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Monday, September 23, 2019

Parking Your Car

     Two physicists, Paul Krapivsky of Boston University and Sidney Redner of Santa Fe Institute, recently published an article in the Journal of Statistical Mechanics where they took a look at a classic optimization problem...parking you car. 
     When you pull into a parking lot and want to minimize the time you spend in the parking lot should you park in the first spot you come to or drive to the door and hope to find a spot near it? 
     Obviously, the parking place by the front door is ideal...unless you have to circle the parking lot several times to get it. In order to reduce the time spent driving around the lot and walking across it, what’s the best strategy? “Mathematics allows you to make intelligent decisions,” Redner says. “It allows you to approach a complex world with some insights.” 

A) Meek strategy - grab the first space available You don’t waste any time looking for a spot 

B) Optimistic strategy - gamble on finding a space right next to the entrance.  With this strategy you drive all the way to the entrance hoping to find a spot near the entrance. If you can’t find an empty parking space you circle around to the closest empty spot. 

C) Prudent strategy - drive past the first available space, betting on the availability of a closer space. When you find what looks like a reasonably close space you take it. If no spaces exist between the furthest parked car and the entrance, prudent drivers circle back to the space a meek driver would have taken right off. 

    Discounting all the mathematical observations which strategy is best? Overall, the meek strategy is inefficient because it causes you to have to make a long walk to the entrance. The optimistic strategy is next. If you’re lucky you get a close spot and a short walk...if not you end up wasting time circling. Overall the prudent strategy costs drivers the least amount of time. 
     As the authors pointed out, their study didn’t take into consideration all the variables such as how fast people drive and walk, the actual designs of the parking lot and spaces and the realization that every parking situation is different.  Of course, some people would rather park farther away and walk a bit rather than circle the lot for five minutes looking for a space close to the door.

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