Top-down four-way junction with queues, Webster delay theory and a green-split sweep.
The science
A fixed-time signal alternates two phases with a short all-red clearance (2 s) between them. During a green the stopped queue discharges at the saturation flow s (about 1800 vehicles per hour per lane) after a start-up lost time; the effective green fraction is L = (g - lost) / C with cycle C = gA + gB + 4 s. Capacity is c = s L and the degree of saturation is x = q / c.
For uniform arrivals the average delay per vehicle is Webster's first term d1 = C (1 - L)^2 / (2 (1 - L x)); random arrivals add a second term that grows sharply as x approaches 1. This page runs a seeded random-arrival simulation of all four approaches (0.25 s steps), a fluid model for the numerical check, and sweeps the green split to show where the flow-weighted delay is smallest. Above x = 1 the queue never clears and grows by (q - c) every hour.
Simplifications: one lane per approach, no turning movements, no yellow phase (folded into lost time), no pedestrians, instant vehicle spacing in the queue, fixed-time control.