Stand at a crossroads with a watch and the signals resolve into a pattern that repeats. That repetition is the design. A junction is a machine for dividing a fixed quantity of seconds among people who all want the same rectangle of asphalt, and nearly every argument anyone has had about traffic lights is, underneath, an argument about the division.

Nora Whitfield takes the pattern apart. Four quantities describe it — the length of the cycle, how it is split, when each junction starts relative to its neighbours, and the order in which movements are served — and everything else follows from one unavoidable cost. Each time right of way changes hands, several seconds pass in which nobody moves. That lost time is a tax on switching. It does not shrink when the cycle shrinks, which is why granting a phase to one movement always takes capacity from everyone else.

The consequences run in opposite directions, and that is what makes the subject interesting rather than merely technical. A longer cycle dilutes the tax, so capacity rises. A longer cycle also means a longer red for whoever is stopped, so delay rises. The classical result sits between the two and has a revealing property: as demand approaches capacity, the delay-minimising cycle runs away towards infinity. No cycle is long enough for a junction that is genuinely full, and the honest response is to stop minimising delay and start choosing where the queue is permitted to stand.

A chapter goes to the yellow interval, which is computed rather than chosen by custom. It has to be long enough that a driver travelling at the approach speed can either stop before the line or clear it, and the uncomfortable finding is that a band of distance exists in which neither is possible. Lengthening yellow relocates that band rather than removing it. Every number inside the calculation is an assumption about a person — a reaction time, a comfortable rate of deceleration — which is why an interval that suits a car can fail a cyclist.

Then the parts nobody thinks about. The coil of wire cut into the road that senses a vehicle by the change it makes to an inductance, and the motorcyclist waiting at a light that will never turn because the coil never noticed. Coordination, where offsetting each junction by the driving time between them produces a wave of green in one direction and, almost always, a wall of red in the other. And adaptive control, deployed and evaluated for decades, with results that depend enormously on how badly the previous timing had been neglected.

Two dozen bespoke diagrams sit in the text, and thirty-two references — federal manuals, national standards, patents and state evaluation reports — follow the final chapter. Where a figure appears in the text it is an illustration and says so. Interval lengths, capacity rates and grade thresholds that circulate freely have been left out: the tables defining them were not consulted, and the omission is stated in place of the number.