Three Takeaways from Spacemaker’s Parking Research

Spacemaker Team
Spacemaker Team March 19, 2020 4 min read

There are over 1 billion cars in the world today and, according to the International Energy Association, this number will likely triple by 2050. At the same time, real estate prices in major cities continue to climb, making the necessary construction of new places to park prohibitively expensive. With this in mind, how can we design parking lots to take up as little space as possible? Spacemaker’s research team has been looking into the problem and came across some surprising insights.

1. One way access lanes are more efficient

Many parking lots have two access lanes between every parking column: one for each direction of travel. Cars in this configuration can only turn into bays on their right hand sides, or they can interfere with traffic traveling in the opposite direction. But if access lanes were only one-way, we would only need one lane between parking columns. Cars could turn into bays on either side without colliding with another direction of traffic. This means savings in efficiency, or the required area per parking bay. You can see an example of these two layout schemes and their associated space requirements in the figure below. Parking bays are drawn in blue, and the path of cars through the lot is drawn in grey.

Two way lots require more area for the same number of bays than one way lots. These plots break the total number of bays in each configuration into the product of the number of columns (along the x axis) and the bays per column (along the y axis).

2. Efficiency is highly sensitive to bay angle

Parking bays don’t have to be set at right angles, as in the plot above. We often can get better efficiency if we set them at a smaller angle. We can see an example of this approach below.

Example of a 70m x 40m lot with bay angle of 50⁰. Note that the right side of each parking column has missing bays, as these would be inaccessible to cars turning between access lanes.

The smaller the bay angle, the narrower we can make a lot’s access lanes and parking columns. At the same time, smaller bay angles decrease the number of bays that can fit in a parking column; the best bay angles have to balance these two competing space requirements. This much is pretty intuitive. But as one of their more subtle consequences, bay angles also influence where cars can turn between access lanes.

Car turning path approaching the last bay in a column. Between 80⁰ and 90⁰, the path of turning cars switches from tracking the bay’s top left corner to tracking its bottom left. This influences the amount of space at the top of the lot that must be reserved for turning as well as the number of inaccessible bays on the right side of each parking column, affecting overall efficiency.

The figure above shows the path of a turning car around the last bay in a parking column. We want this path to pass as close to the bay as possible, or we’ll use up unnecessary space. As we can see in the figure above, for smaller bay angles, the turning path tracks the back left corner of the top bay in the column, while larger bay angles are governed by the front left corner. This discontinuity means that the area requirements for a set of bays depend on the bay angle in a highly idiosyncratic way. You can see this erratic function in the plot below.

Number of bays possible in a 50m x 50m lot. Although it is not convex, the function has a limited number of local maxima. Experiments show that a standard golden section search after dividing the search space into 50 partitions is usually sufficient for finding the global optimum.

Although the irregularity of of this function makes it hard to find a globally optimal bay angle, there are few enough local maxima that a modern laptop can still find the best angle within milliseconds.

3. Split lots allow for arbitrary entrances and exits

Lots that direct cars around a series of parallel parking columns work best when entrances and exits are at the corners of the lot, like the examples above. But a minor tweak to the same parallel column layout also facilitates entry along the sides of the lot: just split the lot into two sub-lots. Take a look at the example lot below.

Middle entry for 60m x 40m lot. Both left and right sub-lots, after rotation, can be seen to have entrances at the lower left corner and exits at the top right. An exit lane at the top of the right sub-lot connects the sub-lot’s exit to the global exit.

The left side is a sub-lot of parallel columns with standard entrances and exits. So is the right side: it’s just rotated 90 degrees to the right. Similar transformations allow us to put entrances and exits anywhere at along the boundary of the lot, wherever the traffic conditions of the area demand them.

These observations just scratch the surface of what we can learn from Spacemaker’s parking model. For more details about the project, check out out the full paper here.

Sam is a data scientist at Spacemaker. He works with architects on mathematical modeling and holds a degree from Yale in Computer Science.

Karoline is a data scientist and the Office Lead in Spacemaker’s Boston Office. She works with predictive models and mathematical optimization. She holds a Master in Business Analytics from MIT’s Operation Research Center.

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