Bubbles and Barriers

It's crossed my mind that perhaps I shouldn't be announcing the existence of bubbles like this. I mean, what if there's not enough room in the bubbles for everyone who wants to sit there? What then? I don't think this is an idle question. For one thing, people at present really aren't aware of bubbles—it's quite rare that I see another driver make use of one. For another, although I'm sure there are plenty of people who will always be in too much of a hurry to want to sit in a bubble, I don't imagine they're a vast enough majority to make the question moot. But, the way I figure it, any driver aware enough to want to sit in a bubble is probably aware enough to cooperate in working out some other suitable arrangement.

I sometimes wonder what the traffic patterns would look like if all other drivers thought as I do. My best guess is that the distribution of cars would be uniform and porous, and would follow the principle of relative speed.

There's one other thing I should point out about bubbles, which is that they're not stable. You may be able to sit in one for quite a while with just a few other cars passing through, but sooner or later you'll find yourself back in the midst of things. I'm not sure how it happens, exactly, but when it does, you just have to speed up or slow down until you find another one.

It's not just the bubbles that are interesting, though. The parts of traffic that are not bubbles, i.e., the bunches of cars, also have some interesting properties. (By the way, the two can be thought of as figure and ground.) If it helps, here's a picture, with car A catching up to an established bunch of cars.

In the picture, I've tried to illustrate what I see as the primary cause of bunches, namely, that the cars in front have unintentionally formed a barrier by driving with insufficient relative speed. I say “driving” rather than “attempting to pass” because I want to suggest that car C is not entirely blameless, but in point of fact the most likely direct cause of the barrier is that B thinks ve's passing C.

Although I've drawn the picture with two lanes, barriers definitely do occur even on three-lane highways. I assume they occur on larger ones as well, but I don't have enough direct experience to be able to say. It's a function of traffic density, of course—if, on a three-lane highway, there are so few cars that only two at a time ever meet, well, of course there won't be barriers.

I bet one could see barriers even in a simple mathematical model. Take a half-infinite highway, say, with cars entering at the origin, traveling at fixed speeds, and avoiding collisions. Set the density by adjusting the rate of entry, choose each car's fixed speed from some distribution, and voilà! The only real problem is how to characterize the barriers; maybe it would be enough to show that the cars bunch up, that their positions become correlated. Exact solution, anyone?

Here are a few other thoughts about barriers.

Although I didn't think to point it out at the time, what I said in Via Tailgating, that I like to change lanes, fall back, and let one of the cars behind me do all the work, is a strategy for dealing with barriers. Another strategy I like is to just drop back and wait for the barrier to fall. There's a slight difference … in the first case, I want to get through quickly without tailgating, while in the second, I want to sit well back and not deal with the barrier at all.

For some reason, it seems natural to me to assume that bunches are symmetrical, but really they aren't. In front they're dense, then they gradually thin out, ending with a few stragglers in back. They're not even symmetrical across lanes, because for example people who want to get through tend to congregate on the left side.

I was telling someone about barriers, just now, and she immediately knew what I was talking about, and said she'd heard them called wolf packs. That seems like a good name.

To my mind, the concepts “bubble” and “barrier” are only valid in the context of controlled-access multilane roads. Similar structures do form in other contexts, however.

On one-lane roads, it is more difficult to pass, enough so that I think it gives the barriers a qualitatively different feel. In a long line of cars, for example, a passing car will often advance by only a few positions before merging back in. That's something you don't often see on a two-lane road.

To put it another way, thinking of the number of lanes as a parameter, it's not unusual for the limiting case to be degenerate.

What about roads without controlled access? In that case, it all depends on whether the road has traffic lights. If it doesn't, well, all I can say is that the barriers just feel different to me; but if it does, then the barriers really are different, because they form at the traffic lights rather than behind slow drivers. As a result, the barriers appear at regular intervals, and are quite dense.

Another thing about roads without controlled access is that it becomes impolite to sit in the middle of a bubble. Any car that wants to turn onto the road, or even just cross it, needs lots of room, so to be polite, or cooperative, you should make available as much room as possible. Sitting in the middle minimizes the length of the longest gap, and so is the exact worst thing you can do.

I'm no altruist, so I ought to clarify my rule: you should make available as much room as possible, without inconveniencing yourself in any way. In practice, I like to move as far toward the front of the bubble as I can without getting tangled up in the barrier. (I like to move toward the front rather than the back because it's easier to maintain your distance from something that's in front of you, where you can see it.)

I like to do the same thing at night, even on controlled-access highways. It's nice to have cars in front of you to show you where the road is, and light it up for you; also, if there are deer or other animals (chickens?), they, like cars, need lots of room to cross the road, and you want to make sure that room is behind you.