1.An approach at a signalized intersection with a 70-second cycle gets 25 seconds of displayed green time. Yellow time is 4 seconds and all-red is 2 seconds (lost time is to be determined from standard assumptions). At the beginning of an effective red there are 4 vehicles in the queue and the saturation flow is 818 veh/h. The arrival rate is given as v(t) = 0.17 – 0.002t [with v(t) in veh/s and t in seconds after the beginning of the effective red]. What is the total vehicle delay for this approach at the end of the cycle (until the next effective red) that started with the 4 vehicles queued at the beginning of the effective red? (Assume D/D/1 queuing.)
2. At the beginning of an effective red, an approach has 7 vehicles in a queue with vehicles arriving according to the function v(t) = 0.2 + 0.00111t [with v(t) in veh/s and t in seconds after the beginning of the effective red]. The saturation flow is 1800 veh/h, the cycle length is 60 seconds, and the effective red is 20 seconds. What is the total delay for the approach until the queue first clears? (Assume D/D/1 queuing.)