The lane next to you is more likely to be slower than yours

Saw this link on Hacker News the other day: The Highway Lane Next to Yours Isn’t Really Moving Any Faster

The article describes a phenomenon unique to traffic where cars spread out when they go fast and get more compact when they go slow. That's supposedly the explanation.

There's a much simpler explanation that works for any queue. Let's consider a supermarket checkout with two lines. One of them has a slow worker and will take 10 minutes. The other one has a fast worker and will take 5 minutes. You don't know which one is which so you pick one at random.

With $$ p=1/2 $$ you will pick the slow one, of course. But let's say you go to this supermarket every day for a year. Here's the interesting thing: on average you will spend $$ 2/3 $$ time in the slow queue. So if you sample any point in time where you are standing in line uniformly, with $$ p=2/3 $$ the other line will be faster.



Tagged with: misc, math