This the type of method to design the signal time in junction of roads.

1. WEBSTER
METHOD OF
SIGNAL DESIGN

2. INTRODUCTION
SIGNAL DESIGN WEBSTER METHOD:
The Webster Method is a widely used technique for signal timing
design in traffic engineering. It is typically applied to determine the optimal
cycle length and the signal splits at an intersection to minimize overall delay for
vehicles. The method was developed by the traffic engineer Webster in 1958.
Setting traffic signals in a signal-controlled street network involves the
determination of cycle time, splits of green time, and offsets. This study
considers the network coordination problem, i.e., given a common cycle lime
and green splits at each intersection, determine offsets for all signals. a link
performance function is developed to express the loss incurred by platoons
traveling through a signal-controlled intersection us a function of link offset.
Integer variables enter the formulation because of the periodicity of the traffic
lights: The algebraic sum of the offsets around any closed loop of the network
must equal an integral number of cycle limes.

3. webster method of signal design

4. WEBSTER'S METHOD OF TRAFFIC SIGNAL DESIGN:
Webster's Method of Traffic Signal Design is a classical
approach to optimizing traffic signal timings for isolated
intersections. This method is designed to minimize vehicle delays
and improve overall traffic flow by determining the ideal cycle
length and green times for each signal phase at an intersection.
Webster’s method focuses on balancing the demand from various
traffic flows at an intersection while ensuring that each phase gets
enough green time to accommodate the flow of traffic efficiently.

5. 1.Cycle Length Calculation:
The first step in Webster’s method is to calculate the cycle
length (C), which is the total time it takes for all signal phases to
complete one cycle. This is based on the total lost time per cycle
and the flow ratios of the intersection.
A well-chosen cycle length is crucial for efficient traffic flow, minimizing
delays and maximizing intersection capacity.
The formula for calculating the cycle length is:
C=1.5L+5​
/1-Y ​Where:
L = Total lost time per cycle (seconds)
Y = Flow ratio (calculated below)

6. Lost Time (L):
Lost time is the time when no useful traffic movement is taking place. It
includes:
Start-up lost time: Time taken to start the green phase.
Yellow time: The time for a yellow signal.
All-red time: Time after the green light ends before the signal turns
green again.
Typical lost time values might be:
Start-up lost time: 2–4 seconds
Yellow time: 3–5 seconds
All-red time: 1–2 seconds
For each phase, the total lost time is calculated and summed up.

7. Flow Ratio (Y):
The flow ratio is a measure of the demand versus the
capacity for each signal phase. It is the ratio of the demand
flow rate to the saturation flow rate:
Y=F/S
​Where:
F = Flow rate (vehicles per unit of time) on an approach.
S = Saturation flow rate (the maximum number of vehicles
that can pass through a lane per unit of time during green
light).
The flow ratio is calculated for each approach, and the sum
of these flow ratios is used in the cycle length formula.

8. 2. Green Time Distribution (G):
Once the cycle length is calculated, the next step is to
determine how to distribute the green time across different
phases at the intersection. Webster’s method assigns green
time proportionally based on the demand and saturation flow
rates.
The formula for calculating the green time for each phase is:
G=F C/S
⋅
​Where:
G = Green time for the phase (seconds)
F = Flow rate on that approach (vehicles per hour)
C = Cycle length (seconds)
S = Saturation flow rate (vehicles per hour per lane)

9. Example:
Let’s say the demand flow rate for an approach is 600 vehicles/hour, and
the saturation flow rate is 1,800 vehicles/hour per lane. The cycle length
calculated for the intersection is 60 seconds.
Using the green time distribution formula:
G=600X60/1800=20
So, the green time for this particular phase would be 20 seconds.

10. 3. Optimal Cycle Length and Signal Phases:
For an intersection with multiple approaches, Webster's method calculates the cycle
length and green time for each phase, aiming to allocate green time in proportion to
traffic demand. However, the method assumes a fixed cycle length, and it doesn't
account for varying traffic conditions, which can be a limitation in highly dynamic
traffic situations.
4. Total Delay Minimization:
The goal of the Webster Method is to minimize the total delay across all vehicles at the
intersection. This method provides an optimized solution that balances the green time
and cycle length for all approaches to ensure the traffic flow is as smooth as possible.
The delay at an intersection can be divided into two types:
Stopped delay: The time vehicles spend waiting at the signal (not moving).
Travel delay: The time vehicles take to pass through the intersection.
Webster's method uses these calculations to minimize stopped delays, which is the
primary concern in signal design.

11. Application:
Webster's method is particularly useful in urban areas with moderate to
high traffic volumes. It is generally applied to isolated intersections (not
part of a coordinated network of signals) where demand is relatively
steady.