How to set traffic signal offsets for a green wave
An offset is the number of seconds an intersection's cycle starts after the corridor reference. Set each offset equal to the travel time from the previous signal at the design speed and a platoon released at the first green meets green all the way along: a green wave. This page does the arithmetic on a real corridor and then shows why the same offsets cannot serve both directions.
The one formula
Travel time between two signals is distance divided by speed. With distance in metres and speed in km/h, divide the speed by 3.6 to get metres per second first:
travel time (s) = distance (m) ÷ (speed (km/h) ÷ 3.6)
For a green wave in one direction, the offset of each signal is the cumulative travel time from the reference signal, wrapped into the cycle length if it exceeds it. The first signal is the reference and has offset 0. That is all a northbound or southbound Auto-sequence in SigTDD does in its basic mode; the smart mode adds one refinement described below.
Worked on the example corridor
The Riverside Drive example that ships with the tool has six signals at 350, 400, 300, 450 and 350 m spacings, a northbound design speed of 60 km/h (16.67 m/s) and a 120 s cycle. Each row below takes the previous link's distance and speed, computes the travel time, and adds it to the running total. The final column is the offset stored in the CSV.
| # | Intersection | Link from previous (m) | Travel time (s) | Cumulative (s) | Offset in CSV (s) |
|---|---|---|---|---|---|
| 1 | Riverside Dr & Oak St | — | — | 0.0 | 0 |
| 2 | Riverside Dr & Elm Ave | 350 | 21.0 | 21.0 | 21 |
| 3 | Riverside Dr & Pine Rd | 400 | 24.0 | 45.0 | 45 |
| 4 | Riverside Dr & Cedar Ln | 300 | 18.0 | 63.0 | 63 |
| 5 | Riverside Dr & Birch Way | 450 | 27.0 | 90.0 | 90 |
| 6 | Riverside Dr & Maple Ct | 350 | 21.0 | 111.0 | 111 |
Every cumulative time rounds to the stored offset, so a vehicle leaving Oak Street at the start of green arrives at each signal exactly as its green starts. Because all six signals have the same phase pattern, the whole northbound green — phases A and B less the amber — travels intact, and the northbound bandwidth equals that green: 59 s of the 120 s cycle.
Before and after
When the cumulative time exceeds the cycle
Offsets are stated within one cycle, so a cumulative travel time of 141 s on a 120 s cycle becomes an offset of 21 s; the platoon simply arrives one cycle later, which the diagram shows as the band crossing into the next repetition of the bar. SigTDD wraps the value automatically when auto-sequencing and clamps typed values to the cycle length.
Aligning with the longest green, not the cycle start
The basic rule assumes the progression phase starts at the beginning of each cycle. Where an intersection runs a leading cross-street phase, its northbound green begins some seconds into the cycle. Smart auto-sequence in SigTDD finds the longest run of green phases serving the chosen direction at each intersection and subtracts its start time from the cumulative travel time, so the platoon arrives at the start of that run rather than at the start of the cycle. Basic mode is the textbook calculation; smart mode is what you would do by hand once you looked at the phase sequence.
Why the same offsets cannot serve both directions
Follow a southbound vehicle that leaves Maple Court at the start of its southbound green and travels at the southbound design speed of 55 km/h. Its arrival at each signal, measured within that signal's own cycle, is:
| # | Intersection | Arrival in cycle (s) | Southbound green windows (s) | Meets green? |
|---|---|---|---|---|
| 6 | Riverside Dr & Maple Ct | 0.0 | 0–36, 62–80, 102–116 | Yes |
| 5 | Riverside Dr & Birch Way | 43.9 | 0–36, 62–80, 102–116 | No |
| 4 | Riverside Dr & Cedar Ln | 100.4 | 0–36, 62–80, 102–116 | No |
| 3 | Riverside Dr & Pine Rd | 18.0 | 0–36, 62–80, 102–116 | Yes |
| 2 | Riverside Dr & Elm Ave | 68.2 | 0–36, 62–80, 102–116 | Yes |
| 1 | Riverside Dr & Oak St | 112.1 | 0–36, 62–80, 102–116 | Yes |
With the northbound offsets in place the southbound band is 0 s wide, against 59 s northbound. That is not a mistake in the plan; it is geometry. For a platoon in each direction to meet green at two adjacent signals with identical phase patterns, the travel time between them must be a whole multiple of half the cycle. At 60 km/h and a 120 s cycle that is a spacing of 1000 m or a multiple of it. Riverside Drive's signals are 300 to 450 m apart, so the two directions can only be traded against each other.
The practical answers, all of which the diagram makes visible, are: favour the peak direction per plan (the example is named NB-Green-Wave for that reason, and the tool keeps an AM and a PM plan on the same corridor); change the cycle length so that spacing and half-cycle agree more closely; use phase sequence, leading the turn on one side and lagging it on the other, to move a green without moving the offset; or accept a narrower compromise band in each direction.
Checklist before you trust an offset plan
- Every signal runs the same cycle length, or an exact multiple of it.
- Distances are measured stop line to stop line along the road, not between map pins across a curve.
- The design speed is the speed platoons actually travel at, which is often below the posted limit in dense corridors.
- Amber and all-red are deducted from the usable green; SigTDD deducts a 4 s amber from the end of each green run.
- Queues at the downstream stop line need to clear before the platoon arrives; on saturated links add a few seconds of offset so the queue discharges first.
- The band is checked at both ends of the green, not only at the leading edge.
Open the worked example to see the same corridor built step by step in the tool, or the documentation for the offset slider and auto-sequence controls.