Using Webster Method for calculating "Optimum Cycle length"

1. By
K.Pranuthi,
Urban Transportation Engineering,
Jawaharlal Nehru Technological University,
14011D9010

2. Introduction
Definition and Notations
Design Procedure
Fixed Time Signals
Advantages
Disadvantages
Determination Cycle length
 Saturation flow
Problem
Conclusion

3.  Traffic signals are one of the most effective and flexible
active control of traffic and is widely used in several
cities world wide.
 The conflicts arising from movements of traffic in
different directions is addressed by time sharing
principle.

4.  Cycle: A signal cycle is one complete rotation
through all of the indications provided.
 Cycle length: Cycle length is the time in seconds
that it takes a signal to complete one full cycle of
indications. It indicates the time interval between
the starting of green for one approach till the next
time the green starts. It is denoted by C.

5.  Interval: Thus it indicates the change from one
stage to another.
There are two types of intervals :
1. Change interval and
2. Clearance interval.
 Change interval : It is also called the yellow time
indicates the interval between the green and red
signal indications for an approach.

6.  Clearance interval : It is also called all red and is
provided after each yellow interval indicating a period
during which all signal faces show red and is used for
clearing off the vehicles in the intersection.
 Green interval: It is the green indication for a
particular movement or set of movements and is
denoted by Gi. This is the actual duration the green light
of a traffic signal is turned on.

7.  Red interval: It is the red indication for a particular
movement or set of movements and is denoted by Ri.
This is the actual duration the red light of a traffic signal
is turned on.
Phase: A phase is the green interval plus the change and
clearance intervals that follow it. It allows a set of
movements to flow and safely halt the flow before the
phase of another set of movements start.

8. • Lost time: It indicates the time during which the
intersection is not effectively utilized for any
movement. For example, when the signal for an
approach turns from red to green, the driver of the
vehicle which is in the front of the queue, will take
some time to perceive the signal (usually called as
reaction time) and some time will be lost before vehicle
actually moves and gains speed.

9. Types of Signals:
 Fixed-time Signals : Green Periods and Cycle lengths
are pre-determined with fixed duration.
 Vehicle actuated Signals : Green periods vary and
are related to actual demands made by traffic.
 Semi actuated Signals : Detectors are located only
on the side roads

10. Type Advantages
Fixed time Signals • Simple Construction and
• Inexpensive
Vehicle-Actuated signals • Flexible to adjust accord to
traffic demand
•Delay is minimized to attain
maximum capacity
Semi Actuated Signals Useful for junctions of a low
traffic volume

11. Type Disadvantages
Fixed time Signals • Inflexible
•Cause Avoidable delay
Vehicle-Actuated signals •Require Costly Equipments
such as detectors
Semi Actuated Signals High traffic accidents at times
of light traffic

12. Signal faces we have are :
Red
Amber
Green
 The Amber period is generally taken as
2 seconds.
The Determination of Cycle time is one of most
important steps in fixed-signal designing.

13.  Objective: least delay should be caused to the traffic
passing through the intersection.
 Therefore for each traffic flow there is an optimum
cycle time which results in the minimum delay to the
vehicles.

14. Optimum Cycle Length : (Webster Method)
C0 =Optimum Cycle time
L = Total lost time per cycle(in seconds)
C0=

15.  Y = y1+y2+……….+yn
y1+y2+……….+yn are the maximum ratios of
flow to saturation flow for phases1,2,…..n
( i.e q/s where q is the flow and s is the saturation
flow)
The Y value according to Webster is taken as the
highest ratio of q/s

17.  Saturation Flow :
S= 525 w PCU/hr
S = Saturation flow
W= lane width of approach road in meters measured kerb
to inside of centre-line

18. Width w in meters Saturation flow in (PCU/hr)
3 1850
3.5 1890
4 1950
4.5 2250
5 2250
5.5 2900
Type of Vehicle PCU Equivalent
Heavy or medium goods vehicles 1.75
Light goods vehicles 1.00
Bus 2.25
Motor cycle 0.33
Pedal Cycle 0.20

19.  Loss time is also considered :
L = n l+ R
L = The Total lost time
l = lost time for the phase
R = The time during each cycle when all signals
display red simultaneously (including amber
time).

20. Effective Green Time :
Effective green time available in a cycle can be
divided into different phases so as to give the least
overall delay to the traffic using intersection.
g1:g2…….gn = y1: y2……….yn
y1,y2……….yn= maximum of y values
g1:g2…….gn = effective green times allotted to phases
1,2,3…..n respectively.

21. North South East West
Flow ,q 800 400 750 600
Saturati
on flow ,
S
2400 2000 3000 3000
y=q / s 0.33 0.2 0.25 0.2
y (max)
values
0.33
0.25

22. Loss of time = n l + R
No. of phases considered are 2
= (2 * 2) + 2 +2
= 8
Optimum Cycle Time =
C0 =

23. =
 C0= 40 Seconds
 Effective green time per cycle = C0 – L
= 40 – 8
= 32 sec

24. The effective green times for the phase can be
calculated as :
g N-S =
g E-W =

25. 2 s 18 s 2s 18s
22s 2s 14s
2s

26. Controlling the traffic based on the traffic
demand is more productive and has less delay
time .Therefore Vehicle Actuated signals are
more advisable to avoid unnecessary waiting
time.

27. Thank You