Question: Vehicles arrive at a single toll booth beginning at 8:00 A.M. They arrive and depart according to a uniform deterministic distribution. However, the toll

Vehicles arrive at a single toll booth beginning at 8:00 A.M. They arrive and depart according to a uniform deterministic distribution. However, the toll booth does not open until 8:10 A.M. The average arrival rate is 480 veh/h, The toll booth attendant interacts with each vehicle for 6 seconds. Assuming D/D/1 queuing. (1) When does the initial queue clear? (5 pts) (2) What is the total delay? (5 pts) (3) What is the average delay per vehicle? (5 pts) (4) What is the wait time of the 100th vehicle (assuming first-in-first-out)? (5 pts) (5) If vehicles arrive at the toll booth according to the function (t) = 15.2 - 0.20t, where (t) is in vehicles per minute and t is in minutes. What the longest queue length (in vehicles)? (10 pts) (6) Let the average arrival rate be 480 veh/h and Poisson distributed from 8:00 A.M. What is the average length of queue (in vehicles), and average waiting time in the queue assuming M/D/1 queuing? (10pts)

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