6 electric car charging points have been installed at a service station on a busy motorway. It is estimated that 1,200 vehicles pass through every hour, and that around 3% will stop to charge.

Each customer takes an average of 20 minutes to charge their car, pay and then free up the space for the next customer. If all six bays were taken, the customer would park his car behind an occupied bay and wait until it was free (the customer would not change bays while waiting). If all 6 bays and the 6 waiting spaces behind each bay were taken, a new customer would charge his car at another service station.

Part 1. Calculate the use of the charging points, the average number of cars in the station (charging or waiting to be charged) and the average time a car spends in the station.

Part 2. We would now like to reorganize the kiosk space to accommodate a single queue. Consequently, if all six terminals were taken, a new customer would wait in a queue until a terminal became available. However, the queue could only accommodate a maximum of 3 cars.

Recalculate the use of the terminals, the average number of cars in the station (charging or waiting to charge) and the average time a car spends in the station.