Are you the driver in the lot who parks in the first spot you see? Or do you circle around and around looking for a spot by the door? Physicists Paul Krapivsky of Boston University and Sidney Redner of the Santa Fe Institute explored the mathematics of parking. The research required different equations and simulations to model the benefits of the various parking approaches. From EurkeAlert!:
In their paper, Krapivsky and Redner map three simple parking strategies onto an idealized, single row parking lot. Drivers who grab the first space available follow what the authors call a "meek" strategy. They "waste no time looking for a parking spot," leaving spots near the entrance unfilled. Those who gamble on finding a space right next to the entrance are "optimistic." They drive all the way to the entrance, then backtrack to the closest vacancy. "Prudent" drivers take the middle path. They drive past the first available space, betting on the availability of at least one other space further in. When they find the closest space between cars, they take it. If no spaces exist between the furthest parked car and the entrance, prudent drivers backtrack to the space a meek driver would have claimed straightaway.
So which strategy is best? As the name suggests, the prudent strategy. Overall, it costs drivers the least amount of time, followed closely by the optimistic strategy. The meek strategy was "risibly inefficient," to quote the paper, as the many spaces it left empty created a lengthy walk to the entrance.