The city of Aarhus is considering the deployment of electric battery charging stations across the city, such as to promote the use of electric cars to mitigate air pollution. Each charging station has 3 charging points and each charging point can accommodate 1 vehicle at a time. The time it takes to charge a vehicle is exponentially distributed with an average time of 20 minutes. After the charging is completed, the point is made available to the next vehicle. The arrival of vehicles to a charging station follows a Poisson process with a rate of 6 vehicles per hour. If upon arrival a vehicle finds all stations busy it waits in an adjacent parking lot. The system to analyze comprises of the vehicles which are currently being charged at the station and the vehicles that are waiting for their turn. Vehicles that are waiting for their turn, are served on a first-in-first-out manner (i.e., first-come-first-serve). For each of the below questions, please justify your answers, i.e., explain your reasoning. (1) (5 points) What type of queueing system is represented here? Use Kendall notation to classify it. (2) (5 points) Define the state transition diagram for this system. Clearly define any notation used. (3) (7 points) What is the probability that upon arrival a vehicle has to wait in line? Give an analytical and a numerical answer (write down the equation first, then solve it). (4) (8 points) What is the probability for the single event of having 3 vehicles arriving between 8:00am and 8:15am and 5 vehicles arriving between 8:15am and 8:30am? Give an analytical answer and a numerical answer.