This is rather odd as a Google Search for traffic wave (singular) turns up over 700,000 hits and Bill's site is number three and number four on the ranking. A search for traffic waves (plural) turns up over 170,000 hits and Bill's is number one and two on the ranking with additional links to his site starting around number ten. Surely a little research could have turned up this perfect example of Prior Art. Posted by DaveH at December 21, 2007 7:13 PM | TrackBack