Space Requirements
A new sandwich shop is nearing completion and a parking lot needs to be designed. The
storeowners anticipate that, on the average 12-hour day, 360 vehicles will visit the
sandwich shop. The owners also anticipate that the average vehicle will remain parked for
10 minutes. How many parking spaces need to be provided in order to guarantee that no more
than 1 vehicle in 50 will be unable to find a parking space?
[Solution Shown Below]
Solution
First, we need to determine the traffic load. The incoming flow rate is calculated as
shown below.
Q = 360 vehicles/12 hours
Q = 30 vehicles/hour
The average parking duration is 10 minutes or 0.167 hours. The traffic load is
calculated as shown below.
A = 30 vehicles/hour * 0.167 hours
A = 5
The maximum probability of rejection is 1 in 50, or 0.02. Using the probability of
rejection equation, we can solve for the number of spaces required.
P = (AM/M!)/(1 + A + A2/2 + . . . + AM/M!)
Where:
P = the probability of rejection (0.02),
A = the traffic load (5), and
M = the number of parking stalls.
Solving the equation for M yields a value of 10. The parking lot at the sandwich shop
must have at least 10 spaces, in order to meet the owners expectations.
Note that we have used average parking rates in this analysis. The sandwich shops
particular situation could dictate that more spaces are required. For example, say that
the shop serves 80% of its customers between 11 A.M and 2 P.M. The majority of the
customers are arriving during a much shorter time frame than the 12 hours that we used to
find the incoming flow rate. In this case, more parking spaces would be required.
|