Work out queue length at signal instantly with clear inputs, formula shown and shareable results.
During red, vehicles accumulate at the arrival rate, so the queue at the start of green is arrival flow times red time. It then discharges at the difference between saturation flow and continuing arrivals, so the clearance time is longer than a simple division by saturation flow would suggest. Multiplying the queue by about six metres per vehicle gives the storage length needed.
Queue at end of red
Vehicles = arrival flow per second x effective red time
Discharge time
Time = queue / (saturation flow - arrival flow), in vehicles per second
Vehicles = arrival flow per second x effective red time. During red, vehicles accumulate at the arrival rate, so the queue at the start of green is arrival flow times red time.
If the queue exceeds the available storage it blocks an upstream junction or a turning lane, and the resulting spillback can gridlock a network far beyond the original approach.
This calculator takes 4 inputs: Arrival flow, Effective red time, Saturation flow, Queued vehicle spacing. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.