Question

Traffic is stopped at a railroad crossing for 10 minutes. The flow rate of traffic on the approach was 400 veh/h at a speed of 50 mph, while the capacity flow rate of traffic on this roadway is 900 veh/h, at a speed of 45 mph. Using shockwave analysis, determine the length of the queue, the time needed for the queue to dissipate, the number of vehicles stopped, and the total delay. Assume that the Greenshields model is accurate for this roadway

Answer 1

One the approach:

Flow = 400 veh/hr and Speed = 50 mph. Density at this flow = 400 / 50 = 8 veh/mile.

Traffic is stopped for 10 minutes or (1/6) hour.

So that length of the queue = (400 veh/hr) X (1/6) hour = 66.66 veh. (Number of vehicles stopped)

Length of the Queue = 66.66 / 8 = 8.33 miles.

When the traffic if released, Flow = 900 veh/hr and Speed = 45 mph. Hence, the density = (900/45) = 20 veh/mile

Speed of shock=wave = (900 - 0)/(20 - 0) = 45 mph

Time required to dissipate the queue = (8.33 miles / 45 mph) = 0.185 hours or 11.11 minutes.