Problem 2: Queueing Theory Electric vehicles (EVS) are more and more popular with the concerns of environment and energy sustainability. Unlike a combustion vehicle, an EV typically takes several minutes to be recharged via a DC fast charging point at a charging station. Consider the queue problem at a charging station. Suppose that EV arrive to get recharged according to a Poisson process with an average rate of 5 customers per hour. In addition, suppose that it takes on average 30 minutes to recharge each EV, with a standard deviation of 10 minutes. a. If there are three charging points available, what is the utilization? (3 points) b. If there are three charging points available, how many customers there will be waiting in line on average? (3 points) c. If there are three charging points available, what is the average wait time for customers in the line? (4 points) d. If there are three charging points available, how many customers there will be on average in the charging station (either waiting in line or getting recharged)? (4 points) e. Suppose that the manager of the charging station wants to reduce wait times. To accomplish that, he considers two options: a. Add an additional charging station that has the same charging time as the three charging stations already available. b. Upgrade the three charging stations so that the time to recharge is exponentially distributed with average time 20 minutes, Which option should the manager choose? (6 points)