Adequacy Analysis

Over the course of an 8-hour day, 96 vehicles enter a local electronics store’s parking lot. The parking lot has 5 spaces and the average customer stays in the grocery store for 15 minutes. Calculate the probability that an incoming car will be rejected.

[Solution Shown Below]

Solution

First, we need to calculate the incoming flow rate. This is done as follows:

Q = 96 vehicles/ 8 hours
Q = 12 vehicles/hour

Since we know the average vehicle is parked for 15 minutes, or 0.25 hours, we can calculate the traffic load as follows.

A = Q*T
A = 12 vehicles/hour * 0.25 hours
A = 3 vehicle

Now that we have the traffic load, we can find the probability of rejection using the equation below.

P = (A^M/M!)/(1 + A + A²/2 + . . . + A^M/M!)

Where:
P = the probability of rejection,
A = the traffic load, and
M = the number of parking stalls.

P = (3⁵/120)/(1 + 3 + 3²/2 + 3³/6 + 3⁴/24 +3⁵/120)
P = 0.11

Each entering vehicle has an 11% chance of being rejected. As a result, the electronics store loses one out of each 10 customers entering their lot.