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."

Re:Old news

[Billosaur]

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.

What About HOV Lanes?

[slas6654]

I'd be curious to see whether these geniuses analyzed the impact of HOV lanes? http://www.thenewspaper.com/news/02/292.asp [thenewspaper.com]

Re:Old news

[dyefade]

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.

Re:only works in certain cities?

[Ohio Calvinist]

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.

Re:Old news

[cyphercell]

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:only works in certain cities?

[sir 8ed]

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.

Re:Arrgh!

[Chosen Reject]

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.

Java simulator

[alanw]

There's a nice java simulator of traffic flow at http://vwisb7.vkw.tu-dresden.de/~treiber/MicroApplet/ [tu-dresden.de]

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.

Re:Stop tailgating

[j_166]

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.

Ask a Bicycle Racer

[asphaltjesus]

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.

Untapped potential of braking expressiveness

[GPS Pilot]

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:two comments...

[orclevegam]

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 the safest method is simply to allow space for the compression wave to dissipate (some college group actually modeled this IIRC and showed how "bubbles" form in traffic and can be used to clear compression points).

Re:Untapped potential of braking expressiveness

[demopolis]

There is another variation I saw on this while back. Basically, the pressure on the brake was equated to a horizontal VU meter on the back of the car. At the lightest touch, it would show the standard lights, but more lights would be added inward as the pressure increased. A hard stomp would basically create a solid light bar across the back of the vehicle. It was very intuitive and would definitely get my attention.

Re:Untapped potential of braking expressiveness

[neapolitan]

>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 noticeable if you ever see it in action.

FWIW, car companies have been pretty response to stuff like this, but driving habits are difficult to change. I wish the US would go on a public education campaign against idiot driving habits, which are for some reason generally accepted. To me, it is as bad as drunk driving.

Re:Old news

[DudeTheMath]

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."

Re:Untapped potential of braking expressiveness

[regularstranger]

"And indicates that you will have some serious traffic accidents and deaths when some epileptics (including people who don't know they have it) go into seizures from those rapidly flashing strobes." Do those flashing strobes on snow moving equipment and on emergency vehicles also cause people to go into seizures?