It's Saturday afternoon and you have a few errands to run at the mall. So, it seems, does everyone else. The mall parking lot is crowded. So, where should you park your car if you're trying to save time – at the first spot you see, no matter how far away from the entrance, or just drive up and down lanes looking for an elusive spot closer in?
There's a Study for That
In a study published in September 2019 in the Journal of Statistical Mechanics, physics professors Sidney Redner (from the Santa Fe Institute) and Paul Krapvisky (Boston University) applied their mathematical prowess to pinpoint the best parking spot search strategies. (Here we define the "best" spot as the one nearest the mall entrance. Some people might favor a spot on the top floor of a parking garage to prevent their car from getting dinged. But that's another story.)
Redner and Krapvisky divided parking personas into three categories: meek, optimistic and prudent.
- "Meek" drivers immediately settle for the first spot they find, which may leave spots near the front unfilled, plus incur a long walk.
- "Optimistic" drivers aren't afraid to hunt, certain that eventually they'll triumphantly land their primo spot, no matter how many times they have to circle the lot to find it.
- "Prudent" parkers are a bit more aggressive that meek drivers, bypassing the low-hanging fruit in hopes of a closer spot, but unwilling to circle several times to get just a bit closer to their destination. They may end up backtracking to a spot a "meek" driver would have claimed initially if they don't find something better immediately.
After identifying their categories, the scientists created a simulation, using processes such as probability theory and rate equations. The researchers found that the "prudent" strategy was the best because it costed drivers the least amount of time, followed by the "optimistic" strategy and then the "meek" strategy.
Redner is quick to point out that this particular exercise is purely mathematical. "We tried hard to minimize the number of free parameters by judicious choices, such as assigning the same speed for walking and driving," he says via email. Of course, they couldn't account for every variable. "The main complication was the inherent many-body nature of the parking process; namely, one doesn't know in advance which spots are free and the game is whether to pick the current spot or try another spot (which may not be open) closer to the destination."
They also omitted real-world variables like driver speed, intense competition for spots or the irrationality of harried human beings.
The Real World of Parking
OK, so that's the mathematical side of the story. But is there a parking lot strategy that better accounts for the quirks of real people?
"It is important to note this simple fact: The success of my parking strategy is, in part, dependent upon which parking strategy the other drivers select," emails Andrew Velkey, an associate professor of psychology at Christopher Newport University in Virginia. "It is an excellent application of Game Theory (e.g. the Prisoner's Dilemma). My 'best' strategy is only better if enough other drivers select one of the other alternative strategies. If everyone tried to play the same parking strategy, it would no longer be optimal."
Velkey notes that most people spend too much time looking for the "closest" spot. Ideal parking spaces (like right in front of your final destination) are usually unavailable.
"Time and perceived scarcity are the two biggest factors that affect parking strategies. People will spend time looking for a parking space and incur a travel-time cost from their vehicle to their final destination after they have parked their car. It appears that people are often attempting to reduce the travel-time cost and often incur a greater acquisition time cost as a result," he says. "It's most interesting to note that people will try to get a parking spot that is closest to the door of the gym/exercise club they are about to enter."
To answer our parking lot question, Velkey referred to a 1998 paper published in the journal Transportation Science "where they determined that the optimal strategy was to randomly pick a row and go to the closest apparent space in the row ('Pick a Row, Closest Space (PRCS)'), rather than driving up and down rows looking for a closer spot ('Cycling')."
In other words, the time saved in finding a spot made up for the longer time spent walking to the front door. It wasn't a huge time savings though. In that model, the expected time to the front door from the spot using the PRCS method was 61.31 seconds; with the Cycling method it was 70.70 seconds.
Velkey says those few times where we do score a spot at the front become very memorable to us. But "perhaps even more memorable are the times when we park our cars and come across a space right in front on our way to the entrance of the destination – we will employ a counterfactual 'if I had only driven around more' process when we notice these spaces we 'missed,'" he says. "As a result, people will over-predict both the likely availability of these spaces and their own likelihood of obtaining these spaces."