Fundamentals of Transportation/Traffic Signals/Solution
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.
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