Stuck in Traffic? Mathematicians Might Have An Explanation
by Andrew Posner, Rhode Island, USA on 12.24.07
You know the feeling: you're cruising down the freeway when all of a sudden, and without apparent cause, a traffic jam brings you to a standstill. Before long, traffic is flowing again, and you have no idea what triggered the problem. Sure, you have your theories, but wouldn't the whole thing have been far less frustrating if you had had a mathematical model that could explain it? Well, you're in luck, because that's just what a team of mathematicians from the Universities of Exeter, Bristol and Budapest have created. The model "revealed that slowing down below a critical speed when reacting to an [unexpected] event, a driver would force the car behind to slow down further and the next car back to reduce its speed further still."
The end result is that "several miles back, cars would finally grind to a halt, with drivers oblivious to the reason for their delay." While the findings might seem fairly intuitive, they were previously unknown and poorly understood. It turns out that high volumes of traffic are not necessarily the cause of jams; rather, the model demonstrates that "it really matters how hard you brake" when reacting to unfolding events, because a sudden stop in the flow of traffic can cause a chain reaction several miles back. So this holiday season, be sure to drive smoothly. Or, better yet, if possible, take a train, bus, bicycle, or other contraption, and don't drive at all!
Via: ::Physorg.com
i think there is also a formula for this. something like
if the amount of cars per feet of highway exceeds a certain amount, than youre in a traffic jam
It's "brake" not "break." I'm baffled that the original article spelled it right and this summary got it wrong. Ever heard of "copy and paste?"
When I was a student some years ago at one of the country's leading science/engineering schools, my roommate, a mathematics major, happened to mention that he had interviewed for a job with a company that consulted for cities in "queueing" - the optimization of traffic control to minimize waiting at red lights. Aside from the fact that what he really planned to do was stay in school until he had more letters after his name, he said that he didn't think he knew enough mathematics to do that job. The problem you describe seems much simpler, as it deals with one road at a time, but it's still not surprising that it took quite a bit of work to understand it. That is one of the major problems with political issues that can only be understood through the application of major science and technology. We would like to be able to trust the people who specialize in the relevant field to understand the problem, find out whether there is a solution, and tell us the truth. Somehow, papers get published that I would be ashamed to put my name on, and news media that should know better pick them up and write articles that deceive the public. Sometimes when the experts disagree, the rest of us may be able to look at what they are saying and discern the truth that is hidden in the storm of controversy; indeed, we have little other choice.
And, BTW, since it ain’t always true that us engineers, we don’t need no English, maybe you should watch out for homonyms: “...the model demonstrates that "it really matters how hard you break" when reacting to unfolding events... :-)
Dick Hatzenbuhler
Deering, NH
Heh, not too long ago I came across a website about one man's observations on traffic behaving like standing wave forms, and the experiments he did relating to what he called traffic waves. Notice the dates... not exactly a new breakthrough in ideas here :)
http://www.amasci.com/amateur/traffic/traffic1.html
http://en.wikipedia.org/wiki/Traffic_wave (references the above site too, spiffy)
While this particular result might be new, the overall dynamics of traffic are fairly well understood. 20 years ago as a civil engineering undergraduate I already knew about wave propagation in traffic.
I also had an opportunity to watch a textbook case on Manhattan's East Side Drive, from 35 stories up. A car had some trouble and pulled over, though this effectively blocked one lane. Traffic began to slow, and the slowing propagated upstream as more cars came in than went out. The trouble was fixed about 20 minutes later (I don't recall what it was), and the car either drove away or was towed away.
In any case, the obstacle was cleared, but now there was a mile or more of slow moving traffic. The interesting part is that when the obstacle was removed, a new wave of speeding up started to propagate upstream. Since the overall flow was moving forward, the wave was moving slowly on the ground, and I could see it for about 40 minutes. People were still slowing down over half an hour after the original obstacle was gone, and ever farther from the spot the obstacle had been at. It took a full hour for traffic to be completely normal again.
I imagined the people in the cars wondering why everybody was slowing down, as had happened to me many times. From my bird's-eye view I could see them all as particles following an equation, unaware of the full picture. I now realize a lot of what we do is like that, for instance in the way we choose to consume.
This is nothing new. I did this as a CS project back in undergrad. It's a very simple simulation. This work was actually done back in the 60's by some guys who couldn't find funding for their CS research so they converted it to traffic. They found that Traffic behaves much like computer networks.
This has recently been discussed here: http://forum.ecomodder.com/showthread.php?t=309
It is an interesting topic to be sure, but those of us that put a little thought into it can often work it out so that we do not take the gas mileage hit that others do, and in some cases, we even end up smoothing the thing out a bit (by preventing the people behind from slamming the brakes and the gas).
My advice is just to take it slowly, if you have to drive. But if you don't, don't!
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Benjamin Jones
http://ecomodder.com
In traffic jams I try to trim the number of times I move forward. If a guy ahead of me moves two times, each for 8 feet, I'll not move until it's clear I can move 16 feet with one move. I notice other people do it too. That limits the number of stops and starts and through some magic sync/complexity algorithm that I couldn't possibly understand it smoothes the flow out. I know it's a lot less nerve-wracking for me, provided the guy behind me doesn't lean on his horn.