Capacity of a Signalised Approach

A signalised approach is not doing anything subtle. While it has the green it discharges a standing queue at its saturation flow; while it has the red it discharges nothing. So over a full cycle its capacity is the saturation flow scaled by the fraction of the cycle it owns: $c = s\,g/C$. One line, and it is the bridge between what a controller is programmed with and what the intersection actually delivers in vehicles per hour.

The arithmetic is trivial and both inputs are traps, so it is worth spending the time on them.

Saturation flow is not a constant, and this site will not supply one. It is the rate at which a queue of vehicles crosses the stop line once it is properly moving — measured, by convention, from about the fourth vehicle onward, because the first three are still absorbing the startup lost time. A base figure near 1900 vehicles per hour of green per lane gets quoted, and taken bare it is close to meaningless: the real value has to be adjusted for lane width, approach grade, heavy-vehicle percentage, parking manoeuvres, bus stops, turning movements, opposing flow for permitted lefts, and pedestrian and cyclist conflicts. Those adjustment factors live in the Highway Capacity Manual, which is copyrighted, or in your own agency's manual. Better than either: measure it on the approach in question. Time the headways of a standing queue from the fourth vehicle to the last one that clears, average them, and divide 3600 by that average in seconds. A two-second average headway is 1800 veh/h; 2.2 seconds is 1636. The difference between those two is larger than most of the adjustment factors people argue about.

Effective green is not the green indication. It is the displayed green, plus the portion of the amber that drivers actually use, minus the startup lost time at the head of the queue. The two usually land within a second or two of one another, and that is exactly why the substitution gets made carelessly — the numbers look close enough. On a 40-second phase a two-second error is 5 %. On a 12-second protected left it is nearly 17 %, and short phases are where capacity is tightest. The idealisation behind "effective green" is that discharge is a rectangle: nothing, then saturation flow instantly, then nothing. Real discharge ramps up over the first few vehicles and trails off through the amber. Effective green is the width of the rectangle with the same area as the real curve, and it is a bookkeeping device rather than something you can read off a controller.

Notice what the equation does not contain. It knows nothing about the demand — a movement can have generous capacity and still fail if enough vehicles turn up, which is what the degree of saturation is for. It knows nothing about lane use: a shared through-and-left lane behaves quite differently from either movement alone, and an approach's lanes rarely load evenly, so the critical lane rather than the average one governs. It knows nothing about permitted turns, where capacity depends on gaps in the opposing stream rather than on the green at all. And it assumes a queue is present for the whole green; a movement whose queue clears early is not capacity-constrained and this equation is not describing it.

Run backwards it becomes the design tool: name the capacity a movement needs, and read off the green it takes. Then check that number against the minimum green your standard requires — and on a wide crossing, the pedestrian walk plus clearance interval frequently governs and has nothing whatever to do with vehicle capacity.