A model of parking at the mall

Kate Anderson,

Chris Fowler

Ryan Muldoon

Intent: To examine parking behavior of shoppers weighing a desire to park near the mall against the costs (in time) of searching for a spot to park.

Basic Model:

Description: This is the most basic implementation of our model. Agents are homogenous in their parking strategies (threshold is set by the user) and all of them have complete information on the number of cars ahead of them and the number of free and full parking spaces. The points of greatest interest are how changing the strategy (threshold) alters the total cost of the experience (driving time + walking time + regret over walking past empty parking spaces)

Space: Linear, there are 20 parking spaces, if a shopper gets to the closest spot and it is taken she must return to the back of the parking lot. There is only a single lane, so drivers cannot advance when the driving lane ahead of them is blocked. Cars pulling out of the parking spaces must drive to towards the mall before exiting and returning to the furthest point in the queue as a new shopper.

Time:  Synchronous: Each car makes its decision about parking conditions at exactly the same moment

 Asynchronous: Actual implementation of the moves is done asynchronously and in random order to arbitrarily decide outcomes of potential collisions.

Agents: Genetically homogenous, heterogeneous in their experience of the world based on their different states (moving, parked, leaving), and on their position (positions 1-20 in the driving lane or parking spaces 1-20)

Decision Structure:  See below

Parameters tested for robustness:

• Number of cars (0-20) 
• Threshold (0-1)

Criteria for judging outcomes:

• Average distance to Mall
• Average time to park
• Trip Cost =
• Time spent driving * dislike of driving

• Time spent walking * dislike of walking

• Regret (number of empty spaces passed while walking to the mall * dislike of walking)

Model

The model can be run from the applet below. Begin by pressing the "setup" button, then press "go"

The mall is assumed to be at the right edge of the screen, the yellow strip is for parking and the white strip is the lane in which the cars drive. Cars that are looking for a space are colored red, cars looking to exit the lot are colored blue.

Parameters: Modify the threshold, a higher threshold means that cars will be more likely to try for a spot closer to the front, a low threshold means they are more likely to settle for the first open spot they see.

Outcomes:

The model behaves largely as expected. With complete information about the availability of spaces drivers are relatively successful
at finding parking spaces close to the front.


Parameter tests confirm that this behavior is robust across the range of traffic (1-20 cars) and across a range of thresholds.

Figure 2: Model Outcomes with changing values for threshold and number of cars.

Note that the threshold value is relatively unimportant when there are fewer cars in the parking lot. Because there is so little traffic the
decisions that would require a threshold test are rarely used. It is only when the number of cars in the model rises that the threshold
becomes an important determinant of disutility
Also note that cost is minimized (and therefore utility is maximized) for a threshold value of approximately .4. This is a relatively low
risk threshold.

Continue to Examine Model II