The Mathematics of Parking Cars

Update: the graph now has a description

The beauty of mathematics is that if you think hard enough, you can apply it to nearly anything. And this especially goes for parking spaces.

Here's one awesome way to lay this out:

We will assume that the street is long enough to enable a parallel parking of many cars. Moreover we assume that there are no driveways or side streets in the segment of interest and that the street is free of any kind of marked parking lots or park meters. So the drivers are not biased to park at some particular positions. On the contrary: they are free to park the car anywhere provided they find and empty space to do it. In addition we assume that there are no cars parked permanently on the street (i.e. we assume that the majority of the cars leaves the street during the night).

The standard way to describe such random parking is the continuous version of the random sequential adsorption model known also as the “random car parking problem”...

It turns out by assuming equal car lengths and non-overlapping parking (apparently this needs to be laid out clearly) or other clearly defined assumptions, numerous mathematicians have done some pretty complicated mathematics (even using ideas from theoretical gas models) to understand the distribution of the distances between cars. Some scientists have even gathered empirical data on this, by examining parked cars in London. And equations can indeed be constructed that fit what we see in the real world:

Ultimately, there is a lot of math that can be, and has been, applied to this problem. And maybe it has some policy implications for urban planners. But even if not, rest assured: math can explain many more aspects of society than you ever thought possible.

Top image: Chelsea Oakes/Flickr/CC