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Queue Length At Signal Calculator

Work out queue length at signal instantly with clear inputs, formula shown and shareable results.

About Queue Length At Signal Calculator

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.

Formulas

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

Worked example

With the default values below, Queue Length At Signal Calculator returns Queue at the end of red of 8.33. Change any input above and every figure here is recalculated in your browser.

Inputs used

Arrival flowminimum 0 veh/h
600 veh/h
Effective red timeminimum 1 s
50 s
Saturation flowminimum 1 veh/h
1,800 veh/h
Queued vehicle spacingminimum 3 m
6 m

Results

Queue at the end of red
8.33 veh
Queue length
50.0 m
Time to discharge the queue
25.00 s
Net discharge rate during green
1,200 veh/h

Step by step

  1. 1Values used
  2. 2Queue at end of red
  3. 3Discharge time
  4. 4Queue at the end of red= 8.33 veh
  5. 5Queue length= 50.0 m
  6. 6Time to discharge the queue= 25.00 s
  7. 7Net discharge rate during green= 1,200 veh/h

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Queue Length At Signal figure worked out?

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.

Why does storage length matter so much?

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.

What values do I need to enter?

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.

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