Hi! I've been dealing with a situation like this for a couple of years now and it made me start thinking...(adsbygoogle = window.adsbygoogle || []).push({});

A city is populated entirely by infinitely logical drivers (I know, it's hypothetical :) .

This city has two major N-lane highways (N > 1) which intersect each other at a traditional interchange (there's one exit lane at the right side of the road). This is a busy intersection and a backup of some length is expected on all lanes.

At any given time, a ratio X (0<X<1) has to transfer from one highway to the other. They have to therefore get into the rightmost lane to exit the highway.

The question is this. Assume that the lanes are numbered from right to left (the exit lane is 1, the one adjacent to it is 2, and so forth up to N).

If you are an infinitely logical driver, which lane do you choose to get to your destination the fastest? There are two cases: (1) you are planning to take the exit ramp, and (2) you are planning to not take the exit ramp.

You may change lanes until you reach the traffic jam, at which point you're more or less stuck in whichever lane you choose (unless you're forced at some point to get into the rightmost lane to exit the highway).

This is trickier than it sounds. Suppose you decide that since everyone is going to be trying to merge into the lane 1 to exit the highway, you want to get to lane N, as far away as possible. The net result is that everyone will jam up in lane N.

What about randomization? Randomization may work, except that you'll need a weighted randomization algorithm to avoid lane 1 or something like that if you're trying to stay on the highway.

For people getting off the highway, an obvious solution would be to use lane 2 and drive by all the people expected to be stalled on 1 until the last minute. Of course, since everyone is logical, then lane 2 will back up.

Any ideas?

ACG

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Traffic lane selection problem

**Physics Forums | Science Articles, Homework Help, Discussion**