Degree of Saturation

Demand divided by capacity, for one movement, over one analysis period. It is the plainest ratio in the field and the single most useful number at a signal, because it says in one figure whether the timing plan works.

What makes it so informative is that it is the term every delay and queue model divides by. Below about 0.85 an approach clears its queue on most cycles and delay is moderate and predictable. Between 0.85 and 1.00 it is clearing most cycles but failing some, and delay becomes sharply sensitive to demand — a five percent swing, a bus in the lane, one badly timed cycle and the queue survives the green and waits again. At 1.00 it is exactly saturated, and at that point steady-state delay theory has no finite answer: the formulas divide by zero because there is no repeating cycle to average over. Above 1.00 the approach is oversaturated, the queue grows every cycle, and delay is no longer an average wait at all — it is a queue that keeps getting longer for as long as demand lasts, and it must be modelled with time-dependent queueing rather than with a steady-state formula.

That sensitivity near one is not an artifact. It is real queueing behaviour, and it is why designers aim at 0.85 or 0.90 on the critical movements rather than 0.99. The gap is not timidity: it is the room needed to absorb the variation that an average count conceals.

Now the confusion this page exists to head off, because it appears constantly in review comments and in tables that compare two studies. "Degree of saturation" and "volume-to-capacity ratio" are often used interchangeably, and they are the same arithmetic — but the numerator can be a completely different quantity depending on the horizon the analysis was written for.

An operational degree of saturation is computed on a peak flow rate: typically the busiest fifteen minutes multiplied up to an hourly equivalent, or the peak hour volume divided by a peak hour factor. That is what the signal actually has to serve at its worst, and it is what belongs in a delay calculation. A planning-level v/c ratio is frequently computed on something else entirely — an average annual hourly volume, a design hourly volume, or an AADT converted with a K factor and a directional split. Each of those describes a real thing, and they are not the same thing.

The consequence is that one intersection can be honestly reported at 0.72 by a planning study and 0.95 by an operational one, with no error in either. Only the second describes what happens at ten past five on a Thursday. When you see a saturation figure quoted, ask what flow the numerator is and over what period; when you write one, say so. And never place an operational $x$ and a planning v/c side by side in the same table as though the reader could compare them — that is how a movement that fails every afternoon ends up documented as acceptable.

One further caution about the denominator. Capacity here is for a specific lane group under specific timings, so a degree of saturation is only meaningful alongside the timing plan it was computed with. Retime the signal and every $x$ at the intersection changes. That is the point of retiming, and it is also why an $x$ copied from an old report is worth very little.