1. A left-turn movement has a maximum arrival rate of 200 veh/h. The saturation flow of this movement is 1400 veh/h. For this approach, the yellow time is 4 seconds, all-red time is 2 seconds, and total lost time is 3 seconds. The cycle length is 120 seconds. What minimum displayed green time must be provided to ensure that the queue in each cycle clears, and what is the movement’s total delay per cycle and delay per vehicle for this green time? (Assume D/D/1 queuing.)
2. Vehicles begin to arrive at a signal approach at a rate of v(t) = 0.2286 + 0.0008t [with v(t) in veh/s and t in seconds] at the beginning of the cycle (the beginning of an effective red) and there are 2 vehicles already in the queue that are left over from the effective green of the previous cycle. The signal is designed so that the effective green starts when there are 10 vehicles in the queue. The saturation flow rate is 1800 veh/h. What is the approach’s total vehicle delay after one cycle (cycles are 60 seconds long) and when will the effective green start in cycle #2 (or, equivalently, how long will the effective red be in cycle #2)? (Assume D/D/1 queuing.)