# Probability of finding an available spot in a parking lot

A small store has a parking lot with six available spots. Customers arrive randomly according to a Poisson process at a mean rate of ten customers per hour, and leave immediately if there is no place to park. The time a car remains in the parking lot follows a uniform distribution between ten and thirty minutes.

1. What percentage of customers is lost by not having more space available?
2. What is the probability of finding an available spot in the parking lot.
3. What is the average percentage of available spaces?

I ran a one year simulation, getting the following results:

• 87304 customers arrived, but only 75873 were able to park.
• 11431 customers (13.09%) did not find where to park and left the store.
• Average availability: 37.17%

My question is: how do I get the probability of finding an available spot in the parking lot? Is it the same than the average availability?

The probability of a randomly chosen customer finding an available space equals the fraction of all arriving customers that do find a space. From your simulation, this is approximately $\frac{75873}{87304} \approx 0.8691$.