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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;
20 fucking years ago.
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.
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?
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'd be curious to see whether these geniuses analyzed the impact of HOV lanes? http://www.thenewspaper.com/news/02/292.asp
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!
:)
Support the 30 Hour Work Week!!!
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
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.
Deleted
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.
- Flow Equals Density Times Velocity
- Conservation of the Number of Cars
- Experimental Observations
- Traffic Density Waves
- After a Traffic Light Turns Green
- Wave Propagation of Auto Brake Lights
- Stationary Shock Waves
- Effect of Red LIght or an Accident
and so on. It made for an interesting class (and the only math class where I ever assigned a paper!). I recommend the book. If only we could train people to behave in traffic as if they were an incompressible fluid, we would never have traffic jams; but to do that, you'd need to be trained to speed up when traffic got heavy.And the corollary to this are the crazed "must get there now" drivers who, despite traffic backed up for miles, will persistently move back and forth between lanes, causing more cautious drivers around them to repeatedly brake.
I hope you are referring to drivers trying to time when they hit a light and not about cities timing the lights so that people don't have to stop. Glendale, AZ and a lot of the west side of Phoenix did that several years ago when I lived there and it was beautiful. If you went the speed limit you would hit green lights the vast majority of time. I have fond memories of driving down 67th Ave from I-10 all the way to Camelback Rd. The only red light I got was right off the freeway and even that was hit or miss. But after that I just drove the speed limit and never saw a red light again. It was fun to see people speed way up, get to the next light and stop, then when it turned green I would fly by them at the speed limit and they would be accelerating like it was the Daytona 500.
Alas, where I live now there are lights nearly every 2/10s of a mile. It's impossible to time lights like that. When lights are every mile (like the west side of Phx) you can do it. As it is, I live in a small community of ~30,000 now and because of the lights traffic is no better than in Phoenix. It's really sad.
Stop Global Warming!
Just say no to irreversible processes!
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.
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 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.
Hey KID! Yeah you, get the fuck off my lawn!
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
One thing I've noticed in my state is that if the light is a left turning lane arrow, it might not give you the opportunity to go first if you coast up to it while its red, and instead lets the opposing traffic go first. But if you were stationary in front of it while red it would have let you go before the opposing traffic.
That is not to say its smart to speed up to it and brake suddenly if its red. But it is annoying when there is a guy in front of me and we both are approaching a turning lane where I know if we were sitting there during the red it would give us the arrow to go first, but he just coasts up to it and screws us all.
Not road rage annoyed mind you, just mildly annoyed.
The article referenced was actually published in the September 2006 edition of the Proceedings of the Royal Society A: http://journals.royalsociety.org/content/h107x295723j3734/fulltext.pdf
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
If you don't touch the brakes at all, the ABS does nothing. Much less "take over and spin you around a couple times".
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.
Got Trader Joe's? friendwich.com RSS feeds work now!
Scratching their asses doing nothing while several lanes are closed that messed up traffic.
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.
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.
If we were to automate cars the left two lanes of most freeways would be vacant. I commute on a motorcycle and have observed the ins and outs of traffic (what with my life depending on it and all) and those people are seriously F-ed in the head, I propose a formula for the mathematicians to try that will give the real reason for traffic: Norman Person + oversized vehicle + minor competition = Total Fuckwad. Basically these people should be killed for our national security: 3,620 people die monthly due to automobile accidents, while 2,974 died from 9/11.
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.
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.
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.
That's one of the main reasons I drive a manual transmission: I can adjust my speed without having to use my brakes. Makes the brake pads last longer too.
I swear, we could reduce the amount of idiots on the road by making two things mandatory for new drivers: (1) learn on a manual transmission first, and (2) make parallel parking part of the driver's test (again).
Will draft for food...
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 merge in. The cars at 60ft now need to slow down to increase their distance. Once said car slows down, the car behind has to slow down too, except someone is merging in front of him, and so on.
That goes for stop lights too. You have a bunch of people driving 30ft apart come to a stop. They all don't start instantly, they have to wait for bonus ft. When you're the 10th car, you need an extra 300ft to get going.
09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0
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.
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.)
Village idiot in some extremely smart villages.