Are you the person who parks in the first open space you find, or the person who tries to find the space closest to where you’re going? Turns out both of these methods are inefficient ways of navigating a parking lot — and there’s a mathematically better option.
As Jennifer Ouellette explains, in Ars Technica:
Paul Krapivsky of Boston University and Sidney Redner of the Santa Fe Institute decided to build their analysis around an idealised parking lot with a single row (a semi-infinite line), and they focused on three basic parking strategies. A driver who employs a “meek” strategy will take the first available spot, preferring to park as quickly as possible even if there might be open spots closer to the entrance. A driver employing an “optimistic” strategy will go right to the entrance and then backtrack to find the closest possible spot.
Finally, drivers implementing a “prudent” strategy will split the difference. They might not grab the first available spot, figuring there will be at least one more open spot a bit closer to the entrance. If there isn’t, they will backtrack to the space a meek driver would have claimed immediately.
After doing the maths, the two physicists came up with this conclusion:
Entering from the back of the lot and parking in the first spot you see is inefficient because it requires a lot of walking.
Trying to find the best possible spot is inefficient because it requires a lot of driving.
Driving towards the entrance, skipping any open spots at the end of the row and parking in the first gap between cars minimizes both your driving and your walking time.
Don’t believe me? Here’s a visual:
Why does this strategy work? Krapivsky and Redner explain it in terms of how molecules attach to microtubules, but here’s a version the rest of us can understand:
When you drive into a parking lot (assuming you’re approaching from the back), you’ll pass a bunch of cars parked in the first spot they found.
You can drive to the front of the lot and look for the best spot, but that wastes time.
Instead, look for the first open space between the existing parked cars. These are the parking spots that neither the “meek” nor the “optimistic” drivers consider, which means they are the most efficient option for the “prudent” driver.
Of course, these types of mathematical problems don’t always translate well to the real world (and it’s worth noting that this particular model imagines a parking lot that consists of a single straight line, instead of the circular or rectangular structures that more often exist). Sometimes you want the best possible spot because of weather, or because you or your passengers can’t walk long distances. Sometimes every single parking space is full, and your only option is to circle the lot until something opens up. Sometimes you’ll grab a space in the first gap you see and walk past several better spots that you could have taken.
But if you’re looking for a quick parking strategy that can save time on walking, driving, and asking yourself whether it’s better to park in the first available spot or circle the lot for a better one, this tip could work often enough to make it worth it.