Signal Cycle Time (Webster)

Signal cycle time (Webster)

How long should the full cycle of a traffic signal last? Cycles that are too short waste capacity (too much relative time spent on phase-change transitions); cycles that are too long impose excessive waiting on everyone held at red. In 1958, F. V. Webster derived, through simulation and queueing theory, the cycle that minimizes total vehicle delay at the intersection: C = (1.5·L + 5) ÷ (1 − Y). Here L is the total lost time per cycle — the sum of the intergreen intervals (yellow plus all-red) and the start-up delays of the queues, time during which no queue makes productive use of the green. And Y is the sum of the critical flow ratios: for each phase, take the largest ratio (demand flow ÷ saturation flow) among its movements, and add up those critical ratios across all phases. Y represents how much of the intersection capacity is committed to demand. The formula behaves in a revealing way: as Y approaches 1, the denominator (1 − Y) tends to zero and the optimum cycle shoots off to infinity — the mathematical signal that the intersection is saturated, meaning total demand has reached capacity and no cycle, however long, can clear it all (lanes must be added, movements removed or the intersection redesigned). For Y < 1, the Webster cycle typically lands between 40 and 120 seconds. Once the cycle is set, the green time of each phase is distributed in proportion to its flow ratio. This is the fundamental formula for timing isolated traffic signals. Enter the total lost time and the sum of the flow ratios.