Grid Layout of Parking Population Modeling

A set of Stores arranged in a line
Each parking row is parallel to the line of stores
Each row has the same number of parking spaces as there are stores
The preference of each customer is assigned uniformly randomly

The parameters considered in the model are:

The arrival rate of cars
The departure rate of cars
The strategy used by each car to choose the parking space depends on its proximity to the store of preference.

This graph shows a parking lot as a 10x10 grid where cars arrive with a Poisson probability distribution with mean of 10. There is no departure. The cars arrive and have a favorite column to park in which is linked to the preference of the store that the driver chooses. This is a Depth First Population model

DFP with no departure

Average Distance Summary:
  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.00    2.00    5.00    4.95    8.00   10.00

The cars now arrive and fill up with a Breadth First approach

BFP with no departure

Average Distance Summary:
 Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.00    2.00    5.00    4.95    8.00   10.00

If the rate of departure is similar to the rate of arrival:

DFP with Same Departure Rate as Arrival - Poisson Arrival with mean 10

Average Distance Summary:
 Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   3.000   6.000   5.616   8.000  10.000

BFP with Same Departure Rate as Arrival - Poisson Arrival with mean 10

Average Distance Summary:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   3.000   5.000   5.336   8.000  10.000

The models now consider a fixed rate of departure (1/10).

DFP width Fixed Departure rate (1/10) and Poisson Arrival with mean 10

Average Distance Summary:
  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.00    3.00    6.00    5.72    8.00   10.00

BFP with Fixed Departure rate (1/10) and Poisson Arrival with mean 10

Average Distance Summary:
 Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   4.000   5.831   5.709   8.000  11.660

DFP with Fixed Departure rate (1/10) and Poisson Arrival with mean 100

Average Distance Summary:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   3.000   6.000   5.521   8.000  10.000

Observations

The results, while considering only a 10x10 grid, show that the average distance to the store of preference is greater when the drivers park using a Breadth First model than a Depth First model.
Under the assumptions of this model (uniform distribution of store preferences, distribution of arrivals...) the results show that when designing a parking lot, it appears that it would be more beneficial to lay the parking spots in a column style facing the stores rather than in a line.

Implementation

The model is implemented using the R language and is available here.

Last modified: Wed Jul 11 18:37:44 MDT 2007