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 8 veh/min and the average departure rate is 10 veh/min. Assuming D/D/1 queuing, when does the initial queue clear and what are the total delay, the average delay per vehicle, longest queue length (in vehicles), and the wait time of the 100th vehicle to arrive (assuming first-infirst- out)?

Through the Walla Walla Road to the entrance of the E-1 parking lot at the University of Washington, vehicles begin to arrive from 7:40 A.M. at a uniform deterministic rate of 480 vph until 8:20 A.M. and from then on at 120 vph. It takes 10 seconds for a vehicle to go through the paying process at the gate. If the parking lot is open at 8:00 A.M., determine (a) when the queue will dissipate, (b) the total delay, (c) the average delay, (d) the maximum queue length (in vehicles), and (e) the longest vehicle delay under FIFO. Show your results graphically. [Hint: D/D/1 analysis]