Webster’s method
- Determination of ‘cycle time’ is an important step in the design of fixed time signal.
- Main consideration in selecting the cycle time should be that the least delay is caused to the traffic passing through an intersection.
- In selecting a cycle time, another guiding factor is the proportion of the time lost (in the intergreen period and by starting delays) to the cycle time.
- If the cycle time is small, the proportion of the time lost to the cycle time will be high, resulting in an inefficient signal operation and legthly delays.
- On the other hand if the cycle is large, the proportion of the time lost to the cycle time will be small and the signal operation will be more efficient.
optimum cycle time,
Co = (1.5L + 5)/(1 – Y) seconds
Where,
Co = optimum signal time
L Total lost time per cycle (in seconds)
Y = y1 + y2 + y3 + … + yn
y1, y2, y3, … are the maximum ratios of flow to saturation flow for phases 1, 2, 3, …
y = q/s = flow/saturation flow
The total time lost in the above formula can be understood with reference to below fig., indicating the rate of flow against time.
The figure shows that as soon as green phase is given, the rate of discharge begins to pick up and some time is lost before the flow reaches the maximum value (saturation flow). Similarly, at the termination of the green phase, the flow tends to taper off, involving a further lost time.
The lost time for the phase is given by :
l = k + a – g
Where,
l = Lost time for the phase
k = Green time for the phase
a = Amber time for the phase
g = Effective green time = b/s
b = Number of vehicles discharged on the average during a saturation flow
s = Saturation flow
The total time lost due to starting delays per cycle will be nl, if there are n phases in the cycle.
∴ total time lost,
L = nl + R
R = time lost when all signals display red
Green times for phase 1 and 2 are given by :
G1 = y1/Y[Co – L]
G2 = y2/Y[Co – L]
