Basic concepts and formulae regarding design of traffic signals
The conflicts arising from movements of traffic in different directions is addressed by time sharing principle. The design principles of traffic signal are:
- phase design
- cycle length design and
- green splitting.
In this regard, the concepts of saturation flow, capacity, and lost times are important.
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 is denoted by C.
Interval: Thus it indicates the change from one stage to another. There are two types of intervals - change interval and clearance interval. Change interval is also called the yellow time indicates the interval between the green and red signal indications for an approach. Clearance interval 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.
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. Thus, during green interval, non conflicting movements are assigned into each phase. It allows a set of movements to flow and safely halt the flow before the phase of another set of movements start.
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.
The signal design procedure involves six major steps. They are:
- phase design
- determination of amber time and clearance time
- determination of cycle length
- apportioning of green time
- pedestrian crossing requirements and
- performance evaluation of the design
There is no precise methodology for the design of phases. It is often guided by:
- the geometry of the intersection
- the flow pattern especially the turning movements and
- the relative magnitudes of flow.
A trial and error procedure is often adopted. The first issue is to decide how many phases are required. It is possible to have two, three, four or even more number of phases.
Cycle time is the time taken by a signal to complete one full cycle of iterations. i.e. one complete rotation through all signal indications. It is denoted by C.
As the signal is initiated, the time interval between two vehicles, referred as headway, crossing the curb line is noted. The first headway is the time interval between the initiation of the green signal and the instant vehicle crossing the curb line. The second headway is the time interval between the first and the second vehicle crossing the curb line.
The first headway will be relatively longer since it includes the reaction time of the driver and the time necessary to accelerate. The second headway will be comparatively lower because the second driver can overlap his/her reaction time with that of the first driver’s. After few vehicles, the headway will become constant. This constant headway which characterizes all headways beginning with the fourth or fifth vehicle, is defined as the saturation headway, and is denoted as h.
The saturation flow rate s= 3600/h
Start-up lost time (L)
Green time (T) to clear N vehicles
Effective green time is the actual time available for the vehicles to cross the intersection. It is the sum of actual green time (Gi) plus the yellow minus the applicable lost times.
The ratio of effective green time to the cycle length (gi/C) is defined as green ratio. We know that saturation flow rate is the number of vehicles that can be moved in one lane in one hour assuming the signal to be green always. Then the capacity of a lane can be computed as,
Saturation flow rate can be computed as,
Lane capacity is
y is the length of yellow interval in seconds
t is the reaction time of driver
V85 is the 85th percentile of speed of approaching vehicles in m/s
a is the deceleration rate of approaching vehicles in m/s2
g is the grade of approach as a decimal
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