Ivars Peterson's MathTrek
If the lot is really jammed, you take the first spot that you can findno matter where it is or how inconvenient it might be.
At other times, you might seek a spot that keeps the distance you have to walk to the mall entrance to a minimum or cuts down the amount of driving that you have to do to find a spot (or a combination of the two, represented by the total time it takes you to reach the mall's front door).
In one approach, you enter the parking lot, select a row near the lot's fringe where you entered, and take the first open space.
Alternatively, you could gamble by driving to the row nearest to the mall entrance to look for the closest open space. If there isn't an open space in the first row, you "cycle" to the next adjacent row and take an open space, if one is available. Otherwise, you return to the first row and again look for the closest open spot.
Several years ago, C. Richard Cassady of Mississippi State University and John E. Kobza, then at Virginia Tech, compared the two strategies: "park and walk" versus "cruise the lot." Their study appeared in the journal Transportation Science.
Cassady and Kobza used a probabilistic approach to evaluate the two space-seeking strategies, treating driver decisions and parking space availability as random experiments in a "typical" parking lot (four entries, seven rows with 72 spaces each, handicapped parking, employees spaces, shopping cart return locations, and directional restrictions).
The researchers considered three performance measures of what constitutes a "good" parking spot: the total walking distance between the space and the mall's front door (including distance walked to the door, back to the car after the shopping trip, and to return a shopping cart), driving time in search of a space, and the amount of time to reach the front door after entering the lot.
Their comparison showed that, in their model, the "park and walk" approach takes an average of 61 seconds, from entering the lot to reaching the mall entrance, whereas the "cycling" strategy requires an average of 71 seconds. The first approach usually involves more walking, but you tend to get to your shopping faster.
So, to save time at the mall, "park and walk" works bestmost of the time.
Copyright © 2005 by Ivars Peterson
1998. Finding a parking space can be a science, operations research study shows. Institute for Operations Research and the Management Sciences news release. March 22. Available at http://www.informs.org/Press/ParkingScience.html.
1998. Researcher advises: To save mall time, park at walk. Mississippi State University press release. April 1. Available at http://www.msstate.edu/web/media/detail.php?id=489.
Cassady, C.R., and J.E. Kobza. 1998. A probabilistic approach to evaluate strategies for selecting a parking space. Transportation Science 32(January):30-42. Abstract available at http://portal.acm.org/citation.cfm?id=767678.768139.