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Do the math: Traffic jams a shockwave
Sarah Butzen has seen the math: bottlenecks are a shockwave, driving faster will slow you down and ants are better drivers.
Posted April 09, 2012
It was on I-85 South, just an hour or so north of Durham, North Carolina, when the traffic began to slow. It slowed. And slowed. Soon all the cars were crawling along in the July evening heat, every now and then leaping forward madly when an open car's length gave false hope, only to lurch sloppily to a halt. When it began to break up after about thirty minutes, you could sense the excitement: what would we see? Smoking wrecks, at the very least. Perhaps body parts, if we were lucky. Aha! It's a Prius ... pulled well off the road ... and apparently in fine condition? And in the field at the side of the road was its presumed owner, a young man, also in fine condition, not bleeding to death. Picking flowers.

Let's set aside, for now, the question of how this guy escaped from the plot of Never Been Pollinated or whatever romantic comedy spawned him. How did he make all of us slow down - not for the few seconds it takes to register "Guy picking flowers. Huh." and speed away, but for half an hour? Yes, he did look good in his Dockers. But not that good.

Believe it or not, there's a mathematical formula that explains this very phenomenon. Now, this is a bit technical, so follow closely: Where A equals the number of cars and B equals the average speed and β equals the number of times the Dockers guy works out every week... you know what? Let's go with the non-technical version: Traffic jams are your own dumb fault.

That, at least, is the finding of a team of Japanese scientists who have demonstrated with a real-life experiment how "shockwave" traffic jams form - that's the name for the kind that are the most frustrating because they seem to come out of nowhere, or require very little trigger. They're called that because the mathematical theory, which has been around for more than 15 years, suggests that the smallest fluctuation in a steady flow of traffic, when the traffic is at or near maximum density, will ripple backwards at the rate of 20 km/h, until it has created a large cluster of slowed or stopped traffic. So slowing just a bit on a crowded road because of a slight uphill grade, pretty flashing lights on the shoulder, or a unicorn grazing in the median strip, will eventually bring everything to a soul-crushing standstill.

You can see how this works in a YouTube clip of their experiment, which involved 22 cars on a single-lane loop told to drive at a steady pace of 30 km/h. Watching the cars imperceptibly begin to slow, then cluster until they're actually stopped, is mesmerizing - though not as much as the computer simulation you can find here, which is a great way to lose an afternoon. (Try turning the politeness down to zero, velocity to maximum, giving them an uphill grade and a lane closure, and then clicking "Add Perturbation!" You can practically see the little colored rectangles giving each other the finger.)

One interesting implication of this theory is that when traffic is at equilibrium speed and distance between cars, on a road that's at maximum density, a car that's attempting to go faster than the others can trigger a shockwave traffic jam just as easily as one that slows down a bit. You can see this in the science and intuitively, if you think about it. The scientific explanation is that the concept of density (generally defined as the number of vehicles per unit area of the roadway) is not quite adequate to the task of expressing how crowded a road is. It leaves out two things: the size of the vehicles on the road, and how fast they're traveling. It's obvious why size matters (in this situation, at least): bigger cars are taking up more space. But why should speed matter?

It matters because the flow of traffic is a function not only of space but of time. A vehicle that's traveling faster requires more space in a given unit of time than a slower one does. Most people acknowledge this fact in their driving, consciously or unconsciously, by leaving more room in front when they're driving faster, because they know they'll require more stopping time. (Incidentally, this is one reason that motorcycles are so vulnerable to deadly accidents in high-speed traffic; auto drivers are used to thinking of stopping time as being the same for all the vehicles on the road, and forget that a motorcycle can stop much more quickly than a car can.)

So: Slow down a little bit, and you'll cause a shockwave traffic jam, a bottleneck without the bottle, so to speak. Speed up, and you'll cause a shockwave traffic jam. Merge even just a little bit stupid, and you'll... you get the drift. Is there anything we can do about this?

As a matter of fact, there are several viable ideas on the table. The U.S. Federal Highway Administration, for one, has put together a guide to avoiding bottlenecks, and it contains many quite sensible and safety-promoting driving tips, such as "Relax. Allow motorists to merge at-speed or fill gaps as opportunity allows" and "Remain orderly and fair. Do not line jump." The only problem with these is BWAHAHAHAHAHAHA. Yeah, we're not doing that. FHWA actually cheerfully acknowledges that "human nature simply won't allow for the patience and orderliness to make this work." What else you got?

We could learn from ants. Apparently they never get stuck in traffic, and yes, they have traffic - haven't you seen those long lines coming out of your sugar bowl? Seriously, scientists have been studying how ants manage the lines coming in with delicious chunks of poisony goodness from those traps you laid out, and the lines going out to look for more. Even in very confined spaces, the ones going out always give the right-of-way to the ones coming in with food. Of the ones coming in, some have lighter loads and could move faster - but they just slow down behind the ones with the bigger loads. All in the service of feeding the colony.

Hey! No way! We're not some kind of giant hive-minded collective! We're individuals, okay? We will not - oh hey, is that some super-cool self-driving technology that talks to other cars, removes our individual penchants for narcissistic disruption and lets traffic flow smoothly and serenely? And we could watch TV while we're driving? All right, we're listening. Resistance is futile, anyway.

Sadly, free-flowing self-drivers are still a good ways in the future. But you can see why technology is needed to solve the universal shockwave issue. We're just not that collective. Still, until then, when traffic gets to be too much for you, you can always just stop and pick some flowers.
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Newsroom Notes
Do the math: Traffic jams a shockwave

File Under:
Driving, Research / Study, Automotive, New Journal of Physics
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