How traffic jams are born

A couple of years ago, Cory posted a really interesting story about the mathematics behind seemingly cause-less traffic jams. It's pretty interesting. Shorter version: The researchers think jams like this are caused by one person braking, and the response to that slow down moves through dense traffic in a way that is mathematically very similar to the shock wave from an explosion. Once you have enough density of cars on a road, jams are inevitable.

Cory's post included a simulation, showing what the mathematics might look like in the real world. Basically, a computer algorithm figured out how drivers would behave if the mathematical theory were correct and turned that behavior into a little cartoon of cars moving around a track.

But here's the really cool thing. This effect has actually been demonstrated in meatspace. Yesterday, a friend sent me a video from 2008, showing real life drivers behaving in almost the exact same way as the simulation video from Cory's post. That's what you see posted above. Now, these are not exactly real-world conditions. A flat circular track may, or may not, be a good representative for what happens on the highway—I, for one, would be interested in seeing how on/off ramps, hills, and curves change the patterns. Also, the drivers in this case were other students and faculty from the Nakanihon Automotive College, and the study doesn't say whether they knew why they were driving in circles. Again, these details could affect the outcome.

I've not been able to find any studies that test this mathematical model by documenting real-world traffic flows. But if you've got links, I'd love to see them! The idea behind this theory certainly makes sense and it would be interesting to know whether it matches up with the reality you and I experience.

Video Link

Thanks, Andrew Balfour!


  1. And the fix remains the same: don’t tailgate or unnecessarily accelerate in a traffic jam.  Idle along at a constant speed so the people behind you don’t have to brake.   The guy in front of you may get more or less distant, and some other jerks may thoughtlessly change into your lane in front of you, but you’ll be doing the right thing for everyone behind you.

    1. I agree, but that’s only half the problem.  All cars can decelerate much more quickly than they can accelerate, which leads to that slinky-like effect in heavy traffic.  If one could eliminate unnecessary and excessive braking, that would help a lot.  This situation is worse at night when the driver has less visual information available to him.  All he has is the nearby brake lights, which are either on or off. 

      I think traffic, and safety, would greatly improve if we required our cars to display our deceleration rates to the cars behind us.  The easiest way I can imagine is to have the brake lights flicker at a rate proportional to the deceleration.  Slow flicker = gentle braking.  Solid light = maximum braking.  Easy fix, amirite?

  2. Dammit.  I hate that when I’m driving around in circles.  Can’t they install an extra lane or something?  Granted, I might be driving around in circles slower while construction is going on, but I’m sure the city will assure us that things will be far more efficient in the future.

  3. traffic jams are a classic example of emergent phenomena. there is a plenty of literature on the topic.

  4. This is also considered to be expected behavior by anyone who works on control systems with feedback. The time delay between the detection of the car in front’s brake lights and the application of your own will result in this behavior. It’s too bad that you can’t tune the loop parameters of a human driver the way you can a PID controller.

  5. > The researchers think jams like this are caused by one person braking

    Really? I doubt it.  It’s a common public misconception that the cause is “one person braking,” but I think that researchers actually know the real cause.

    The waves were found to be “emergent phenomena” which always appear under the right conditions. After all, if humans are removed from the system,  and all cars made identical, computer simulations still give the same results.

    The waves grow spontaneously, and at some point a car must brake to avoid collision. “One person braking” just means that the waves finally grew large enough, that taking your foot off the gas won’t prevent you from slamming into the back of the wave.

    How to solve the problem? Find the guy that hits the brakes? Nope, you’d find that NOT hitting the brakes would cause an accident. The cause is positive feedback, where system noise gets amplified into a huge oscillation. To prevent waves, just STOP FREAKIN TAILGATING. If there’s no room for someone to zip in ahead of you, then you’ve set yourself up as a wave-amplifier.

    1. But if there IS enough room for someone to zip in front of you, someone WILL and you’ll have to brake anyway, with the added aggravation of some f**k cutting in front of you. 

    2. In the case of this particular experiment there might be a simpler explanation:  a zero upper-bound. Since cars can’t go faster than 30 MPH by the rule, but can always go slower (and often must), the average speed of the circular system must get dragged down.
      A computer-driven car could stay very close to a constant 30 MPH, which would reduce (though not eliminate) this inevitable reduction.

      note: above idea not edited for wrongness.

      1. A computer-driven car could stay very close to a constant 30 MPH

        Does the speedometer even go that low?

      2. What you are saying is roughly that, if everyone drove at exactly 30mph, then whatever spacing pattern the cars started with would simply rotate around the circle. While that’s true, it misses the point. The important feature that you are missing is that the drivers can see the distance to the car ahead of them and will slow down in order avoid hitting it. 

      1. I read an opinion piece decades ago where the author referred to pokey drivers as the Anti-Destination League.

  6. It reminds me of high speed ski lifts where the chairs derail from the main cable. They slow down and bunch up for boarding, but then they speed up and spread out after the skiers have gotten on board.

  7. I know of at least 2 “tests” of this behavior in the (german) TV.  One  I trust, the other… don’t know. Entertainment TV. Unfortunately the first one seems to be depublicised and the second don’t store.

    1. This method is exactly being used by CDOT (Colorado DOT) to regulate traffic flow on I-70 through the mountains, during extremely busy ski season times.

      A patrol car puts its lights on, and enters the interstate, letting a large block of stopped cars on with it. It maintains a constant pace down the mountain, and everyone follows it’s lead, no passing allowed. In the end, releasing cars in these “pulses” gets everyone down the mountain faster.

  8. My dad subscribed to motorcycle magazines, and I guess it would’ve been around 1967 that I remember reading an article that mentioned a bunch of motorcyclists traveling together on the highway and observing the “banjo-string effect,” which I understood to mean an inevitable bunching and unbunching that traveled along the line of riders like a wave (and I don’t know why it was called “banjo-string,” unless maybe that had something to do with the way vibration occurs on a string). Isn’t the shockwave phenomenon described in the post the same thing? In which case, bikers were sufficiently aware of it 45 years ago that they were already blase about it.

  9. I first read about this in a book about catastrophe theory called “Ubiquity”, by Mark Buchanan. However I don’t have it with me right now to check the references.

  10. A lot of people smack the brakes at the first sign of an impending slowness in front of them. This is considered a staple of defensive driving, it seems; but it shouldn’t, because relative to what’s behind you, it’s rather offensive — inspiring a chain of defensive-offensive reactions.

    I brake as little as absolutely necessary. Let up on the gas to slow down, change lanes to avoid slowness if you can, and brake when you determine that it’s not going away and you can’t avoid it.

    I also avoid stop-and-go, though this is not always productive. Instead of gas, then brake, then gas, then brake, instead let up on the brake and coast to the car in front, then brake. More braking leads to more jam behind you. (It’s also not great for your engine or MPG.) The only problem with this is that if the “go” of the stop and go is long enough, people will inevitably sneak into the space. And oddly, drivers behind you seem to dislike this, because you’re not going fast enough, regardless of the fact that accelerating, then stopping short, is not going to get you anywhere any faster.

      1. I got the same instructions. We even had a film that told us the benefits would be not just to traffic, but to our cars, as the brakes would last longer.

        As a result, I don’t typically spend a lot of time braking unnecessarily. Coasting into slowing traffic may be good for your car, but when a full slow down is coming, a quick, light tap of the brakes lets the people behind you know to watch out for it. Some drivers completely forget to do this! It can be really dangerous to not give any warning to other drivers that they should watch out for a change in speed. I’ve seen accidents happen just that way.

  11. I think the big thing here isn’t the realization that this phenomenon exists – as people mention it has been known about intuitively for a long time, but the newer ways of mathematically describing the phenomenon in a way that can be modeled. It is easy to talk about and intuitively consider, but harder to describe quantitatively and build models around.

  12. Traffic jams appear to behave like non Newtonian fluids. When there is no stress, i.e. someone braking for any reason, or if there’s an accident, traffic behaves like water. Add a stress, and the flow begins to solidify. You can easily replicate this phenomenon with some corn starch and water. At the right ration of starch to water, the mixture solidifies in one’s grasp, then liquifies and flows when released. Any comments?

  13. Some of the people you think are just driving like asses, well, they are driving like asses, but are doing so because they see this math real time. 

    Not that its an excuse, but it is a talent. 

  14. I saw this talked about on a old PBS series Scientific American Frontiers with Alan Alda.  They had part of one episode called “Why Does Traffic Jam?” and they talked about this phenomenon.  Found a video link to it…

    You have to launch a seperate window and it only works in Windows or Real Media, but advance the video to about 55 seconds for the computer simulation and discussion of the wave.   Great segment.

  15. I’m a traveling technician and spend a lot of time driving. Early on, I realized that cruise control was simply the best way to drive on the interstate. It also made me realize that most other drivers can not or will not maintain a constant rate of speed. Since then, I’ve spent a lot of time ruminating over this subject and find it endlessly fascinating.

    Personally, I like the concept presented in the film Minority Report – specifically that a driver should give up a large amount of autonomy to networked computer control once entering a freeway-like environment.  Most traffic/congestion comes from variations in rate of travel among many vehicles and the inability of drivers to make accurate decisions based on a macroscopic view of their surroundings (i.e. seeing if traffic is stopped five miles down the road). If vehicles on the interstate system could be controlled more like a network we’d all likely use less energy, cause fewer accidents, and spend less time in traffic.

    Of course this would require a massive dedication to updating the existing infrastructure and a universal desire to give up autonomy for efficiency – both of which are nearly heretical in today’s America.

    1. I’m with you on all counts, sir.  I drive a truck for a living (although a local route rather than over the road), and have done a decent amount of driving trips longer than a couple thousand miles, and I agree how much people tend to suck at interstate driving.

      Mostly though I like the idea of less autonomous, more efficient transpa to get our sorry asses to work and back (or walking/bicycling).  That way we can have enough dino juice left to run our fewer remaining cars for fun on occasion.   And I guess breathable air would be a benefit too.

  16. I used to work in the Black Tower at Universal City, with an eye-in-the-sky view of the 101 Freeway through the Cahuenga Pass. I would constantly see what I called the Slinky Effect: a car slows down, the cars behind it slow down, and there’s a thickening of slowed traffic that you can actually see travelling back from the original braking car.

    Meanwhile the initially slowed cars have resumed freeway speed, so that cars in front of and behind the thickening are much more widely spaced, making the traveling Slinky thickening all the more pronounced. It was fascinating to watch.

    1. I first noticed the slinky effect at a Boy Scout National Jamboree in 1977. On several occasions they had all 30,000  Scouts marching to a central amphitheater for a program or entertainment (I got to see Burl Ives LIVE!). One entrance path, the one my troop used, went up hill and made a slow curve so that the whole route was visible from the bottom of the hill. You could see the waves of movement pulse down the hill as troops moved. I can’t precisely remember, but I recall that there was usually three to four nodes moving at a time in a queue that was abound 1/2 to 3/4 of a mile long, containing several thousand Scouts. Everyone else was standing still.

  17. The case can be made for red light cameras directly influencing the behavior of drivers — the change in driver speed whether speeding up or slowing down in anticipation of a light change certainly influences driver decision.  Add merging traffic to the equation and you can already predict the mess such calculations make.  If the goal is to make traffic patterns more efficient, safe and to conserve consumer energy, red light cameras may not be as beneficial as traffic safety might have us believe.

  18. There is a 2 second rule that would help, but I don’t think there are many people that understand it let alone be able to practice it.
    (The latest thing that drives me nuts are the people that come up behind you when you’re in the middle lane and have to pass you on the right, like hey I’m not speeding, I’m in the slow lane)

    1. The left lanes are for passing (in my state that’s codified in vehicular code).  If you aren’t passing, but are being passed by cars on your right, you are in the wrong lane.  

  19. Old hat … this is why marching troops move about on commands, so all hands and feet start, stop and turn together. Watch any parade and you will see the exact same slinky effect when the leads in a group change stride length for whatever reason.

  20. Be interesting to see a repeat with superhuman reflexes (ie, robocars).  I’d assume a robo carousel.

    a repeat with a mixed driver cohort.  Can one lone human screw up a robo carousel?  Would a minority of humans do it?  Half-and-half?  Or could a mere salting of robocars nudge the density of condensation up so the jams happen less?

    1. I live in a resort that fills up with Minnesotans and Manitobans every winter. Here it’s: “Slow down, Floyd! There’s a palm tree!”

        1. One of the comic (by which I mean tragic) aspects of driving in the desert is that, when it rains or even drizzles, people slow down to one mile per hour because it’s so rare that they’ve forgotten how moisture might affect the road.

  21. I remember noticing this effect about 20 years ago in, of all things, a shot of moving traffic in “Koyaanisqatsi”.  It wasn’t one of that film’s many time-lapse shots, but rather a normal-motion shot in which the camera gradually tilts upward to reveal a long line of cars on a freeway.  Quite by accident, the shot happens to capture a slinky-effect shock-wave traveling slowly up the line of traffic.  I remember noticing the wave and saying, “Of course!  That would have to be how a traffic slow-down works!”  So for the last 20 years — as others have indicated here in their posts — I have kept a generous distance between me and the car in front of me, while maintaining as near a constant speed as I can.  (It takes some restraint, since you have to decouple your own car speed from that of the one in front of you, and resist the urge to close the gap when it starts receding from you.)

  22.  It’s really interesting that even though the science is explicitly and accurately summed up with “Once you have enough density of cars on a road, jams are inevitable,” some of us here still comment as though blame can be assigned to someone, somewhere. To some class of habit, to some style of behavior, to some demographic of drivers, etc.

    But there’s no mystery here. If you’re in a traffic jam, it’s your fault; you are part of the density that made the jam happen. You knew it was a possibility when you got behind the wheel; be an adult and stop blaming other people for your stupid first-world problems. Jesus.

  23. Way back in the late 1980s I took a civil engineering survey course to fulfill a required out-of-major elective.

    One third of the class was about traffic flow & controls, and I remember this effect being covered pretty well even back then.

    They even used the term “shock waves” to describe the compression of cars traveling away from where it began.

    More modern reference, but look though the references, many dating from the 1980s and before.  

    I imagine a lot of topics are like this.  Casual web browsers operating outside of their areas of specialization think something is new, while specialists in the topic are so far removed from the conversation that they don’t bother to engage in a dialog.

    (Ah, the benefits of a classical [engineering] education.)

  24. Growing up in L.A. I used to listen to “The Car Show” on the local Pacifica radio station.  For a while, the hosts would close the show by saying “don’t lift” (makes sense if you do any high performance driving, relates to weight transfer) and “look down the road”.

    I think drivers’ failure to “look down the road” contributes to these traffic waves.

    No one obeys the tw0-second rule (supposed to be 3 or 4 seconds if road/traffic conditions are bad), and nobody is aware of anything that happens more than three car lengths ahead of them..  Hence multicar pileups in rain/fog/smoke.  Maybe one driver in 20 uses cruise control on the open road.

    Won’t be fixed until human nature is fixed.

  25. Emergent traffic jams are a kind of hidden ecology that most of us recognize, tolerate or not. But from my experience drivers of the same sections of road or highway are as attuned to the ecology of traffic as any good hunter is to the signs of game in the woods. Is it past 3:15? Watch for that exit ramp and merge lane combo. Is it late after a ball game? (Or hockey in my neck of the woods) then expect a number of high speed mergers coming off the on ramp. We complain secondarily to witnessing and experiencing.

  26. In astronomy, we call this a density wave and it is what makes the lovely swirly characteristic of spiral galaxies.

    1. Unfortunately, the car companies bought the government planners six decades ago and people now live fifty miles from where they work. So unless you have an extremely powerful magic wand, it’s not that simple.

  27. Also a phenomenon to be seen on London Underground escalators.

    People walk up on the left, but then often stop just before stepping off. With enough people behind, a jam spreads back down the escalator.

    Leave a gap in front of you as you walk– be a jam-buster.

  28. I want to know why, every day,  while driving at the posted speed with cruise control when there is over 100 yards in front and behind me that a car in the on ramp will inevitably appear directly beside me with the driver glaring at me to move out of his way.

  29. I once sat in a traffic jam in a 3 lane motorway that wasn’t/barely moving for 2 hrs.


    They closed 2 lanes to install some cat eyes in the middle of the lane, and people who were about to clear the narrow bit were driving slow so they can see what’s going on.

    And I see this almost every time, whenever someone sits in a traffic jam for ages that’s caused by narrowing of the road, their reaction is to drive away slowly once they reach the end of narrow bit, keeping everyone else in there at the same slow pace they are, instead of putting their foot down. In other words (and I’m sorry for swearing): “Fuck everyone else, I’m out of it”.

    Typical lowlife selfish behaviour.

    A very similar thing happens is when someone is waiting in a long queue, and once it’s their turn, they decide to rest their weary balls on the counter and tell the counter clerk their life story.  Anyone who acts that way is scum according to me, and a lesser life form.

    Sorry for being so harsh, but such behaviour pisses me off so much.

    “If it doesn’t affect me, why should I care.”

  30. The solution to all our problems is self-driving cars like Google is working on. We should be dumping tons of money into that research. It will revolutionize transportation.

  31. 1. It is possible to drive very long distances without braking at all.  (long distance is relative, I’m in the UK…but have made it from Lincolnshire to Devon only braking when I need to come to a complete stop.  Made it all the way from Birmingham to Plymouth without braking at all!)

    2. Tailgating seems to cause a lot of the problems on motorways.  I’ve seen cars that are determined to get in front of the next 10 cars by sitting on their ass, constantly braking and accelerating.  If folks calmed down a little then maybe there would be less jams.

    3. Perhaps it’s time to start teaching people to drive in packs rather than waves.  You know what I mean.  When waiting at a stop light, each car waits for the one in front to move off, leaving 3-4 seconds between each car starting to move.  This long-existing wave method only gets a few cars through the intersection at a time.  If each driver was part of a pack and they all moved off at the same time much more traffic could get through (like the ski season methods mentioned above).  For this to work properly some kind of automation would need to come into play at intersections with lights I guess…

  32. Long ago, 1985, I was interviewing with the NY DEP at Stonybrook, LI, and over lunch we talked about this exact same phenomena, where beyond a certain speed (30MPH) the elasticity of the vehicles (yeah, they aren’t very elastic, but you get my drift) creates a wave front. I first saw an example of this in Toronto as a kid – an explanation of sound waves that involved a Slinky. Holds true with cars (didn’t get the job – too young). (extra credit: go to the kitchen sink, turn on the water, and observe. Same thing.

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