Illustration by Julia Harrison

Parallel Thinking

Can painted boundaries tighten up the inefficiencies inherent to parallel parking?

Raise a hand if this urban frustration sounds familiar: Have you ever not been able to find a parking space along a block even though the aggregate of free area between each pair of consecutive cars would provide more than enough room to slot your vehicle?

In other words, there’s sufficient cumulative free space to accommodate your car, it just happens to be divided into a bunch of small, unusable intervals. If you could somehow scrunch the entire caravan into one direction, all that free space would be spat out at the other end, giving you a place to park.

Worse yet, your tormentor remains faceless, since responsibility for this problem lies with no single driver. Each one simply picked an available spot which, unless it was a perfect car-length multiple away from the closest car in front or behind it, invited an unavoidable element of waste into future developments. It’s another example of unsynchronized decisions causing inefficiency.

The urban engineer’s solution to this problem is to impose standardization by chopping the available length into marked units. That way, intermittent arrivals are encouraged to file into the same tightly ordered layout that they would achieve via a synchronized and collaborative group decision. You see this approach in action anywhere that parking spaces have been explicitly demarcated with painted borders:

Painted parking spaces cut down on choice while increasing efficiency.

The implementation of parking borders may seem like a routine organizational tactic, but there are actually subtle trends worth digging into, starting with how large the metered areas should be. In particular, there’s a trade-off between capacity and flexibility as you increase the distance between demarcations. If you paint the lines as close as possible to one another, you will squeeze more spaces out of a single stretch but they will only be accessible to very compact vehicles.

As you increase the length of the parking space, you welcome more variability in the size of vehicles, albeit at the cost of total capacity. Consider the two extremes: a 1,000-ft. block split every foot can fit a thousand cars but only if they’re the length of a shoe box. Slice the same block into 500-ft. halves, and you can dock ships between those painted lines…but only two of them.

What about all the points in between? Well let’s run with that same, theoretical 1,000-ft. block for a bit. First we must know how long a typical car is. The 2017 models of two very popular cars, the Honda Civic and the Toyota Corolla, are 181 inches and 183 inches, respectively. However, the 160-inch Ford Fiesta Hatchback and the 205-inch Chevrolet Silverado 1500 (regular cab) showcase the wide range of available car lengths. For simplicity, let’s assume cars are normally distributed around an average of 15 feet, or 180 inches.

Of course, some buffer space is required for vehicles to maneuver in and out of spaces, so we’ll require a space to be two feet longer than any car that wishes to park there. That’s pretty tight, but here in New York not an inch of curb is left unclaimed. Now that our parameters are set, we can tie together three sliding measurements: the length of the painted parking spaces, how many of those spaces you could make with a 1,000-ft. stretch (referred to as “capacity”), and the proportion of vehicles that would actually fit into one of those spaces (“coverage”):

To get the length of each space, divide the 1,000 feet by the capacity; to get the coverage, use a computer to determine the area of the appropriate normal curve to the left of that length, once the two-foot buffer is removed.

To the far left you see our ship-docking scenario of 100% coverage with single-digit capacity; to the right you see capacity maximized but for cars of unimaginably short length. In between, the graph demonstrates the treacherous exponential decay of the normal curve. One could chop the curb up into 52 individual 19-foot spaces and be nearly assured of never turning down a car on account of its size. Get a little greedy and shoot for 59 individual 17-foot spaces, and suddenly your blueprint rejects over half of potential incoming vehicles. Push any further and your parking lot borders on complete uselessness.

As interesting as the graph is, we really can’t quantify our efficiency gains without knowing how the block plays out without painted boundaries. So let’s simulate it! Without too much difficulty, we can create a mock digital scenario whereby vehicles arrive at a curb and fill in randomly wherever open space still exists. For consistency, we’ll keep the block a thousand feet long, the cars normally distributed around 15 feet in length, and the requirement of needing a foot of space in front and behind. Here’s a printout of the simulator in action:

The simulator speeds up at the end because it has less available space to check.

Run this simulator a hundred times and you’ll get an average of 43.8 cars parked along the thousand-foot curb. Comparing that figure to the above graph shows that the delineated strategy adds somewhere between 10 and 15 more spots to the block’s capacity, depending on how long you cut your painted spaces.

Still, our re-creation is unrealistic. Even though the world of parallel parking can feel like a lawless jungle at times, the reality is that people only randomly pick a parking spot when there is truly an abundance of space. That is, the first handful of parkers to arrive at the untouched 1,000-ft. stretch might pick any old spot, as our first simulator dictates, but once a few starting points have been established, subsequent drivers will likely pick one and align themselves in front of or behind it. The difference is illustrated here:

The question then becomes: how many “leaders” are required for free parking to outpace delineated parking? We can modify the simulator to test this out. Instead of allowing all cars to be randomly placed, we’ll let a select few pick spots and then have subsequent drivers align themselves in front or behind those pacemakers. Starting with a single leader, we can run trials for each incremental increase and watch the capacity shrink as we afford freedom to more and more drivers:

If comparing to first graph, note that “Capacity” here is dependent variable but independent variable earlier.

The block can hold almost 60 cars when drivers follow a single leader. From there, the capacity decreases linearly as we allow more and more cars to pick a spot at random. By the time you let 40 cars pick their spots, the model is barely distinguishable from simply letting everyone choose at random. In summary, having somewhere between five and ten leaders achieves a capacity around 55, which in theory is slightly better than some of the “roomier” delimited approaches near the top of the first graph’s descent.

One thing to note though is that by definition no car is turned away using the leaders method since we haven’t imposed a standard space. So, for example, to match the 56-car capacity of a five-leader system, the delimited model must paint spaces of about 17.9 feet…and also reject around 20% of incoming cars.