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traffic jam math

There's a thread on Slashdot discussing how some mathematicians have solved the traffic jam problem. This problem has actually been solved; I remember my queueing theory professor at UCLA discussing it. He gave an example of how people on the 405 followed each other too closely, and as a result, a small slowdown could result in a serious traffic jam a few cars back. He also said that truck drivers were instructed to leave a certain spacing between themselves (e.g. in a convoy) so as not to excessively contribute to traffic jams. After that, I modified my driving so that I don't follow too closely, and try to match my speed to the car ahead of me (even if it's a few car lengths ahead). If that car slows down, so do I, and anyone behind me is not quite as affected. I try to slow down enough so that I keep moving, just to keep everyone else behind me moving. (An unfortunate side effect of this is that sometimes cars will cut in front of me, even in near-standstill traffic.)

I thought that type of analysis was cool; it's what I went to grad school for. OTOH, I was dismayed that this type of insight didn't lend itself to some of the things that were giving me problems, such as graph theory (taken in the same quarter).

Along the lines of early exposure to science, etc. I remember when I was very young, asking my father why traffic jams occurred. I didn't understand why we couldn't drive at 55, even though that's what the given speed limit was, because people kept slowing down. I wondered why we couldn't just be given a "slot" that would allow us to move at the speed limit. (I didn't realize that I was describing is now a principle behind several types of data communications.) He didn't know; he had driven a truck in the Army, but perhaps the mathematics of traffic jams hadn't been solved yet. Anyway, this is the sort of thing I've been talking about – kids I know have parents, or friends of parents who know about science and can tell them things. For example, my choral director's son talks to one of our sopranos' husbands, holder of a Stanford PhD in materials engineering, about Stanford. He wants to study mechanical engineering there. The director knows all sorts of things about the curriculum, down to what the summer programs for kids thinking of studying engineering are like.

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( 3 comments — Leave a comment )
gconnor
Dec. 23rd, 2007 12:13 pm (UTC)
I am a big fan of leaving a gap in front of my car, as you said. Even if we're stop and go or barely creeping, I feel like it's important to spread the congestion further out behind me.

People constantly merge in front of me because of this. I've gotten used to it. If this happens 10 or 15 times in a 1-hr commute, that ends up being less than 1 minute of difference to my time.

Somewhere I heard that an accident, stall, or other feature beside the road that causes people to look, will always have a slowdown forming behind it, but once the accident or other visible feature is gone, the slowdown will slowly move backward until it dissipates.

Compressing congestion forward rather than opening up space to push congestion back is causing more people to slow to almost a stop, I think.

Another thing I have noticed around this area is "stupid" merges with no metering, not enough distance to really get up to speed and merge, etc. Also, people don't know how to legally merge - I believe the law says something like 1. if the arrow is in your lane, you must merge, meaning you must yield to anyone not *completely* behind you, and 2. where the separator line runs out, that's the last possible place to merge, and travelling next to someone without a line dividing the space into two lanes is illegal, just as tooling along in the shoulder might be. But, too often I see people going all the way up to where there's no more room for 2 abreast, well after the dividing line has disappeared, and just "waiting" there for what they think is "their turn". Hate to break it to you folks, but if the arrow is in your lane (usually the right-most) then it's your job to match speed with those next to you while the dividing line is still there, even if they are going slower or stopped.

It's worse than just casual abuse too... people literally don't know how to merge properly. This is to the point where if you match speed with the other lane, before the dividing line runs out, people will either honk at you, or go even further right into the real, live shoulder to pass the person matching speed and merging legally/politely.
gconnor
Dec. 23rd, 2007 12:26 pm (UTC)
After reading the linked article, the previous thing I'd heard about a wave moving backward makes more sense now. This makes me feel even more strongly that following too close is to blame for making everyday traffic non-events into huge traffic jams.

Based on this, I wonder how hard it would be to have lights on the back of your car that signal "back off" when the person behind you is too close for the current speed. This is probably much easier to design than an automatic braking system, and may have similar effects. If new cars had these, even if, say 1 in 10 cars had these, I think the effect on other drivers would be quick and quite tangible.
fauxklore
Dec. 23rd, 2007 12:40 pm (UTC)
A guy I knew in grad school had done some work on traffic modeling. What's interesting is that at the time (in the early 1980's) most of the models didn't reflect people's experience, e.g. they didn't show the development of traffic jams from sheer volume. He discovered that this had to do with the sampling method they were using to digitize the equations in the models. Basically, they were undersampling and, hence, didn't see the higher frequency effects.

Here in northern Virginia, I am convinced that most people believe they have lost somehow if they ever let somebody get in front of them. Part of Pennsylvania has painted dots on certain roads with signs that tell you to keep a certain number of dots between you and the car in front of you. (I'm a bit vague because it's somewhere I've only been once and it was a while ago.) That seemed to work well, but it's hard to tell because it was already a semi-rural area.
( 3 comments — Leave a comment )

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