Traffic Signal Timing Calculator

Signal timing divides a repeating cycle among conflicting movements and inserts change intervals so vehicles already committed to the intersection can clear it. The yellow interval follows the kinematic form Y = t + v / (2 x (a + g x G)), with t the perception-reaction time taken as 1.0 second, v the approach speed in ft/s, a a comfortable deceleration near 10 ft/s squared, g equal to 32.2 ft/s squared, and G the approach grade as a decimal, negative on a downgrade so the interval lengthens. The all-red interval is the time to traverse the conflict area, (W + L) divided by v, with W the intersection width and L the design vehicle length. The MUTCD confines yellow to between 3 and 6 seconds and generally caps all-red near 6 seconds. Green time is then apportioned. Each phase carries roughly 4 seconds of lost time from start-up and clearance, so effective green over a cycle is cycle length minus total lost time. Splitting the remainder in proportion to critical flow ratios, with saturation flow nominally 1,900 passenger cars per hour of green per lane, equalises the degree of saturation across phases. Webster's optimal cycle Co = (1.5L + 5) / (1 - Y) minimises average delay, where L is total lost time and Y is the sum of critical flow ratios. Cycles typically run 60 to 90 seconds for two-phase operation and 100 to 150 seconds for complex multi-phase intersections; as Y approaches 1.0 the formula diverges and the intersection is over capacity regardless of how the time is split.

Interval-based traffic control long predates any theory of it. A manually operated gas-lit semaphore was installed outside the Houses of Parliament in London in 1868, and the first electric red-green signal was placed at Euclid Avenue and East 105th Street in Cleveland in 1914 by the American Traffic Signal Company. Three-colour operation with a distinct amber phase spread through the 1920s, with Detroit and New York among the early adopters, and the amber interval was set by judgement rather than calculation. Two pieces of analysis put signal timing on a formal footing. In 1958 F. V. Webster of the Road Research Laboratory in Britain published Traffic Signal Settings as Technical Paper No. 39, deriving the delay-minimising cycle length and the rule that green should be split in proportion to critical flow ratios. In 1960 Denos Gazis, Robert Herman and Alexei Maradudin, working at the General Motors research laboratories, published an analysis of the amber signal problem in the journal Operations Research, showing that a yellow interval which is too short creates a dilemma zone where an approaching driver can neither stop comfortably nor clear the intersection legally. Their kinematic expression, later adopted and promoted by the Institute of Transportation Engineers, remains the standard basis for setting change intervals in North America.