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End of the Cycle

1. Vehicles arrive at an approach to a pretimed signalized intersection. The arrival rate over the cycle is given by the function v(t) = 0.22 + 0.012t [v(t) is in veh/s and t is in seconds]. There are no vehicles in the queue when the cycle (effective red) begins. The cycle length is 60 seconds and the saturation flow rate is 3600 veh/h. Determine the effective green and red times that will allow the queue to clear exactly at the end of the cycle (the end of the effective green), and determine the total vehicle delay for this approach over the cycle (assuming D/D/1 queuing).

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2. At the start of the effective red at an intersection approach to a pretimed signal, vehicles begin to arrive at a rate of 800 veh/h for the first 40 seconds and 500 veh/h from then on. The approach has a saturation flow rate of 1200 veh/h and an effective green of 20 seconds, and the cycle length is 40 seconds. What is the approach’s total vehicle delay two full cycles after the 800-veh/h arrival rate begins? (Assume D/D/1 queuing.)

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