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September 04, 2006

Highway game theory

UPDATE in the extended post...

Yesterday, I drove my Number One Son back to school in the New York area. We met my older sister and her family and my mother in Manhattan for dinner. My sister found a shul where we were able to say kaddish, and then I drove my mother home. I stayed overnight at my mother's house, and drove back home today. Surprisingly, Labor Day traffic was not bad at all, but there was one segment in Delaware where there was road work, and I was backed up for about 20 minutes.

So I'm going to pose a driving-related question here, and I'll place my analysis in the extended post. Feel free to read it before or after you've thought about the problem and to agree or disagree with my solution.

My question is: Assume you have to comply with all traffic laws. You're on a highway with four lanes in each direction, and traffic is fairly heavy. You see a sign telling you that the two left lanes will be closed in 2000 feet. What's your best strategy to minimize the time you will be delayed? (Using the shoulder isn't a legal answer, because the traffic laws don't permit it.)

Let's call the four lanes 1, 2, 3, and 4, from left to right, where 1 and 2 are the left lanes that are going to be closed, and 3 and 4 are the two right lanes. Which lane or lanes do you drive in?

My answer is: Stay in Lane 1, the far-left lane, the first of the two to be shut down, as long as you possibly can. Then move into Lane 2 from the left and stay there as long as you possibly can. Don't move into Lane 3 or 4 until you absolutely have to.

This is my thinking (and I've road-tested it): Lanes 3 ane 4 already have fairly heavy traffic. Lane 2 has fairly heavy traffic, PLUS cars moving in from Lane 1 on the left. So Lane 2 has very heavy traffic. But if you stay in Lane 1, most people in front of you will pull into Lane 2 before they have to, and you will move quickly to the end of Lane 1, at which point you can move to Lane 2. Once you're in Lane 2, the same principles will apply. People in front of you in Lane 2 will pull into Lane 3 ahead of time, leaving traffic ahead relatively light. When you finally reach the end of Lane 2, you can pull into Lane 3, and you'll have moved well ahead of the people who pulled into it earlier. Those people have to contend with the traffic that was already in Lane 3, PLUS the cars continuing to move in from Lane 2.

There's a lot of jerk-y behavior on the highways, but this is totally legal. Unless you cut someone off when switching lanes, you're not being a jerk. On the other hand, I've confessed to being a jerk here (scroll to bottom). And I'll also confess that when I was a lot younger, I did some jerk-y stuff when I drove my brother to Shea Stadium to see the Mets. The exit ramp from the parkway was always backed up onto the parkway itself because of the crowds. In fact, the backup clogged the two right lanes. So I would drive up on the clear third lane until, maybe, 50 yards from the exit. My brother would roll down the passenger window and politely ask the people in the backed-up lane if we might please move into the lane. That, I confess, was jerk-itude. What saved us from being major league jerks was my brother's polite request to the other drivers.

UPDATE (9/6): jk does an economic analysis at Three Sources: "The lane is a scarce resource, by merging early, you are increasing the scarcity -- why not use all 2000 feet? More significant still, all that early merging creates 2000 feet of stoppage. At the end of the lane, there is a natural merge point where everyone can choose the same spot." All true, and it gives a high-sounding excuse for my behavior: "scarcity." In a comment there, I mentioned that a driver really should move into a lane that will end in 2000 feet. It will help the driver for the reasons outlined above, and it will reduce the "scarcity" of space in the other lanes.