Parking Perplexity

Article by Davis Jacobson

Who wants to waste time walking if you could just drive? If only there were a perfect way to find a parking space in a big lot….

Spoiler alert: There isn’t! But there are glimmers of ways that are reliably not as bad as the worst you could do! It turns out that this problem fits within a category called sequential search problems, and there has been a bit of study. I’ll touch on that at the end.

First, should you even care?

It’s not like it costs anything. Right?

One-Car Garage, a large parking structure with only one vehicle in it.

One-Car Garage, by O Paulson
(License Asserted CC BY 2.0 as of 2-20-2013)

Suppose I’m a typical working suburban family who drops off kids at school, does a little grocery shopping, goes to two jobs, what have you, and parks a car on average three times per workday for about 220 workdays per year.

Average fuel consumption of idling passenger vehicles is about .6 liter of fuel per hour per liter of engine displacement. (Idling is not much different from cruising around a parking lot.) Let’s just guess a 2-liter engine is fairly typical for passenger vehicles. (Being American, I’ll convert to US dollars and “customary units.”) At today’s price of $4.19 per gallon, that’s $0.22 to park a car if finding a space takes 10 minutes.

That’s 660 parking spaces per year, or 110 hours and $145 in fuel cost per year of parking convenience.

Or Is It? 

Turns out, I might be spending over 28 of those daily minutes and 139 of those yearly dollars for no advantage at all — or quite likely even a penalty. Am I wasting the very time I hope to save by looking for good parking spaces?

I just Google-Earthed the parking lot at the local grocery store: it’s almost exactly 400 feet from the store entrances to the worst parking spaces on the lot. At a typical adult walking speed of 4 feet per second, that’s about 3 minutes and 20 seconds walking both ways from the worst space to the door. I’m no mathematician, but I don’t see how it makes sense to spend more than half that time looking for a better space — assuming I get the average space over time. (Half is where I’ve spent the same amount of time driving that I can hope to save walking between the best and worst parking spaces.)

But Wait! There’s Less!

But I don’t get the average space. I get better than the average space.

According to the article I cited, parking lots typically fill to about 35% capacity, but I’ve observed that parked cars tend to be a bit scattered out, leaving good spaces between. I’m going to guess that on a typical trip, I might be able to save myself something like half the time it would take to walk from the space that’s only half as bad as the worst space on the lot if I find a pretty good space some of the time.

Therefore, I don’t think it makes sense to spend more than 25 seconds looking for a better space than the first one I see — about 4% of the time drivers routinely spend looking for parking spaces. I’ve often waited longer than that to turn around at the end of the aisle. So what’s the point?

On the stated assumptions, I’m simply wasting more than 105 hours per year parking my car.

But Still.

You might get lucky. You wouldn’t want to not look, right? I look. So what’s the best way?

I did happen across a paper in which 7 strategies were studied using computer models: Car Parking as a Game Between Simple Heuristics (Hutchinson, Faneslow, and Todd, 2012).

Real mathematicians with serious computing power. What do they conclude? Nobody knows the best way to park a car. Too many variables. But

 Nevertheless, our idealized model system proved illuminating when assessing other plausible sorts of simple parking heuristics. All could give rise to [states in which no variant strategy could do better] yielding a similar mean performance and distribution of parked cars; but when we allowed different heuristics to compete, a mixture of the fixed-distance and linear-operator heuristics consistently prevailed.

In English.

The parking strategies that do best amount to going down one side of a parking aisle, taking a good space if one presents itself (with some bias for early selection depending on how many spaces are already full), and else turning around at the end and taking the first space that presents itself.

Like I said, it’s not the worst you could do — and think how less stressed you’ll be if you just take what you can get and get on with your life. And the sooner you’re out of the lane, the sooner the person behind you can park. Just imagine if the guy in front of you were doing it that way.

Would you like to spend less money and be less exasperated for the “cost” of better physical fitness? I would.

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One Response to Parking Perplexity

  1. Paul Smith says:

    Is this an American thing? Here in the UK we just park. In the first available slot. The parking garage (as you would call it) usually fills up near to the entrance first but spiral round a couple of floors and there are usually spaces galore. I go there. The only problem is often having to wait behind someone who has stopped to let someone out just so they can nab their space.

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