If you are like me, you have driven up and down parking lot rows searching for the perfect spot. The seemingly simple task of choosing a spot can actually be stressful when there are so many options and it is hard to decide whether to take the easy-to-pull-into-but-isolated spot far away or the conveniently-located-but-tight spot right by the entrance. Luckily for me, and all other drivers as well, a recent article from Phys.org answered my question of where to park my car. 

The article featured physicists Paul Krapivsky and Sidney Redner, who collaborated in a study to determine where to park your car. The physicists measured the quality of parking spaces by the time they require drivers to spend in the lot, with minimal time being ideal. 

According to Krapivsky and Redner, there are three types of parkers. First, the “meek” parker grabs the first available space, which is often close to the edge of the parking lot and far from the entrance of their destination. Next, the “optimistic” parker gambles on finding a spot right by the entrance. This type of parker will often drive to the entrance, find that there are no spots, and backtrack to the closest vacancy. Lastly, the “prudent” parker takes the moderate route, passing the first available space and taking the closest space between cars.

So which of these strategies minimizes time spent in parking lots? According to their mathematical calculations, the prudent parker is most efficient. 

The physicists solved the meek strategy using microtubules with scaffolding within living cells. According to their report, “a car that parks immediately after the furthest car corresponds to a monomer glomming on to one end of the microtubule. The equation that describes a microtubule’s length—and sometimes dramatic shortening—also described the chain of ‘meek’ cars that accumulate at the far end of the lot.”

Unlike their research for the meek strategy, Krapivsky and Redner solved the optimistic strategy with a differential equation. They found the prudent strategy much more complicated and approached it by formulating a simulation that computed the ratio of the average density of spots to the amount of backtracking required. 

Kaprivsky and Redner admitted that they recognize a margin of error in their study since their equations and experiments do not account for competition between cars. Redner said in his study that there were a few more factors to be considered that would have made the study more conclusive.

“If you really want to be an engineer you have to take into account how fast people are driving, the actual designs of the parking lot and spaces,” Redner said. 

Whether or not the physicists’ finding is particularly helpful to you, their research did reveal that math can have relevant real-life applications.