Once you know the total cycle length, you can subtract the length of the amber and all-red periods from the total cycle length and end up with the total time available for green signal indications. Efficiency dictates that the cycle length should be long enough to serve all of the critical movements, but no longer. If the cycle is too short, there will be so many phase changes during an hour that the time lost due to these changes will be high compared to the usable green time. But if the cycle is too long, delays will be lengthened, as vehicles wait for their turn to discharge through the intersection. Figure 1 provides a graphical portrayal of this phenomenon.
Figure 1: Cycle Length versus DelaySeveral methods for solving this optimization problem have already been developed, but Websters equation is the most prevalent. Webster's equation, which minimizes intersection delay, gives the optimum cycle length as a function of the lost times and the critical flow ratios. Many design manuals use Webster's equation as the basis for their design and only make minor adjustments to suit their purposes. Webster's equation is shown below. Co= 1.5L + 5
1 - S (V/s) Where:
Co = Optimum cycle length (sec)
L = Sum of the lost time for all phases, usually taken as the sum of the intergreen periods (sec)
V/s = Ratio of the design flow rate to the saturation flow rate for the critical approach or lane in each phase
After you have calculated the optimum cycle length, you should increase it to the nearest multiple of 5. For example, if you calculate a cycle length of 62 seconds, bump it up to 65 seconds. Once you have done this, you are ready to go. If you know the intergreen times for all of the phases, you can then calculate the total available green time and allocate it to the various phases based on their critical movements. (See the module entitled green split determination.)