A small parking lot has room for four cars. The cars arrive according to a Poisson process with a mean rate of 7 per hour. If an arriving driver sees the lot is full, he or she will not wait, but will park at another, less convenient, lot. The time cars spend parked in the lot is an exponential random variable with a mean of 30 minutes. Decide on an appropriate interpretation of N(t) and draw a rate diagram, for this lot below. Be sure to clearly identify all rates.

A small parking lot has room for four cars. The cars arrive according to a Poisson process with a mean rate of 7 per hour. If an arriving driver sees the lot is full, he or she will not wait, but will park at another, less convenient, lot. The time cars spend parked in the lot is an exponential random variable with a mean of 30 minutes.

1. Decide on an appropriate interpretation of N(t) and draw a rate diagram, for this lot below. Be sure to clearly identify all rates.

Determine the long-run steady state distribution for this queueing system. State your answers rounded to three decimal places. You may use MS Excel or MatLab, but not QTS, for this part. If you do this by hand, show your calculations here. If you use a computer, be sure to state your answer here and include the file with your submission.

Determine the average number of cars in the lot, expressed to the nearest hundredth of a car.

Determine the expectation of the number of cars that will enter this lot per hour, expressed to the nearest hundredth of a car.