## Sunday, August 5, 2007

### Highway Exit Numbers: When Simple Was Too Simple

Originally, exit numbers were sequential. So if a highway had 200 exits, they would be numbered 1 to 200. From the motorist’s point of view, it could not have been simpler.

But when a sequentially numbered highway needed a new exit, the scheme’s simplicity went from asset to liability. For example, if a new exit was being added between exits 20 and 21, would the former exit 21 become 22? And would the former 22 become 23? And so on. Given the cost in dollars and confusion, renumbering all the exits from a new exit forward was not an option.

What to do? “Hmmmm, a new exit between 20 and 21....Let’s call it 21A!” And so it was, until another exit was needed between 21 and 21A. On the New York State Thruway, the solution was to go with the sequence 21, 21B, 21A, 22. (If you are asking yourself whether you read that correctly, you did.)

This kind of situation led to the rise of distance-based numbering, where the exit numbers are the same as the highway’s mile markers. Example: Exit 21 would be 21 miles from the highway’s numbering origin. This handles the problem of new exits better than the sequential scheme because a new exit will usually have an unused number waiting for it.

But what if a new exit is within the same mile marker as an existing exit? From the Wikipedia article:

If two exits would end up with the same number, the numbers are sometimes modified slightly; this is often impossible and exits are given sequential or directional suffixes, just as with sequential numbers.

So in a worst-case scenario, exits that are too close together get sequential numbers or letters tacked-on to their distance-based numbers. This is still better than the original sequential-numbering scheme, because the ugliness involved with changing sequential numbers is contained to a few exits at a time.

However, the distance-based system does have an Achilles’ Heel: If a highway’s origin changes, all the mile and exit-number signs would need to change. Although this situation would be as bad or worse than a renumbering caused by a new exit in a sequential-numbering system, it is far less likely. That’s because, out of all the places a new exit can be, it needs to be at the beginning of the highway to disrupt the distance-based system. In contrast, a new exit any place other than the end of the highway would disrupt the sequential system.

So, distance-based numbering is not a perfect solution, but it is a better one. Sequential numbering’s simplicity assumed no change to the system being numbered. When that assumption was violated, sequential numbering proved too simple to adapt. As a result, most U.S. states now use distance-based numbering for interstate highways.

[The image is from Wikipedia’s “Exit number” article, as are other examples below except where noted.]