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Mathematicians Solve the Mystery of Traffic Jams
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."
This has been known for years.
Give me Classic Slashdot or give me death!
Sure. But what they forgot to include was the variable of EVERYONE IN THE OTHER LANE STOPPING TO WATCH.
Physics is nothing like religion. If it was, we'd have an easier time trying to raise money!
Does this mean now there's math to support this?
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$x=~y+ -xz+\0-Tx+;print$_^chop$me for split'',$x;
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.
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.
Eagles may soar, but weasels don't get sucked into jet engines.
maybe mathematicians can solve why old news appears on slashdot.
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.
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.
Forgive my spelling from time to time. I'm often posting during short breaks.
Disgruntled traffic engineers cause traffic jams!
:)
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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.
The effect would be mitigated if everyone would refrain from following other cars so closely.
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.
See my journal for slashdot ID's by year. Mine created in 2005. http://slashdot.org/journal/289875/slashdot-ids-by-year
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.
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.
If you disagree, post your argument. (-1, Overrated) isn't your personal censorship tool for views you don't like.
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's not just the UK, I've noticed the same sort of thing in the US. This style of driving is also a lot more conducive to not getting bent out of shape.
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.
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.
They are also behind LAST years mathematicians. Although by a bit shy of a year. http://science.slashdot.org/article.pl?sid=06/12/27/0350218
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.
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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?"
Xfce: Lighter than some, heavier than others. Just right.
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.
Do what you can, with what you have, where you are.
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.
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.)
That that is is that that that that is not is not.
It seems to me that the major deficiency is in your public transport system. Fixing / building well-interconnected rail, bus and bicycle routes would mitigate your traffic problems in a much more sensible way than somehow modifying your highway system, car technology or road laws.