# Effective Green

1. An approach with a saturation flow rate of 1800 veh/h has 3 vehicles in queue at the start of an effective red. For the first cycle, the approach arrival rate is given by the function v(t) = 0.5 – 0.005t [with v(t) in veh/s and t in seconds measured from the beginning of the effective red]. From the second cycle onward (starting at the beginning of the second effective red) vehicles arrive at a fixed rate of 720 veh/h. The approach has 26 seconds of effective red and a 60 second cycle for all cycles. How many cycles will it take to have no vehicles in the queue at the start of an effective red for this approach and what would be the total delay for the approach until this happens? (Assume D/D/1 queuing.)

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2. Vehicles arrive at a signal approach at a rate of v(t) = 0.3 – 0.001t [with v(t) in veh/s and t in seconds measured from the beginning of the effective red of the first cycle]. The signal has a 70-second cycle length with 40 seconds of effective red. The saturation flow rate of the approach is 1800 veh/h. What is the approach’s total vehicle delay after two cycles (when t = 140 seconds) and when will the queue clear (measured from the beginning of the first cycle) during an effective green (that is, the t at which there will no longer be a queue)? (Assume D/D/1 queuing.)