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A Signal Approach

1. At the beginning of a signal approach’s effective red there are 8 vehicles in queue. The arrival rate over the cycle is v(t) = 0.05 + 0.001t [with v(t) in veh/s and t in seconds]. If the saturation flow rate is 1800 veh/h and the cycle length is 80 seconds, what is the minimum effective green time needed for this cycle to have zero vehicles in the approach’s queue when the effective red of the next cycle starts and what is approach’s the total delay in this cycle with this green time. (Assume D/D/1 queuing.)

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2. A signal approach has 20 seconds of displayed green, 4 seconds of yellow, and 3 seconds of all-red (start-up lost time and clearance times are typical). The cycle length is 60 seconds. At the beginning of an effective red there are no vehicles in queue and vehicles arrive at three-quarters of the saturation flow rate for 30 seconds. Then there is zero flow for 10 seconds, and then one-half of the saturation flow rate from 40 seconds until the end of the cycle. What is the approach’s total delay for this cycle if the saturation flow rate is 1400 veh/h? (Assume D/D/1 queuing.)

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