# D/D/1 SIGNAL ANALYSIS WITH TIME-VARYING ARRIVALS AND MINIMUM GREEN TIME

D/D/1 SIGNAL ANALYSIS WITH TIME-VARYING ARRIVALS AND MINIMUM GREEN TIME At the beginning of an approach’s effective red there are 2 cars left in a queue, cars continue to arrive at the approach at a rate of v(t) = 0.055 – 0.0002t [with v(t) in veh/s and t in seconds after the beginning of the effective red] for the entire cycle. The saturation flow of this approach is 1200 veh/h, the yellow time is 4 s, all-red is 2 s, and the approach has typical lost-time values. The cycle length is 90 s. What minimum displayed green time must be provided to ensure that the queue clears before the end of the effective green, and what is the total delay per cycle for this green time on this approach? (Assume D/D/1 queuing.)

SOLUTION Note: Open boxes in equations “ ” are to be completed by the reader

This problem demonstrates the fundamentals of D/D/1 intersection queuing and also illustrates how to determine the minimum green time required to dissipate queued traffic on an approach. To begin, for the queue to clear by the end of the effect green, the total arrivals during the 90 s cycle, plus the 2 vehicles remaining from the previous effective red, must equal the total departures (saturation flow times the effective greed). With the arrival rate given as v(t) = 0.055 – 0.0002t, the number of vehicles arriving in the 90 s cycle

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