5. A fast-food restaurant has one drive-through window. An average of 10 customers per hour arrive at the window. It takes an average of 3 minute to serve a customer. Assume that interarrival and service times are exponential and the waiting space is unlimited. (a) (5) What does "M/M/1 mean? (b) (3) What is the definition of a Birth-Death process? (c) (2) Let T denote the interval time between two consecutive arrivals. Calculate P(T>0.02). (d) (2) Calculate P(T>1.02 | T>1). (e) (3) Give the state diagram for this queueing system. (f) (5) We know that Ij = (1-P)p'. Derive the formula for the expected number of cars waiting before service (not including the car being served at the window). (g) (3) On the average, how long does a customer spend at the restaurant (from time of arrival to time service is completed)? You can directly apply the formula we derived in class. (h) (3) What fraction of the time are more than 2 cars in the drive-through line (including the car being served at the window and the cars waiting)? (i) (2) If the arrival demand is increased by 50%, how will the answer in part (g) be changed? () (2) If the original arrival demand (10 arrivals per hour) is decreased by 50%, how will the answer in part (g) be changed