# Fundamentals of Transportation/Traffic Signals/Solution

**Problem:**

An approach at a pretimed signalized intersection has an arrival rate of 500 veh/hr and a saturation flow rate of 3000 veh/hr. 30 seconds of effective green are given in a 100-second cycle. Analyze the intersection assuming D/D/1 queueing by describing the proportion of the cycle with a queue, the maximum number of vehicles in the queue, the total and average delay, and the maximum delay.

**Solution:**

With the statements in the problem, we know:

- Green Time = 30 seconds
- Red Time = 70 seconds
- Cycle Length = 100 seconds
- Arrival Rate = 500 veh/hr (0.138 veh/sec)
- Departure Rate = 3000 veh/hr (0.833 veh/sec)

Traffic intensity, , is the first value to calculate.

Time to queue clearance after the start of effective green:

Proportion of the cycle with a queue:

Proportion of vehicles stopped:

Maximum number of vehicles in the queue:

Total vehicle delay per cycle:

Average delay per vehicle:

Maximum delay of any vehicle:

Thus, the solution can be determined:

- Proportion of the cycle with a queue = 0.84
- Maximum number of vehicles in the queue = 9.66
- Total Delay = 406 veh-sec
- Average Delay = 29.41 sec
- Maximum Delay = 70 sec