When you’re searching for a parking space, should you grab the first spot you see or be a bit more daring and look for a spot closer to your destination? In a Journal of Statistical Mechanics paper published in July 2020, Paul Krapivsky, a research professor at Boston University, and SFI Professor Sidney Redner report an idealized model for the optimal strategy to park in the very best spot that’s closest to your destination. The paper was selected by Physics World as one of "The 10 quirkiest physics stories of 2020."
“Our model is of a one-dimensional parking lot, a one-dimensional line, and the destination is off in the distance,” explains Redner. “As you approach, you see parked cars, some empty spaces, and more parked cars. When should you try to snag a parking spot? The optimal strategy is to ignore all open spots until halfway into the lot. Once you get halfway, you should take the first spot available…if you live in a one-dimensional world. This strategy maximizes your probability of actually parking in the best open spot.”
In an earlier paper, Krapivsky and Redner explored strategies they thought were natural, with the same geometry and same situation, but they didn’t have a sense of optimality of strategy. “So we explored some simple strategies and found one was better than another, but didn’t know what we were optimizing,” says Redner. “In our most recent paper, we knew what we were optimizing and developed a strategy that gave us the best outcome for the objective function of maximizing the probability of parking in the best open spot.”
Read the paper, "Where should you park your car? The 1/2 rule" in the Journal of Statistical Mechanics (July 14, 2020)
Read the article in Physics World (December 31, 2020)