Question

Vehicles arrive in a single approach for two consecutive cycles at a signalized intersection. The signal has a 60 second cycle time which consists of a 30 second green interval and a 30 second red interval (ignore yellow interval). The arrival rates are assumed to be constant in both cycles. The arrival rate was 1,080 vehicles/hour in the first cycle and it decreased to 720 vehicles/hour in the second cycle. Assume that all vehicles in the queue formed on red pass through the intersection during the subsequent green interval at the saturation flow rate of 1,800 vehicles/hour immediately after the start of the green interval.

1. Sketch a queueing diagram (cumulative arrival and departure curves over time) the approach during the two cycles
2. Calculate the maximum queue length (maximum number of vehicles in the queue).
3. Calculate 1) the total vehicle delay and 2) the average delay per vehicle during the two cycles

Answer 1