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Math Transportation Science

Mathematicians Solve the Mystery of Traffic Jams 629

mlimber writes "Do you ever find yourself in a traffic jam, thinking, 'Man, there must be a bad accident up ahead,' but as you plod along you see no evidence of any crash? Some mathematicians have solved the mystery by developing a mathematical model that shows how one driver hitting the brakes a little too hard can cascade into a backup miles behind. The mathematicians' future research will investigate how automatic braking systems may alleviate the problem."
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Mathematicians Solve the Mystery of Traffic Jams

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  • Although apparently the mathematicians are way behind Ethan Hunt.
    • Re:Cover Job (Score:5, Informative)

      by jargon82 ( 996613 ) on Friday December 21, 2007 @02:27PM (#21782032)
      They are also behind LAST years mathematicians. Although by a bit shy of a year. []
      • Re: (Score:3, Informative)

        by Shag ( 3737 )
        And they're two and a half years behind Philip Ball's "Critical Mass" which won the Aventis Prize for science books [] that year. Of course, CM dealt with a lot more than traffic jams - but they were in there. (In fact, from the new story's summary, it sounds like the researchers may have read it.)
  • Old news (Score:5, Informative)

    by Hatta ( 162192 ) on Friday December 21, 2007 @01:18PM (#21780860) Journal
    This has been known [] for years.
    • by Henriok ( 6762 )
      Yeah! I was about th write the same. We saw movies on this in high school (when we learned about wave forms) and I've actually have done some calculations on these types of problems myself when I got to the University.
    • Re:Old news (Score:5, Interesting)

      by Billosaur ( 927319 ) * <wgrother@oEINSTE ... minus physicist> on Friday December 21, 2007 @01:22PM (#21780928) Journal

      I was about to write the very same... I remember several studies of traffic that showed that it only takes one driver to slow down traffic, especially on roads that are above their actual capacity. It is kind of like the Slinky effect, where you send a pulse down it and it rebounds. Car stops ahead and the cars behind begin breaking, and this begins a chain reaction... I'd love to catch this in the act at night and film the tail-lights lighting up in sequence.

      • Re:Old news (Score:5, Informative)

        by orclevegam ( 940336 ) on Friday December 21, 2007 @01:28PM (#21781014) Journal

        It is kind of like the Slinky effect, where you send a pulse down it and it rebounds. Car stops ahead and the cars behind begin breaking, and this begins a chain reaction... I'd love to catch this in the act at night and film the tail-lights lighting up in sequence.
        The term you're looking for is standing wave. The problem isn't actually the breaking, it's everyone not giving enough room between themselves and the person ahead of them to absorb small slowdowns. The time between when you slow down and accelerate back up to speed needs to be factored in. If the people coming into the jam are entering faster than people can accelerate out of the jam, it will either remain static or become worse.
        • Re:Old news (Score:5, Interesting)

          by cyphercell ( 843398 ) on Friday December 21, 2007 @01:36PM (#21781144) Homepage Journal
          sounds good to me, the solution I've always driven for (no pun intended), is to slow down at traffic jams to the point where you can plod along without actually stopping. This does a good job of equalizing the in/out ratio. I wonder why this isn't taught in driver's ed.
          • Re:Old news (Score:5, Informative)

            by bcattwoo ( 737354 ) on Friday December 21, 2007 @01:57PM (#21781496)

            I wonder why this isn't taught in driver's ed.
            Meh. I imagine they also teach you to use your signal, not speed, not tailgate, not run red lights, not drink and drive, stop at stop signs, and a million other rules and good driving practices that people ignore.
            • Re:Old news (Score:4, Insightful)

              by Achromatic1978 ( 916097 ) <robert@c[ ] ['hro' in gap]> on Friday December 21, 2007 @03:54PM (#21783282)
              As a recent arrival in America from Australia, I find myself amazed by how seldom people use their turn signals. Almost never. Annoys the hell out of me, and my other pet peeve: when I signal that I'm going to overtake a slow vehicle. Turn signal on, wait for lane beside me to clear, only to have some fucking clown decide he wants to get past both of us and shoot right out from behind me, no signal, nearly rear ending me in the process, and then has the audacity to blow his horn at me. Gah.
          • Re:Old news (Score:5, Insightful)

            by Hatta ( 162192 ) on Friday December 21, 2007 @03:17PM (#21782758) Journal
            Because people aren't smart enough to do that. You see the same people who will do 40mph up to a red light just to sit there. I on the other hand try to guess when the light is going to change and just brake a little, so that I hit the intersection just when it turns green and still have some momentum left saving myself some fuel and time. People just don't think about what they're doing, and if you explain it to them they don't listen.
        • Re:Old news (Score:5, Insightful)

          by Spy der Mann ( 805235 ) <spydermann.slashdot@ g m> on Friday December 21, 2007 @01:54PM (#21781432) Homepage Journal

          The problem isn't actually the breaking, it's everyone not giving enough room between themselves and the person ahead of them to absorb small slowdowns.

          Yeah, but when you start giving enough room between you and the car ahead, an idiot besides you speeds up and steals your place :-/

          Conclusion: Traffic jams are caused by idiots.
          • Re:Old news (Score:5, Insightful)

            by Scrameustache ( 459504 ) on Friday December 21, 2007 @02:42PM (#21782314) Homepage Journal

            The problem isn't actually the breaking, it's everyone not giving enough room between themselves and the person ahead of them to absorb small slowdowns.

            Yeah, but when you start giving enough room between you and the car ahead, an idiot besides you speeds up and steals your place :-/

            Conclusion: Traffic jams are caused by idiots.
            Well of course, that's because it's a race, they HAVE to be in front of you, they HAVE to get to the next red light before you.
          • Re: (Score:3, Insightful)

            by value_added ( 719364 )
            Yeah, but when you start giving enough room between you and the car ahead, an idiot besides you speeds up and steals your place :-/

            True. That rudeness is endemic and remains as painful today as it did in days gone by is also true. The alternative to not maintaining a safe distance to prevent others from merging into their own unsafe distance is ... wait for it ... driving too close. Sounds more like a comedy of errors than a strategy, doesn't it?

            What should offer you satisfaction is that you're adopting
          • Re:Old news (Score:5, Insightful)

            by CodeBuster ( 516420 ) on Friday December 21, 2007 @03:13PM (#21782708)
            Is it idiotic to do what is best of your own self interest? The answer is more complicated than you might think, it depends upon what your adversaries do. This situation sounds very similar to the prisoners dilemma [] or indeed any other situation where individuals acting in their own self interest collectively reach a worse result (for each of them individually) than would otherwise have occurred if they cooperated instead of taking the greedy approach (i.e the Tragedy of the Commons []).
          • Re: (Score:3, Insightful)

            by Hatta ( 162192 )
            So? Let them have it, and then give them enough space so that you won't have to brake. You'll *STILL* get through there faster than if you rode the ass of the guy in front of you and caused a traffic jam.
        • two comments... (Score:5, Insightful)

          by Quadraginta ( 902985 ) on Friday December 21, 2007 @03:43PM (#21783116)
          Courtesy of a course I audited at MIT on discrete mathematics, about 20 years ago, which included a fascinating section on the mathematics of traffic...

          (1) They're not really standing waves, which are composed of traveling waves going both forward and backward (and waves can't propagate forward in traffic). They're ordinary traveling waves. The best analogy is to the flow of a compressible gas in a pipe. You can easily get strong shock waves at various densities and flow rates when you introduce obstructions or change the flow rate at various branch points.

          Part of the problem in our expectations is that we (unreasonably) expect traffic flow to be more like the flow of an incompressible fluid like water, where, generally speaking, more pressure simply equals faster flow. It's the presence of compressibility that makes gas flow in certain critical regions much more complicated than water flow, so that, for example, an increase in pressure (e.g. an increase in cars entering at a given on-ramp, or a constriction due to an accident) can result in drastic decreases in flow. The compressibility comes about in traffic because the density of cars is quite variable.

          (2) Along those lines, the density per se -- the space between the cars -- really has very little to do with the peculiarities of traffic. It's the fact that the density can change locally which makes the "car gas" compressible, and allows for density waves (traffic jams, stop-n-go traffic, etc.).

          But the reason the density changes locally is not because people don't leave enough space between their car and the car ahead, but because of human reaction time. If the car spacing (i.e. density) changes here at time t, human reaction time means it cannot propagate very fast -- it will change there at some time t' significantly later than t. That is, a density wave must propagate. Under the right conditions, it's quite easy for such a density wave to grow in amplitude as it goes. Hence, a very small initial perturbation in the density -- one driver slamming on the brakes -- can grow much larger as it propagates, so that at some distance away large numbers of cars must come to a halt.

          The only real solution is to make the car "gas" much less compressible, and that requires greatly raising the speed at which density fluctuations can propagate, in other words, tremendously shortening the time it takes for cars to respond to slight changes in spacing. Presumably, that suggests computer control of cars.
          • Re: (Score:3, Interesting)

            by orclevegam ( 940336 )
            As to point 2, wouldn't allowing more space allow for the compression wave to be dissipated as each successive car has to brake over a longer distance and then at some time t + x there will essentially be no compression wave left? That is, with each successive car they don't need to break nearly as hard, and they can accelerate back up to speed once the person ahead of them also accelerates up to speed. I do agree however that the optimal solution is computer control, but until we reach that point it seems
    • Re: (Score:2, Informative)

      by Gregb05 ( 754217 )
      I actually remember reading this from a series of books called Imponderables [], years ago.
    • Re:Old news (Score:5, Interesting)

      by dyefade ( 735994 ) on Friday December 21, 2007 @01:26PM (#21780994) Homepage Journal
      UK motorways are proactive with this in that they adjust the speed limit when the volume of traffic is higher. I remember seeing basically TFA printed a few years ago explaining all this.
      • Hmm...That might actually work, except for one thing: People routinely ignore speed limits. Maybe they don't in the UK? And they don't in Mississippi. I drove through that state once, and nobody was going faster that 65 MPH. I saw one guy get pulled over. Must have been doing 65.1, because he wasn't passing other traffic.
        • Re: (Score:3, Informative)

          by jonbryce ( 703250 )
          On the M25 and M42, two of the busiest roads in the country, the variable speed signs have revenue cameras attached to them, so anyone who disobeys them gets fined.
      • Or they can teach the 3 second rule (Six seconds in bad weather) Where if you drive behind an other car you stay 3 seconds aways from them. So you see the Car past a post you go 1 one thousand, 2 one thousand, 3 one thousand then you should past the same pole. I am not supprised that it is not know in UK Europe because it is rairly used in America. But it is a good rule because it gives you pleanty of time if the car does a sudden stop To evaluate the situation see if there are other cars in the other lan
      • Re: (Score:3, Insightful)

        by Andy_R ( 114137 )
        Very few of our motorways are actually equipped with this system, as far as I know it's only the middle of the M42 near Birminham and the Western 1/3 of the M25 London ringroad. As I have to drive on both of these occasionally, I am all too aware that while the idea might be sound, the implementation is hopeless. The M25 system is very basic, and unless you go there in the dead of night, you'll have to fight through exactly the sort of standing wave that this system is supposed to get rid of, caused by cars
    • Indeed. Even looking at Orosz's website [], his most recent publication regarding traffic that appeared in Proc. Royal Soc. London was in 2006. Sounds like this work is old, even for him.


    • The article you linked is simply a hypothesis, not backed up by any actual evidence other than conjecture. The article in the story actually tests this hypothesis. Nothing was "known" until now.
    • Watch the movie (Score:3, Informative)

      This was shown in a time-lapse sequence in a movie called Koyaniskatsi (or some spelling similar to that)
      Produced about 20 or 30 years ago.

      Cool movie.

      If anyone can find it or confirm the proper spelling, I'd appreciate an update.

    • Re: (Score:3, Insightful)

      by Machtyn ( 759119 )
      Yes, I thought for any engineer, student of fluid dynamics, this was a known. Isn't this part of bernoulli's equations?

      I usually try to buffer the stoppage effect for people behind me by slowing sufficiently ahead so as to not stop or remain slightly faster than the person in front of me, so that when they speed up, I don't use as much force and energy getting back up to speed and that section of the wave will move slightly faster than it currently was.
  • by TJ_Phazerhacki ( 520002 ) on Friday December 21, 2007 @01:18PM (#21780864) Journal
    Sure. But what they forgot to include was the variable of EVERYONE IN THE OTHER LANE STOPPING TO WATCH.
  • Einstein (Score:4, Funny)

    by imstanny ( 722685 ) on Friday December 21, 2007 @01:19PM (#21780866)
    "Two things are infinite: the universe and human stupidity" - Einstein

    ...and he was only sure about the latter.

    • Re:Einstein (Score:5, Insightful)

      by MyLongNickName ( 822545 ) on Friday December 21, 2007 @01:28PM (#21781026) Journal
      Not necessarily stupidity. if I can see past the driver in front of me, I can make a better decision. I can see that he is simply adjusting speed to allow for a more reasonable space between him and the car in front. If I am stuck behind an SUV in my car, then I am not sure if his tap on the brake is about to turn into a full fledged stomp of the brakes, and I have to adjust, and possible harder that I need to. This becomes a cascading event.
      • Re:Einstein (Score:5, Insightful)

        by PitaBred ( 632671 ) <> on Friday December 21, 2007 @02:17PM (#21781858) Homepage
        Apparently, a lot of people think that their vehicles only have "stop" and "go" modes, without multiple different levels of coasting and slowing down without the brakes for those minor adjustments. I'll take my car out of overdrive quite often to adjust just a bit, rather than hitting the brakes needlessly. That way when I hit my brakes, I actually mean it. Brake lights = slowing down non-trivially. I wish more people did that.
        • by GPS Pilot ( 3683 ) on Friday December 21, 2007 @03:48PM (#21783212)
          Part of the problem is that brake lights themselves only have "on" and "off" modes. They could be designed to convey so much more information than that, by utilizing the entire spectrum ranging from:

          Brake lights glowing dimly: indicates the car is decelerating slightly. (And not necessarily due to active braking by the driver. Perhaps the driver has merely begun to coast, or does not have the accelerator sufficiently depressed while driving up a steep hill. It would be a good idea to communicate these scenarios to other drivers too.)

          Very bright accompanied by a rapidly flashing strobe: indicates the car is braking maximally; antilock braking system is fully engaged. (At times like this, the car should do everything possible to get the attention of other drivers.)
          • Re: (Score:3, Interesting)

            by neapolitan ( 1100101 )
            >Part of the problem is that brake lights themselves only have "on" and "off" modes. They could be designed to convey so
            >much more information than that...

            Very good idea. BMW (and Mercedes IIRC) have exactly this technology if you own one or have driven behind one. They call it "Adaptive brake lights" (Mercedes has its own trade name.) Google it for more info.

            Basically with light braking one red bar lights up, and with hard braking there is two red bars with a white bar too. It is easily noticeabl
  • Traffic Waves (Score:4, Informative)

    by Phroggy ( 441 ) <.moc.yggorhp. .ta. .3todhsals.> on Friday December 21, 2007 @01:19PM (#21780870) Homepage
    Does this mean now there's math to support this []?
  • 20 fucking years ago.
  • Not suprised (Score:4, Insightful)

    by plague3106 ( 71849 ) on Friday December 21, 2007 @01:21PM (#21780896)
    I've often seen this. People slow down too much for no reason, especally near ramps. I've actually gotten pretty good and figuring which jams are accident related and those that are just people being retarded.

    It doesn't help that speed limits on interstates get lowered as you approach larger cities. This is a good reason to remove enforced upper limits on these roads completely. Much of the braking is due to the few goody-goodies cramping the whole flow.
    • by dkleinsc ( 563838 ) on Friday December 21, 2007 @01:26PM (#21780988) Homepage
      I've actually gotten pretty good and figuring which jams are accident related and those that are just people being retarded.

      Most accidents are also due to people being retarded.
      • Re: (Score:3, Funny)

        by bhima ( 46039 )
        Me too. I remember the last traffic jam I was in where it was just people being retarded.

        It was 1960.
    • We saw this very clearly in the SF Bay Area a few years ago when they were repairing the Bay Bridge. They put these inch thick metal plates down in the roadbed. No end of exhortations from Caltrans could get people to drive normally over them. People would brake and cause just such a cascade, causing horribly traffic on the bridge. (Well...even more horrible than normal that is.)
    • by suso ( 153703 ) *
      Here [] were my thoughts on it from 3 years ago. Several of the traffic backups I've gotten into on major interstates have not been the result of an accident but just people slowing down or changing lanes. I always wish that I could see a video from overhead.

      Last month, we drove down to Florida and near Gainesville, there was a huge backup that would slow down for a while and nearly stop, then speed up, then a few miles later slow down. This was going on for like 10 miles. It turns out it was all because p
  • How come certain cities seem to have extra bad, slow, etc. traffic? Just go drive in Silicon Valley on the freeway, then come to Columbus Ohio and see how infuriating the difference is.
    • by TheMeuge ( 645043 ) on Friday December 21, 2007 @01:25PM (#21780976)
      The difference is the overall level of asshole-ness of the drivers. Much of the braking in dense traffic is caused by desperate maneuvers. In New York, the maneuvers are caused by the fact that I'd say less than 10% of the drivers will allow anyone to merge ahead of them for ANY reason. In dense traffic moving at 50mph, it's not uncommon to be within 3-4 meters of the car in front of you, or even less. And since nobody will allow you to merge, you're forced to perform pretty daring high-acceleration maneuvers to force yourself into the target lane... which will cause that lane to rapidly decelerate, clearly creating the traffic wave.

      All it would take to stop this from happening, is for people to stop being assholes, and to let you through, when you're trying to get into an exit, 1/4 mile away.
      • The real problem seems to be that it's in everyone's best interest to not be jerks, but if everyone's not a jerk, any selfish individual can be a jerk and do (marginally) better than everyone else. The situation with traffic we have now is the worst scenario of all... Everyone's being a jerk, causing the worst outcomes for all.
    • by Ohio Calvinist ( 895750 ) on Friday December 21, 2007 @01:31PM (#21781056)
      I lived in Columbus for 5 years, then moved to So Cal, so I know exactly what you're saying. When I get back there, I think "why can't it be like this in Cali?" I love it, I can just sail down the 670 to the college from the airport.

      I think some mid-major cities like Indianapolis and Columbus have a good surface street infrastructure so people going in-city (or from the suburbs) take the surface streets. I think you have people living closer to work too... You also don't have entire towns communiting to the city to work, trying up the freeway (the only way) to get to work at the same time in the morning. There are very few good jobs in the town I live in, but it is the only place working class folks can ever hope to buy a house, so... the commute begins." I mean, I took a $25,000 pay raise to work in San Bernardino, but inheritied 1:15 commute each way, if I'm lucky.

      When I moved to Cali we started visiting my wife's parents every Sunday, like an hour away. I lived 1:30 from my parents (in Cincy) when I was in Columbus and going home was a huge weekend affair, not a afternoon trip. Strange how that all works out.
  • The problem would be alleviated quitre a bit if dimwits would stop tailgating, and even more annoying, braking for no reason whatever.

    Here in Springfield they race to the red light, but brake going through a green light. If the dimwits would let off the gas when the light ahead turned red, and even speed up a bit if the light is green, they would save themselves a lot of gasoline, global warming, and aggrivation.

    I don't like the idea of "automatic braking systems" as I try to keep my foot off the brake. Eve
    • Yeah, automatic breaking would really be kind of pointless unless the car was actually doing the driving itself. I remember watching a science show years ago (thinking it was Scientific American Frontiers, but could have been Nova) where they were discussing the automation of driving and showed a group of cars driving around a circular track bumper-to-bumper, maintaining speed and distance using sensors and each cars' on-board computer to hold the cars steady relative to each other. They claimed that this w

    • I live in the mountains, and what really annoys me is people who brake going uphill, slower than the speed limit, on a 2-lane road. Yes, there are curves. Yes, there are rocks everywhere, it is the rocky mountains. That doesn't mean you are going to die if you go the speed limit, or even faster. Especially in summer when it is 90 degrees outside.

      When going downhill I usually try to let my engine slow me down when necessary, but I have this incredibly mysterious thing called a manual transmission, which lets
    • by db32 ( 862117 )
      Actually there has been research showing that attempting to time lights causes a huge number of accidents. You are far safer when you come to a complete stop at a red light, and then wait a moment before leaving when it turns green just so you can avoid the people trying to adjust their speed to time the lights.

      You are right on the money with tailgating, I freaking hate that crap, it is dangerous and it causes all manner of traffic problems.
  • Nervous brakers? (Score:5, Insightful)

    by Anonymous Psychopath ( 18031 ) on Friday December 21, 2007 @01:23PM (#21780936) Homepage
    One of the most irritating driving habits I can think of are people who obsessively cover the brake every 20-30 seconds or so. Usually soccer moms in Suburbans or elderly in the largest Lincoln they could find. There's nothing ahead of them, no reason really to tap the peddle, but they do it anyway out of habit.

    If an automatic braking system can solve this problem, I'm in for my tax dollars.
    • by Manchot ( 847225 )
      I think that I sometimes annoy people because I like to maintain an above-average following distance. To someone behind me, it might appear that I'm braking for no reason, but in reality, I'm braking to someone pretty far ahead of me. Sure, it has its drawbacks (for example, people frequently use the opportunity to change lanes in front of me), but I think this is one of the reasons that I've never had an accident. Not only does this (obviously) give you the ability to avoid rear-ending people, it also help
      • Re: (Score:3, Insightful)

        by Troed ( 102527 )
        If they are that far ahead of you, why do you _brake_ at all? Just lift off, or downshift. You're one of the persons creating the jams with your driving style.

  • next (Score:5, Funny)

    by kurtis25 ( 909650 ) on Friday December 21, 2007 @01:23PM (#21780938)
    maybe mathematicians can solve why old news appears on slashdot.
    • Re: (Score:3, Funny)

      by mnmn ( 145599 )
      They did. It starts with one editor accepting the story without checking it, and that starts a chain reaction. Dups start coming in faster than editors can check and they're all accepted.
  • In other news.... (Score:2, Insightful)

    by v_1_r_u_5 ( 462399 )
    Scientists discover that if people act in society's interests rather than their own, society is better off. Seriously, how hard is it to follow the two-second rule on the highway?
    • Seriously, how hard is it to follow the two-second rule on the highway?

      It's quite difficult when the majority of other drivers see the space in front of you as an opportunity to "get ahead" in the flow of traffic.

      It's not hard to follow the rule, instead, it's hard to maintain it without ending up going significantly slower than the traffic around you, and you'll still get cut-off occasionally simply out of spite for your perceived slow speed.

      Drivers tend to be very self-centered in their driving actions and habits...even when that's entirely not the case when they're no

    • by berashith ( 222128 ) on Friday December 21, 2007 @01:42PM (#21781226)
      It is absolutely freakin impossible!

      If I give 2 seconds to the car ahead, it is likely that two drivers and maybe a third idiot will wedge into that gap. Now I have to slow down to achieve the new two second gap, which will cause everyone behind me to react with breaking and more slowdowns. Eventually there will be a wave of breaking that causes a huge delay in traffic with no apparent cause. I may even be lucky enough to be run into from behind, and then 2 seconds at zero mph would be the exact lack of distance between our now entangled bumpers.

      Now if we could actually give space to everyone and not have the self-righteous take advantage of these gaps as there way to shave 8 seconds off of their commutes you may have a point.

      Sorry to be cynical to your point, but I live in Atlanta, and people here suck.
      • by kelnos ( 564113 ) <> on Friday December 21, 2007 @02:47PM (#21782394) Homepage
        I tend to do this during heavy traffic. I drive a manual, and shifting in and out of gear over and over gets old real fast. The trick is just to not care. It's hard, I know. Give yourself more than 2 seconds. I tend to go by car lengths, just because traffic conditions vary. In slow traffic (5-25 mph) I'll try to maintain a 10-car-length space or so. This doesn't mean I'm constantly braking and accelerating; if I wanted to do that, I'd just tailgate the guy in front of me like everyone else. If someone cuts in in front of you, let them. They're probably just going to speed up and slam on their brakes when they get to the car in front of you. You can slightly adjust your speed by releasing the gas pedal a little to maintain your space. There's no real hurry -- you have 9 car lengths worth of time to do this. If traffic is heavy and slow enough, you end up with people to the right and left (and behind) you who aren't "cheaters," and people tend to stop cutting in front of you so much. But even if they do, the magic phrase is: "who cares?"
        • Re: (Score:3, Insightful)

          by jbengt ( 874751 )
          I aqree with this completely.
          The only thing that still makes me mad is: Cut me off if you must, but don't hit your brakes immediately after.
  • I think this has been known for _years_.

    I've observed it many times from the vantage point of a light aircraft - in busy traffic times, you can even see the genesis of traffic jams on busy roads - someone jabs their brakes, the car behind hits the brakes harder, and before you know it, you have a standing wave of stopped cars in the traffic maybe 20 or 30 cars deep. It's very interesting to watch from a light plane. It's very frustrating to be in on the ground.
    • Indeed (Score:3, Funny)

      by Colin Smith ( 2679 )
      Once you understand how it works, you can create traffic jams in even relatively light traffic. If you're really good, they're still there when you go home the other direction.

  • by slas6654 ( 996022 )
    I'd be curious to see whether these geniuses analyzed the impact of HOV lanes? []
  • Not only that, but it seems clear that congestion at one time - whatever the cause - can set up a standing traffic density wave that might last for a long time after the original cause is gone. Beyond some minimum traffic level (easily achieved on the highways around DC, for example), at least.
  • Although their proof might be (IANAM). I remember reading this article [] on slashdot around the time it was written. Although, for what it's worth, I don't think it technically qualifies as a dupe.
  • shows how one driver hitting the brakes a little too hard can cascade into a backup miles behind.
    Of course. This is obvious. People generally brake for a little longer than the car in front. I worked this out years ago, and as a result, I try never to use my brakes on a motorway, instead watching the tail lights coming on towards me down the queue, and dropping off back of the last car to try and "iron out the kinks".
  • Some mathematicians have solved the mystery by developing a mathematical model that shows how one driver hitting the brakes a little too hard can cascade into a backup miles behind.

    Some drivers are always under some kind of external or internal influences. Internal influences would include the influence of drugs.

    At a place I normally frequent, I always see "smart/well-dressed respectable men and women" dying to get a fix before getting behind the wheel. By the way, I do not do drugs of any kind.

  • by stewbacca ( 1033764 ) on Friday December 21, 2007 @01:31PM (#21781072)
    I'm with the rest of you. This is hardly a revelation. At Texas Motor Speedway, during a NASCAR weekend with 225,000 fans trying to leave, a person stopping for three seconds causes a 20-minute delay to the last car in line. Until they fixed the number of exits flowing back out to I-35, it usually took 3-4 hours to get out of the parking lot.

    Another cause for bad traffic is the ridiculously easy driving test we have in the States. Couple that with law-enforcement only ticketing speeders instead of bad drivers in general, and you get the traffic we have in most of our cities. I also hate how all accidents are chalked up to "failure to control speed", which makes it sound as if speeding were the main cause of all accidents. In reality, failure-to-yield is overwhelmingly the #1 cause of collision accidents, not speed. But the revenue hungry cops would rather sit on their motorcycles with radar guns than actually pull people over for changing 5 lanes at once, or cutting off other drivers by pulling out in front of them and then NOT accelating.

    Not to mention, hell will freeze over before they ever ticket a slow driver in the left lane.

    • Re: (Score:3, Insightful)

      by dmomo ( 256005 )
      Don't forget drivers who do not use their turn signals. In some cases this is bad for traffic. There are many spots along my commute where I will be stopped at a Stop sign waiting for a car coming from the left to pass so I can keep going only for them to turn right. If they had used their signal, I could have proceeded. Instead traffic gets backed up at the Stop sign. This is true of a couple of rotaries I know as well.

      Another problem I see every day is that of drivers who block intersections at a Red
      • Re: (Score:3, Funny)

        by servognome ( 738846 )

        If they had used their signal, I could have proceeded.
        I learned in traffic school, a turn signal just means the light is working. At best they can let you know what the person might do, who hasn't left a turn signal on for a few blocks?
    • by Greyfox ( 87712 ) on Friday December 21, 2007 @02:29PM (#21782072) Homepage Journal
      Preach it brother! I had a friend visiting from Europe a few years back and she'd go for the "oh shit!" bar whenever I would pass on the right, a maneuver that is more or less required in Florida because there's inevitably some 80 year old doing 5 miles an hour under the speed limit sitting in the left lane. Every few months down there you get some story in the newspaper either about some elderly drivers who got confused and got on the Interstate going the wrong way or about some legally blind driver who took the driving test (!) 25 times and then finally getting a license.

      I'm not just pointing a finger at the elderly either. Stupidity abounds across the age spectrum. A lot of people seem to feel that operating a 2 ton vehicle is "free time" and not time they need to spend actually paying attention to the task at hand, which is OPERATING A 2 TON VEHICLE! Anything that distracts you from doing that and doing it well should be grounds for a ticket. And the training to drill that point home should be required as part of the license process.

  • I already cringe when I hear car ads mentioning Microsoft software. Not to be a luddite, but I'm not so sure I'd feel comfortable letting software partly control my brakes.
  • I first read about this in my Astronomy textbook in high school. The idea is that the spiral arms of galaxies happen the same way, except that instead of braking, we have gravitational attraction between stars. Stars in the arms are stuck in traffic jams; stars between arms are the lucky few who aren't.
  • And these solve the problem permanently. []

  • As a motorcyclist, the idea of "automated braking systems" scare me almost as much as women who are applying makeup while driving SUVs so large they should have "USS" on the license plate.

    Regarding traffic jams, the main cause of traffic jams is very simple, and doesn't require a mathematician to figure out: There are too many people on the fracking road! Whether people are braking perfectly efficiently or not, if enough cars are crammed on the road, there's going to be a traffic jam.
  • Unfortunately, the mathematicians weren't smart enough to follow through to understand the cause of heavy braking: following too closely, less than 2 seconds behind the car in front of you so that when you brake lightly the next guy has to brake hard.

    Nor did they follow that back to its root cause: too many cars on a section of road so that they pack too tightly. Nor did they notice that in light traffic flows fine regardless of braking because the large gaps consume the time lost so that more than a couple
  • I live in Arizona and the drivers here are just dreadful. I see them on the freeways day after day, they have no confidence in their driving skills. They tap their brakes constantly whether something is in front of them or not, and it makes me crazy.

    I can't help but wonder if the onslaught of snowbirds [] that migrate here year after year during the winter.
  • Now what? Seriously, as obvious as this is, what good will it ever do? People aren't going to change their traffic accidents now that's there scientific data to back up what everybody already knew.

    I'm pretty sure we all know that automating driving would get everybody there faster, as long as it works.

    They need to study why IDIOTS slow down when they get to tunnels and redesign the fronts of tunnels to avoid it.

    Or why a guy on the side of the road changing a tire is so damn interesting.
  • by LM741N ( 258038 ) on Friday December 21, 2007 @01:59PM (#21781528)
    The episode where the town charter declares the smartest people to be in charge in the absensce of Mayor Quimby.

    Lenny comes up with the best idea. Traffic lights only have red and yellow, no green. Traffic is speeded up immensely.
  • Java simulator (Score:3, Interesting)

    by alanw ( 1822 ) * <> on Friday December 21, 2007 @02:00PM (#21781572) Homepage
    There's a nice java simulator of traffic flow at []

    The trick when driving to try and iron out these hold-ups is to keep the traffic moving, by slowing down well in advance and leaving a large gap. As soon as the impatient and selfish start driving inches behind the car in front the whole system grinds to a halt.

  • So FEW - drivers - (Score:3, Insightful)

    by FlyingGuy ( 989135 ) <flyingguy AT gmail DOT com> on Friday December 21, 2007 @02:15PM (#21781810)

    So here is the problem, there are two classes of people on just about any road, anyplace:

    • Drivers
    • Motor Vehicle Operators

    Drivers. These are the people you see driving, not overly fast, but driving with intent. They pay attention, they are generally never talking on a cell phone, their eyes are always scanning the road ahead, their mirrors and their instruments. They use blinkers AND turn them off, they can be pretty much any age and any gender. You will notice that they drive consciously.

    Motor Vehicle Operators - These are the people you see driving a car that scare the crap out of you. They are NOT paying attention, they are shaving, eating, reading the paper, putting on makeup, doing their hair. Their cell is glued to their ear, are fiddling with the radio very three seconds. Their left turn blinker is invariably on.

    Some things I would like to see tickets given for:

    • Merging onto the freeway at less then the speed of traffic
    • Changing lanes on the freeway into to an impossibly tight spot and then nailing the breaks. I don't mind if you are a driver and you do this, because if you are a driver, you do the maneuver with grace, authority, you have made sure the person you are going to be in front of knows your intent and keep up the pace.
    • Driving while eating
    • Driving with any sort of animal ( human or otherwise ) on your lap
    • Trying to light any sort of smoking material with a Bic lighter
    • Putting on makeup. Sorry girls, but if you shove the fucking mascara wand into your eye you will crash and probably kill yourself, but worse then that, kill someone else.

    I think that should prime the pump, as I am sure my fellow /.'rs will add many many more.

  • by $lingBlade ( 249591 ) on Friday December 21, 2007 @02:15PM (#21781826)
    I live in Los Angeles and commute 30 miles to work one way. It takes me an hour or more on most days, less at very early hours (pre 5AM). I've made a little mental hobby of traffic pattern prediction and on my route I can accurately predict where the slowdowns will be, and know which lanes to be in on the freeway in order to keep moving. I also know that the pattern changes from time to time and for various reasons and account for that as well.

    By far the biggest problem with traffic here, other than the staggering number of people on the roads, is a false sense of entitlement and/or lack of courtesy for other drivers. I start my drive from a decent neighborhood and go through a pretty big slice of the city hitting East LA, Korea Town, West LA and downtown (including skid row and not in that order). It's not just soccer moms, it's not just the elderly, it's not just the Asians or the Latinos or the Blacks or the Whites or anything. It's ALL of them. For every decent driver out there, there's literally a thousand or more assholes. I moved here from Boston 10 years ago and I remember thinking "what's all this road rage shit I hear about?". How could you possibly get so worked up in your car that you'd want to KILL other drivers. Well I've seen it myself first hand out here.

    About a month or so ago a Mom was killed and possibly her 2 kids as well (not sure) because 2 guys were fighting with each other on a busy surface street. One would hit the gas and then the brakes trying to get the other to rear end him or cutting the other off from getting in a lane or passing. Oh and by the way, yes one guy was about 19... but the other guy? He was in his 40s. You'd think after a certain *I'm invincible* phase people would grow up and mellow out. Most do, but some don't and some just want to go about their business, but when they're pushed, they push back. This is where I fit in. I mind my business and I try to drive quickly and efficiently without being too much of a jerk about cutting people off and I try to let people in when they need to. In other words, I *try* to be a courteous driver. If I'm in the fast lane out here with no one ahead of me, I'll be doing 90 easily, but if someone comes up behind me in a faster car, or just generally wants to drive faster than me, I'll move the fuck out of the way. I pay attention to my surroundings and I realize I'm not driving the fastest car on the road. Same applies no matter what lane I'm in on the freeway. I get the fuck out of the way, safely, efficiently and without waiting an hour. So few people do that here it's sad.

    You say "drive the speed limit" its the law, it's there for a reason. I say, fuck off, I'll drive as fast as I think I can go safely. If I feel safe at 90, then I'm going to go 90. If I think it's safe at 40, I'm going to go 40. But I'm damned sure not going to BLOCK traffic or try to be the amateur police force by sitting in a lane, driving much slower than necessary and making it hard or next to impossible for anyone to get around me. I'm simply going to move OUT OF THE WAY. As for distances between cars, I try to leave plenty of room to stop, meaning at least 2 or 3 car lengths depending... BUT, here's the thing out here. You just CANNOT leave the 3 seconds or more of room that you'd like and still get anywhere. We're all not on a plane. We all don't *get there* at the same time. And yes, I think it's reasonable to assume that most people just want to get to where they're going in the least amount of time safely. Not necessarily in a mad rush. Not race day at the Daytona 500, but relatively quickly. And yet, if you try to observe the simple 3 second rule and leave a nice gap between you and the car in front of you, you get stepped on. Not cut off, but you'll get bumped back, again and again and again.

    Traffic out here is like a line at the bank. Would you, in person, stand in line at the bank and let anyone cut in front of you simply because you didn't take a step or two forward when the person in front
  • Ask a Bicycle Racer (Score:5, Interesting)

    by asphaltjesus ( 978804 ) on Friday December 21, 2007 @02:35PM (#21782192)
    They would have gotten the answer a long, long time ago if only more mathematicians would race bicycles.

    There is nothing worse than flying along at 40+ KMh and having some inexperienced joker using her brakes to back off the wheel in front of her. It sends the riders behind her into convulsions.

    FYI: that's why bicycle track racing (fixed gears) is much safer despite fantastic speeds and tight(!) groups.
  • Scratching their asses doing nothing while several lanes are closed that messed up traffic.
  • by Phoenix666 ( 184391 ) on Friday December 21, 2007 @03:01PM (#21782578)
    is not self-driving cars, but public transportation. And if you need something heavy moved, have it delivered or rent a pickup for a day. Owning and operating cars make sense where the population density falls below a certain threshhold, say in the country, but in sub/urban spaces, which is what we're talking about here, there's no good reason to use the car as the solution to personal transportation.

    And that's just for logistical reasons. When you consider the cost to the environment, the justification weakens more. When you consider the cost to our foreign policy and national security in being dependent upon other countries for oil, the justification weakens still more. When you consider the sheer hassle and productivity lost to accidents, finding parking, breakdowns, time lost sitting in traffic, and aggravation of driving (people cutting you off, getting stuck behind a slow poke, etc), the justification almost evaporates. And when you think about what the $15K you drop on a car and the $5K/yr. worth of insurance, gas, parking, and repairs you have to put into it to keep it running, and the reality that the value of the thing itself loses half its value every year, versus what that money could do for you if you even put it into an index fund, then financially it's the last nail in the coffin for the justification of owning a car.

Our business in life is not to succeed but to continue to fail in high spirits. -- Robert Louis Stevenson