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Mathematicians Solve the Mystery of Traffic Jams
Posted by
Zonk
on Fri Dec 21, 2007 12:16 PM
from the next-they'll-use-geometry-on-the-mystery-of-the-haunted-amusement-park dept.
from the next-they'll-use-geometry-on-the-mystery-of-the-haunted-amusement-park dept.
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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Riding the Failure Cascade 195 comments
An anonymous reader writes "The Escapist has up an article looking at a curve that represents the dissolution of large social groups, like online guilds. Called the Failure Cascade, it's essentially a way of examining the dissociation of members of an organization predicated on a culture of success. They primarily explore this phenomenon using descriptions of EVE corporate alliances. 'These are the two forces at work in [an] alliance's failure cascade: the individual and the guild ... This happens because the failure cascade is the inverse of a network effect. Websites like MySpace define their value by the people that use the service just as guilds define their quality by their members. As bad events cause players to leave or become inactive, the quality drop leads others to do the same in a spiral that rarely stabilizes, until no one is left.'"
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Old news (Score:5, Informative)
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.
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Re:Old news (Score:5, Informative)
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Re:Old news (Score:5, Interesting)
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Re:Old news (Score:5, Informative)
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Re:Old news (Score:4, Insightful)
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Re:Old news (Score:5, Insightful)
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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.
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Re:Old news (Score:5, Informative)
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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.
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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.
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Re:Old news (Score:5, Insightful)
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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.
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Re:Old news (Score:5, Interesting)
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Re: (Score:3, Insightful)
Re: (Score:3, Informative)
Small miscalculation (Score:5, Funny)
Einstein (Score:4, Funny)
Re:Einstein (Score:5, Insightful)
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Re:Einstein (Score:5, Insightful)
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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.)
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Traffic Waves (Score:4, 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.
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Re: (Score:3, Funny)
It was 1960.
Nervous brakers? (Score:5, Insightful)
If an automatic braking system can solve this problem, I'm in for my tax dollars.
Re: (Score:3, Insightful)
next (Score:5, Funny)
Re: (Score:3, Funny)
XKCD (Score:4, Funny)
Disgruntled traffic engineers cause traffic jams! [xkcd.com]
:)
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.
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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: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.
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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.
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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.
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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.
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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.
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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.
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Re:In other news.... (Score:5, Insightful)
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Indeed (Score:3, Funny)
Re:Cover Job (Score:5, Informative)
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