Where you should park your car according to maths

Maths has revealed some of life's biggest mysteries like gravity, the speed of light and motions and space itself. But what if it could be used to help find the optimal car spot at a shopping centre?

It is the classic car park conundrum, do you go for the closest space but you might have to wait, quickly park further out and walk a while to get in, or settle for something in-between.

Physicists Paul Krapivsky of Boston University and Sidney Redner from the Santa Fe Institute investigated how we choose a car spot and published their findings in the Journal of Statistical Mechanics revealing the most effective way to get the perfect spot.

Krapivsky and Redner saw that there are three key strategies drivers employee when approaching parking at the shops and mapped it out on a idealised, single row car park scenario.

If you are the type of person to grab the first spot available, this is called the meek strategy. You waste no time looking for a parking spot, because it is more import for you to get into the shops as soon as you can to maximise shopping time.

If you are the type of driver who takes the gamble on finding a spot right in front of the entrance, you follow the optimistic strategy. You will drive straight to the entrance to find a spot but then will proceed to backtrack to the closest free park.

Those who employ the prudent strategy are drivers that take the middle path. You tend to drive past the first available space you see, betting on the availability of at least another space closer to the entrance. When you find the closest space between parked cars, you take it. If no spaces exist between the furthest parked car and the entrance, prudent drivers will backtrack to the space a meek driver would have taken first.

As the name suggests the prudent strategy gets the thumbs up from the study. It tends to take the least amount of time, followed closely by the optimistic strategy. While the meek strategy was “risibly inefficient” due to the fact many car spots were left empty meaning a lengthy walk to the shop entrance.

Redner does acknowledge that the above strategies and testing approach does not take into account certain shopping centre car park situations such as competition between cars, or assuming that every car follows the same strategy. These are elements they are hoping to address in the future.

“We’re living in a crowded society and we always encounter crowding phenomena in parking lots, traffic patterns, you name it,” says Redner. “If you can look at it with the right eyes, you can account for something.”

So next time you're fighting the crowds at the shops to get the best parking spot, why not consider some background maths and see if the prudent, meek or optimistic strategy works for you.

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