what is the optimal way to find a parking spot?

A paper in Transportation Science exams how to find a parking space using operations research methodologies. Here, Richard Cassady and John Kobza use applied probability models to identify how to find a “good” parking space according to one of three performance measures:

1. (Expected) Total walking distance
2. (Expected) Time to space (ignoring walking distances)
3. Time to door = expected walking distance + time to find a space

They compare two parking strategies:

1. Pick a row, closest space (PRCS): The simple strategy of choosing a row close to the parking lot entrance, and picking the closest available space.
2. Cycling (CYC): a more complicated and aggressive strategy that involves first entering the closest row and parking in the closest of the 20 closest spaces if one is available. If not, the driver proceeds to the next row and chooses the closest of the 40 closest spaces. If one is not available, the driver moves to surrounding rows and selected the closest available space.

To visualize how the analysis in this paper is performed, see the figure on the right that shows one of the parking lot geometries considered in the analysis. The analysis is applied to large, Wal-Mart-like parking lots with multiple entrances. I discuss other parking strategies at the end.

The analysis considers six cases (3 performance measures x 2 strategies), and for each, Cassady and Kobza
use a probabilistic approach “to construct general expressions for the performance measure. The
approach treats the decisions made by the driver and the availability of parking spaces as random experiments. By
conditioning on the outcomes of these experiments, the performance of the strategy can be evaluated using the Law of Total Probability.”

Not surprisingly, the PRCS strategy has a lower time to space, since drivers using PRCS find parking spaces fast. Likewise, the CYC has a lower total walking time, since extra driving time finds spaces that are closer to the front door.

Surprisingly, the PRCS strategy performs slightly better when considering the time to door. That is, the time saved finding a parking spot more than makes up for the extra walking time. In a conversation with John Kobza a couple of years ago, he recommended not to cycle and rather to drive to the front of a row. If a close spot is available, take it. Otherwise, park in the closest available spot in the  next row.

Cassady and Kobza acknowledge that the performance measures considered can be misleading in situations when a parking spot is not guaranteed. They also acknowledge that other issues can be incorporated into the analysis (like taking into account the time pushing a shopping cart over to a cart corral).

Cassady and Kobza  implicitly assume that time spent parking and walking are equally weighted in the Time to Door strategy. I use a variant of this strategy when I parallel park on the street when I come to campus that uses unequal weights. Near campus, decent spots are  not guaranteed, so I sometimes have to walk ~10 minutes to my office door. I try not to cycle in the mornings, but I sometimes cycle to shave a little bit off of my walking time if it is raining or I am wearing heels (the brick sidewalks in Richmond are quite uneven).

How do you find a parking spot?

Citation:

A Probabilistic Approach to Evaluate Strategies for Selecting a Parking Space
C. RICHARD CASSADY and JOHN E. KOBZA
Transportation Science , Vol. 32, No. 1 (February 1998), pp. 30-42