Richardson Municipal Airport has two runways, A and B. In the morning of UTD Founders Day, both runways serve landing flights. When a flight approaches the airport, it radios the control tower and requests permission to land. The air traffic controller responds instantly by assigning the plane a position in queue on a first-come-first-serve basis. The time between two successive landing requests is exponentially distributed with an average of 5 minutes. Each runway can serve 12 flights per hour and the time it takes for a flight to land is deterministic. a. (8 points) On average, how much time elapses between a plane's radioing of the control tower and its eventual completion of the entire landing process in the morning of the first day of school at UTD? Prepare for VUT calculation (fill in the blanks, no need to show calculation): a (average inter- p (average m (number u (average CV. (coef. of CV (coef. of arrival time) service time) of servers) utilization) var.- arrival) var.- service) Show VUT calculation and final answer to the question: b. (4 points) On average, how many planes are circling above the airport waiting for landing? In the evening, airplanes leave Richardson from the airport. There are two types of planes. One is the commercial planes serving residents in Richardson area. The other is the private planes dedicated to UTD students. Commercial planes use runway A and the time between two requests is exponentially distributed with an average of 4 minutes. Meanwhile, private planes use runway B. and their takeoff requests come as a Poisson process at a rate of 15 per hour. The time it takes to take-off is 3 minutes on average for both type of flights, and follows an exponential distribution. All planes have a waiting cost of $600/hour. Hint: The inter-arrival time of a Poisson process (with rate 2.) follows exponential distribution (with mean 1/ 2). Conversely, a process is Poisson if the inter-arrival time follows exponential distribution.c. (8 points) What is the average delay cost per commercial plane? Prepare for VUT calculation (fill in the blanks, no need to show calculation): a (average inter- p (average m (number u (average CVa (coef. of CVp (coef. of arrival time) service time) of servers) utilization) var.- arrival) var.- service) Show VUT calculation and final answer to the question: d. (5 points) If the airport pools the runways (i.e., use both runways to serve both types of planes), how much waiting cost can be saved for each commercial plane and each private plane, respectively? Hint: The inter-arrival time of two combined Poisson process (with rates ) and 12) follows exponential distribution (with mean 1/ (21 + 22))