Tuesday, October 15, 2013

Traffic flow and merging during congestion

A little while ago there was this article about fluid dynamics applied to traffic. Then a couple weeks ago I saw this article pop up on Hacker News talking about the logical errors with the first article. I feel like we still don’t quite have the complete picture here. Both are excellent articles and both speak the truth to some degree or another. I just have a couple points to make. Please note that I’m assuming you have at least skimmed each of those articles.

If you just want to know what I’m getting at here then just jump to the conclusion.

Traffic Flow

The first article proposes that to prevent traffic jams during times of congestion we need to decrease our rate of travel well enough in advance that we can maintain a constant speed and as we finally arrive at the tail end of a “traffic wave” it is beginning to move again. In so doing we can effectively “eat” a traffic wave, avoid stop-and-go traffic and fix traffic jams. This is true. Sort of.

After reading that article I tried it during my regular commute to and from work and I managed to “eat” several traffic waves and maintain a constant speed without having to stop like the cars in front of me.

I can’t speak to what happened to the cars behind me, but the second article makes the argument that by following that proposal you are actually making things worse for the cars behind you. It asserts that, given an average two-second following distance, “there is a limit to the number of cars that can pass by a given point on the highway in a given amount of time, and that limit is one car every 2 seconds, per lane”. Therefore, you can do the math and figure out exactly how many cars can actually fit past the given point. Nothing you can do will change that and therefore you cannot fix a traffic jam. This is also true. Sort of.

In reality, it is very dependent on traffic density. If you are in a bumper-to-bumper traffic jam where all the cars are close together and trying to squish past a certain point, then the second article is correct.

If, however, traffic is less dense, then the first proposal can actually make a difference. Why? Well, you have to account for the time it takes for a car to accelerate. If you just continue riding the bumper of the car in front of you and come to a stop with every traffic wave, then you are maintaining the energy of the wave because you now have to stop and then accelerate which takes extra time. If you back off a bit and maintain a constant speed which allows a great enough distance from the car in front of you then you “eat” the traffic wave and absorb the energy of it. You no longer have to take the extra time to accelerate, and neither do the cars behind you. You also save on gas. The trick, of course, is to do this without causing a traffic wave behind you. Don’t try this in super dense traffic! You will only make things worse.

Traffic Merging

With merging there is yet more to consider. In the comments on the second article there is a comment from a man talking about how, when there is a sign indicating that traffic is merging ahead, he will get over quickly to be courteous or “pro-social”. This is actually a bad idea for a couple reasons.

So, let’s assume that there is construction on a two-lane road two miles ahead and one lane is merging. If most people start merging right away then there is a lot of unused space in the now-empty lane that everyone is merging from. As the second article points out, this only serves to lengthen the distance of the traffic jam. It effectively doubles its length and increases the chance that the jam will “spill out” and affect traffic elsewhere needlessly.

The other problem of course, is that those anti-social, selfish “jerks” (like me) that zoom past in the now-empty lane and merge as late as possible saving themselves from the delay, end up causing even greater delays for those who were courteous. There’s now yet another car that the “pro-social” and “courteous” people have to wait for before they finally get their turn to get through the bottleneck.

The problem is that no matter where you merge, you still take up space and make the jam worse. Whether you merge as late as possible or you merge early, you are lengthening the commute of all the people behind you.

The only thing you accomplish by being “pro-social” is doing yourself and those in the lane you merge into a disservice. YOU are a delay. By merging early you create an uneven distribution of the delay simply moving more of the delay from the lane you are in to the lane you are moving to and decreasing the delay in the lane you are coming from. This gives those in the merging lane an advantage which comes at a cost to the people you are trying to be pro-social or courteous to.

If everyone waited to merge until they had to then everyone would have a similar delay because there would be an even distribution of the delay. The way to be courteous and considerate of everyone is to wait until the last minute to merge if you are merging, or to let one car in front of you at the merging point if you are in the lane being merged in to. This creates the most even distribution.

Conclusion

When you have to merge in dense traffic, please, please do everyone a favor and merge as late as possible. It’s the most courteous and pro-social thing you can do.

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