c) Assume that traffic on a single-lane approach to a signalized intersection observes the Greenshield's speed-density relationship. The jam density on the approach is 180 veh/mile and free flow speed is 60mph. Suppose the current signal is green and the traffic is moving at 40mph and passing through the intersection. After the green time ends, the signal turns red and vehicle queue starts to build up. The signal keeps red for 60 seconds and turns green again. Answer the following questions: 1. How fast does the vehicle queue build up after the signal turns red? 2. How far the vehicles are queued in upstream, i.e. the maximum queue length?

An approach at a signalized intersection with a 60-second cycle gets 30 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 876 veh/h. The arrival rate is given by v(t) = 0.20 - 0.002t [with v(t) in veh/s and t in seconds after the beginning of the effective red]. What is the average vehicle delay for this approach in seconds 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 queueing. Please provide you answer in decimal form without units)

7.24 Vehicles arrive at an approach to a pretimed signalized intersection. The arrival rate over the cycle is given by the function v(t) = 0.22 + 0.012t [v(t) is in veh/s and t is in seconds]. There are no vehicles in the queue when the cycle (effective red) begins. The cycle length is 60 seconds and the saturation flow rate is 3600 veh/h. Determine the effective green and red times that will allow the queue to clear exactly at the end of the cycle (the end of the effective green), and determine the total vehicle delay for this approach over the cycle (assuming D/D/1 queuing).

Recent computations at an approach to a pretimed-signalized intersection indicate that the volume-to-capacity ratio is 0.8, the saturation flow rate is 1600 veh/h, and the effective green time is 50 seconds. If the uniform delay is 11.25 seconds per vehicle, determine the arrival flow rate (in veh/h) and the cycle length.