## Tuesday, October 1, 2013

### How Traffic Actually Works: Don't Let Anyone Merge In Front of You

From A Gentleman and A Scala:
Every so often this article makes the rounds and it annoys me. That isn’t how traffic works and the proposed solutions won’t fix anything. Maybe you can eliminate the annoying stop-and-go, but no one gets home any faster. In fact you can prove that you and everyone behind you get home strictly later than if you had just gone along with the stop-and-go traffic.

The facts
Here’s how traffic works. First, we know from empirical studies that drivers tend to maintain a minimum following distance, measured in seconds. It varies per driver, but typically it’s somewhere between 1.5 and 2 seconds. That works out to a maximum theoretical flow rate of between 1,800 and 2,400 vehicles per lane per hour passing by a given point on the highway. Studies of actual highway traffic have measured flow rates as high as 2,000 vehicles per lane per hour, which works out to a following distance of 1.8 seconds. (I’m just going to call it 2 seconds for the sake of round numbers.)

The important fact: 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. So imagine you are in heavy traffic during rush hour. There are a certain number of cars in line in front of you. Let’s pick a point on the road to call the front of the line — say, the point at which you plan to exit the highway. The line gets shorter by one car every 2 seconds. If there are 1,000 cars in front of you, it’s going to take a minimum of 2,000 seconds for you to get to the front of the line. It doesn’t matter whether people are kind and let cars merge in front of them, zipper-style. It doesn’t matter how much stop-and-go there is. The simple fact is that it takes 2 seconds per car for you to get to the front of the line, and there are some cars in front of you that have to get there before you do.

Merging
Say there are some cars that are trying to merge into your lane a mile or so in front of you. Every time a car merges in, that adds 2 seconds to your trip. If one car merges in every 2 seconds, your trip gets longer by 2 seconds every 2 seconds, which means you are not moving (or will soon not be moving).

Leaving space in front of your car for people who are trying to merge won’t solve anything. Let’s say you slow down to leave some room for an upcoming merge. Now you are 4 seconds behind the car in front of you instead of 2. You’ve just added 2 seconds to the commute of everyone behind you in line. Now a car merges in front of you. At the next merge, you have to leave more space. That’s another 2 seconds for everyone behind you. There is no “simple cure” for this!

If anyone tries to tell you that if only drivers left space in front of them and took turns merging, traffic would flow smoothly, and it’s only because of jerks that there are any traffic jams at all, just ask them what’s going to happen at the next merge. Where is that extra space going to come from? You cannot keep 2 seconds back from the car that has just merged in front of you without, um, slowing down. If the car in front of you is also slowing down for the same reason, you have to slow down even more. This is basically the definition of a traffic jam.

Zipper merging is only beneficial insofar as it reduces confusion on the road, the way any convention does — like who gets to go next at a 4-way stop. Confusion leads to delay, delay leads to anger, etc., etc....MORE
Also at AGAAS:
A Frequentist Approach to Probability