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."
Cover Job (Score:2)
Re:Cover Job (Score:5, Informative)
Re: (Score:3, Informative)
Re: (Score:3, Insightful)
People tailgate and then apply their brakes. This is the proximate cause of the whole thing.
Think of traffic like a rubber band. It has nothing to do with that at all. It's a problem, but not that bad.
The real issue is that the slower you drive, the less distance required to leave between you and the next vehicle. At a stop, the distance is 0, and at 100 km/h it's probably three car lengths - maybe 60ft or so.
Graph it out and it's probably quite a linear relationship - at 50 km/h 30ft is probably acceptable.
So you have a bunch of people driving 60ft apart on the highway, and a bunch of cars m
Re: (Score:3, Insightful)
Old news (Score:5, Informative)
Re: (Score:2)
Re:Old news (Score:5, Interesting)
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)
Re:Old news (Score:5, Interesting)
Re:Old news (Score:5, Informative)
Re:Old news (Score:4, Insightful)
Re:Old news (Score:5, Insightful)
Re: (Score:3, Insightful)
I still do as you do, but I do try to gauge the intentions of cars behind me. If they have their signal on I won't block their way, but if they are one of those that don't si
Re:Old news (Score:5, Informative)
Ummm, no [tirerack.com]. You left out the width of your tire (Google guesses you meant 205/60R15). So the sidewall is 60% as tall as the width, or 123mm. The 15" rims are 381mm, plus 123mm*2 = 62.7cm outside tire diameter. Almost the same number but your formula was completely wrong.
Huh? You're just making that up now, aren't you. Let's try that again.
Another Google guess [audi.co.za] gives it a transmission ratio of 2.714 in first gear, times a final drive ratio of 4.875, for a net ratio of 13.231:1. At base revs, your car is going (850rev/min) / 13.231 * (62.7 * 3.142 cm/rev) * (60min/h) * (1km/100000cm) = 7.6km/h.
The same formula using top revs in 4th gear (0.742 ratio) gives approximately the correct top speed of your car, so I'm pretty sure my formula is right. Since the article is about cars and math, we might as well use correct math when discussing them.
Re: (Score:3, Insightful)
The dickheads that has to press into an intersection even though he sees that it's blocked. It's that dickhead who won't let people change lanes. The dickhead who is blocked from changing lanes and has to stop in the middle of the road to change lanes *now*. That dickhead who drives under the speed limit in the left lane.
When we get cars that drive themselves, we can fit five times more cars on our current roads, with no traffic jams.
And public transport = fai
Re:Old news (Score:5, Informative)
Re: (Score:3, Informative)
Try a motorbike.
My Moto Guzzi 1000 SP III is useless below 30 km/h in second gear. First gear works, but just barely, to trundle along at constant throttle, unfortunately the power/weight ratio is such that the least throttle movement translates into huge jerks. And my experience is that this is typical for Guzzi motorbikes, they have very tall first gears, and a correspondingly higher speed in second, and even though they're V-twins (usually thought of as sedate low-rev trundlers), they're useless below 2
Re:Old news (Score:5, Insightful)
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)
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: (Score:3, Insightful)
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
What should offer you satisfaction is that you're adopting
Re:Old news (Score:5, Insightful)
Re: (Score:3, Insightful)
two comments... (Score:5, Insightful)
(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)
Re: (Score:2, Informative)
Re:Old news (Score:5, Interesting)
Re: (Score:2)
Re: (Score:3, Informative)
Re: (Score:2)
Re: (Score:3, Insightful)
Re: (Score:2)
Indeed. Even looking at Orosz's website [ex.ac.uk], 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.
GMD
Wrong (Score:2)
Watch the movie (Score:3, Informative)
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)
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.
Re: (Score:3, Interesting)
But to give NY drivers their due: The BQE was the very first place I ever saw true alternate merge in reaction to a lane closure (for construction). Each driver in the travelling lane was letting in exactly one driver from the disappearing lane, and nobody from the disappearing lane was trying to "jump". Smoothest construction merge I have ever seen. Everybody seemed to realize that "playing by the rules" would get everybody there faster. This is true "enlightened self-interest."
Small miscalculation (Score:5, Funny)
Einstein (Score:4, Funny)
Re:Einstein (Score:5, Insightful)
Re:Einstein (Score:5, Insightful)
Untapped potential of braking expressiveness (Score:5, Interesting)
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)
>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)
I read about this once (Score:2, Informative)
Not suprised (Score:4, Insightful)
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.
Re:Not suprised (Score:5, Funny)
Most accidents are also due to people being retarded.
Re: (Score:3, Funny)
It was 1960.
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
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
only works in certain cities? (Score:2)
Re:only works in certain cities? (Score:5, Insightful)
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.
prisoner's dilemma anyone? (Score:3, Insightful)
Re:only works in certain cities? (Score:4, Interesting)
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.
Arrgh! (Score:2)
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
Re: (Score:2)
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
Re: (Score:2)
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
Re: (Score:2)
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)
If an automatic braking system can solve this problem, I'm in for my tax dollars.
Re: (Score:2)
Re: (Score:3, Insightful)
next (Score:5, Funny)
Re: (Score:3, Funny)
In other news.... (Score:2, Insightful)
Drivers tend to be self-centered. (Score:2)
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
Re:In other news.... (Score:5, Insightful)
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.
Re:In other news.... (Score:5, Insightful)
Re: (Score:3, Insightful)
The only thing that still makes me mad is: Cut me off if you must, but don't hit your brakes immediately after.
Known for _years_ (Score:2)
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)
What About HOV Lanes? (Score:2, Interesting)
Standing Waves (Score:2)
This is not new math (Score:2)
Dupe (Score:2)
Erm, it's pretty obvious really. (Score:2)
XKCD (Score:4, Funny)
Disgruntled traffic engineers cause traffic jams! [xkcd.com]
:)
Re: (Score:2)
Do not discount this (Score:2)
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.
Bad drivers = traffic jams (Score:5, Insightful)
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)
Another problem I see every day is that of drivers who block intersections at a Red
Re: (Score:3, Funny)
Re:Bad drivers = traffic jams (Score:5, Insightful)
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.
Car software (Score:2)
Astronomy (Score:2)
Yes, we've know for years. (Score:2)
http://news.bbc.co.uk/1/hi/uk/7148731.stm [bbc.co.uk]
Oh, HELL no (Score:2)
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.
Not smart enough (Score:2)
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 call them "brake-happy assholes" (Score:2)
I can't help but wonder if the onslaught of snowbirds [wikipedia.org] that migrate here year after year during the winter.
That's great. (Score:2)
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.
Obligatory Simpsons (Score:5, Funny)
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)
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)
So here is the problem, there are two classes of people on just about any road, anyplace:
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:
I think that should prime the pump, as I am sure my fellow /.'rs will add many many more.
No Mystery here in LA (Score:3, Insightful)
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)
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.
And here I thought it was 19 cops standing around (Score:3)
The best way to avoid traffic jams (Score:4, Insightful)
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.
Re:Stop tailgating (Score:5, Insightful)
Yeah.... I tried this for several weeks. Except everyone took the opportunity to sneak in front of me so they could play a game of changing lanes repeatedly to snake their way through traffic faster.
That is the problem. You can do what is best for the group, but then selfish individuals abuse that for their own gain which hurts the group more. I can't wait until we have self driving cars... I could easily foresee traffic signals going away, much more efficient cars and no more worrying about getting to old to be safe on the roads. Add to this a dropped death rate, and this breakthrough would easily be the greatest advancement of the 21st century.
Re:Stop tailgating (Score:4, Insightful)
Yeah.... I tried this for several weeks. Except everyone took the opportunity to sneak in front of me so they could play a game of changing lanes repeatedly to snake their way through traffic faster.
It's funny how often I hear this. I try to hold back a safe distance all the time, and sure, a handful of morons weave through the gaps and I have to drop back a little more. But I never see this horrendous influx of morons people keep telling me about. I manage to maintain a much better distance (and a much smoother drive in terms of both vehicle speed and mental stress) than most people other than for a few moments if someone cuts in, and since those people usually cut out again almost as quickly, I doubt it even slows me down noticeably.
FWIW, this is the UK, and the comment above apply to both high-speed motorway driving and crowded conditions around the city. I've never driven in the US, but I do hear the same sorts of complaints the parent post was making all the time.
Re:Stop tailgating (Score:4, Insightful)
FWIW, this is the UK, and the comment above apply to both high-speed motorway driving and crowded conditions around the city. I've never driven in the US, but I do hear the same sorts of complaints the parent post was making all the time.
It helps to realize that some people are assholes, and a lot of those assholes are not just bad drivers, they're dangerous to themselves and others. Keeping a safe distance instead of trying to block people probably isn't slowing you down and is definitely increasing your safety margins.
Re: (Score:2)
Car B is following car A at a reasonable distance on a city street. Car A begins to gradually slow down for whatever reason. The driver of car B, whether due to lack of attention or just brutal stupidity, doesn't slow down until it's necessary to apply the brakes strongly. Car B applies the brakes strongly, as do all the cars behind car B who can't see what's going on in front of him a