A retail bank has a drive-through service with a single drive-through teller window. On Friday mornings, customers arrive at the drive-through window according to a Poisson process, with an average inter-arrival time of 2 minutes. Service at the drive- through window is provided at an average rate of 40 customers per hour and follows an Exponential distribution. a. What is the probability that there is no more than one customer in the system at a given point in time? (2 marks) b. On average, what is the total length of time a customer spends in the system? (2 marks) c. On average, what is the total length of time a customer spends in the queue? (2 marks) d. On average, how many customers are in the system at a given point in time? (2 marks) e. Briefly describe the long-term behaviour of the queueing system. (2 marks) A retail bank has a drive-through service with a single drive-through teller window. On Friday mornings, customers arrive at the drive-through window according to a Poisson process, with an average inter-arrival time of 2 minutes. Service at the drive- through window is provided at an average rate of 40 customers per hour and follows an Exponential distribution. a. What is the probability that there is no more than one customer in the system at a given point in time? (2 marks) b. On average, what is the total length of time a customer spends in the system? (2 marks) c. On average, what is the total length of time a customer spends in the queue? (2 marks) d. On average, how many customers are in the system at a given point in time? (2 marks) e. Briefly describe the long-term behaviour of the queueing system. (2 marks)