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Trac signal design-II
42.1 Overview
In the previous chapter, a simple design of cycle time was discussed. Here we will discuss how the cycle time is
divided in a phase. The performance evaluation of a signal is also discussed.
42.2 Green splitting
Green splitting or apportioning of green time is the proportioning of eective green time in each of the signal
phase. The green splitting is given by,
g
i
=

V
c
i
P
n
i=1
V
ci

 t
g
(42.1)
where V
c
i is the critical lane volume and t
g
is the total eective green time available in a cycle. This will be
cycle time minus the total lost time for all the phases. Therefore,
T
g
= C n:t
L
(42.2)
where C is the cycle time in seconds, n is the number of phases, and t
L
is the lost time per phase. If lost time
is dierent for dierent phases, then cycle time can be computed as follows.
T
g
= C
n
X
i=1
t
Li
(42.3)
where t
Li
is the lost time for phase i, n is the number of phases and C is the lost time in seconds. Actual
greentime can be now found out as,
G
i
= g
i
 y
i
+ t
Li
(42.4)
where G
i
is the actual green time, g
i
is the eective green time available, y
i
is the amber time, and L
i
is the
lost time for phase i.
Problem
The phase diagram with 
ow values of an intersection with two phases is shown in gure 42:1. The lost time
and yellow time for the rst phase is 2.5 and 3 seconds respectively. For the second phase the lost time and
yellow time are 3.5 and 4 seconds respectively. If the cycle time is 120 seconds, nd the green time allocated
for the two phases.
Page 2


Trac signal design-II
42.1 Overview
In the previous chapter, a simple design of cycle time was discussed. Here we will discuss how the cycle time is
divided in a phase. The performance evaluation of a signal is also discussed.
42.2 Green splitting
Green splitting or apportioning of green time is the proportioning of eective green time in each of the signal
phase. The green splitting is given by,
g
i
=

V
c
i
P
n
i=1
V
ci

 t
g
(42.1)
where V
c
i is the critical lane volume and t
g
is the total eective green time available in a cycle. This will be
cycle time minus the total lost time for all the phases. Therefore,
T
g
= C n:t
L
(42.2)
where C is the cycle time in seconds, n is the number of phases, and t
L
is the lost time per phase. If lost time
is dierent for dierent phases, then cycle time can be computed as follows.
T
g
= C
n
X
i=1
t
Li
(42.3)
where t
Li
is the lost time for phase i, n is the number of phases and C is the lost time in seconds. Actual
greentime can be now found out as,
G
i
= g
i
 y
i
+ t
Li
(42.4)
where G
i
is the actual green time, g
i
is the eective green time available, y
i
is the amber time, and L
i
is the
lost time for phase i.
Problem
The phase diagram with 
ow values of an intersection with two phases is shown in gure 42:1. The lost time
and yellow time for the rst phase is 2.5 and 3 seconds respectively. For the second phase the lost time and
yellow time are 3.5 and 4 seconds respectively. If the cycle time is 120 seconds, nd the green time allocated
for the two phases.
600
500
900
1000
Figure 42:1: Phase diagram for an intersection
                                          70.75
3
46.25
                                                          73.75 42.25 4
120
Figure 42:2: Timing diagram
Solution
 Critical lane volume for the rst phase, V
C1
= 1000 vph.
 Critical lane volume for the second phase, V
C2
= 600 vph.
 The sum of the critical lane volumes, V
C
= V
C1
+ V
C2
= 1000+600 = 1600 vph.
 Eective green time can be found out from equationas T
g
=120-(2.5-3.5)= 114 seconds.
 Green time for the rst phase, g
1
can be found out from equationas g
1
=
1000
1600
 114 = 71.25 seconds.
 Green time for the second phase, g
2
can be found out from equationas g
2
=
600
1600
 114= 42.75 seconds.
 Actual green time can be found out from equationThus actual green time for the rst phase, G
1
=
71.25-3+2.5 = 70.75 seconds.
 Actual green time for the second phase, G
2
= 42.75-3+2.5 = 42.25 seconds.
 The phase diagram is as shown in gure 42:2.
42.3 Pedestrian crossing requirements
Pedestrian crossing requirements can be taken care by two ways; by suitable phase design or by providing an
exclusive pedestrian phase. It is possible in some cases to allocate time for the pedestrians without providing
an exclusive phase for them. For example, consider an intersection in which the trac moves from north to
south and also from east to west. If we are providing a phase which allows the trac to 
ow only in north-south
direction, then the pedestrians can cross in east-west direction and vice-versa. However in some cases, it may
Page 3


Trac signal design-II
42.1 Overview
In the previous chapter, a simple design of cycle time was discussed. Here we will discuss how the cycle time is
divided in a phase. The performance evaluation of a signal is also discussed.
42.2 Green splitting
Green splitting or apportioning of green time is the proportioning of eective green time in each of the signal
phase. The green splitting is given by,
g
i
=

V
c
i
P
n
i=1
V
ci

 t
g
(42.1)
where V
c
i is the critical lane volume and t
g
is the total eective green time available in a cycle. This will be
cycle time minus the total lost time for all the phases. Therefore,
T
g
= C n:t
L
(42.2)
where C is the cycle time in seconds, n is the number of phases, and t
L
is the lost time per phase. If lost time
is dierent for dierent phases, then cycle time can be computed as follows.
T
g
= C
n
X
i=1
t
Li
(42.3)
where t
Li
is the lost time for phase i, n is the number of phases and C is the lost time in seconds. Actual
greentime can be now found out as,
G
i
= g
i
 y
i
+ t
Li
(42.4)
where G
i
is the actual green time, g
i
is the eective green time available, y
i
is the amber time, and L
i
is the
lost time for phase i.
Problem
The phase diagram with 
ow values of an intersection with two phases is shown in gure 42:1. The lost time
and yellow time for the rst phase is 2.5 and 3 seconds respectively. For the second phase the lost time and
yellow time are 3.5 and 4 seconds respectively. If the cycle time is 120 seconds, nd the green time allocated
for the two phases.
600
500
900
1000
Figure 42:1: Phase diagram for an intersection
                                          70.75
3
46.25
                                                          73.75 42.25 4
120
Figure 42:2: Timing diagram
Solution
 Critical lane volume for the rst phase, V
C1
= 1000 vph.
 Critical lane volume for the second phase, V
C2
= 600 vph.
 The sum of the critical lane volumes, V
C
= V
C1
+ V
C2
= 1000+600 = 1600 vph.
 Eective green time can be found out from equationas T
g
=120-(2.5-3.5)= 114 seconds.
 Green time for the rst phase, g
1
can be found out from equationas g
1
=
1000
1600
 114 = 71.25 seconds.
 Green time for the second phase, g
2
can be found out from equationas g
2
=
600
1600
 114= 42.75 seconds.
 Actual green time can be found out from equationThus actual green time for the rst phase, G
1
=
71.25-3+2.5 = 70.75 seconds.
 Actual green time for the second phase, G
2
= 42.75-3+2.5 = 42.25 seconds.
 The phase diagram is as shown in gure 42:2.
42.3 Pedestrian crossing requirements
Pedestrian crossing requirements can be taken care by two ways; by suitable phase design or by providing an
exclusive pedestrian phase. It is possible in some cases to allocate time for the pedestrians without providing
an exclusive phase for them. For example, consider an intersection in which the trac moves from north to
south and also from east to west. If we are providing a phase which allows the trac to 
ow only in north-south
direction, then the pedestrians can cross in east-west direction and vice-versa. However in some cases, it may
Time
Desired path Actual path
Distance
D
3
D
2
D
1
D
3
= Travel time delay
D
2
= Approach delay
D
1
= Stopped time delay
Figure 42:3: Illustration of delay measures
be necessary to provide an exclusive pedestrian phase. In such cases, the procedure involves computation of
time duration of allocation of pedestrian phase. Green time for pedestrian crossing G
p
can be found out by,
G
p
= t
s
+
dx
u
P
(42.5)
where G
p
is the minimum safe time required for the pedestrians to cross, often referred to as the \pedestrian
green time", t
s
is the start-up lost time, dx is the crossing distance in metres, and u
p
is the walking speed of
pedestrians which is about 15th percentile speed. The start-up lost time t
s
can be assumed as 4.7 seconds and
the walking speed can be assumed to be 1.2 m/s.
42.4 Performance measures
Performance measures are parameters used to evaluate the eectiveness of the design. There are many param-
eters involved to evaluate the eectiveness of the design and most common of these include delay, queuing, and
stops. Delay is a measure that most directly relates the driver's experience. It describes the amount of time
that is consumed while traversing the intersection. The gure 42:3 shows a plot of distance versus time for the
progress of one vehicle. The desired path of the vehicle as well as the actual progress of the vehicle is shown.
There are three types of delay as shown in the gure. They are stopped delay, approach delay and control delay.
Stopped time delay includes only the time at which the vehicle is actually stopped waiting at the red signal.
It starts when the vehicle reaches a full stop, and ends when the vehicle begins to accelerate. Approach delay
includes the stopped time as well as the time lost due to acceleration and deceleration. It is measured as the
time dierential between the actual path of the vehicle, and path had there been green signal. Control delay
is measured as the dierence between the time taken for crossing the intersection and time taken to traverse
the same section, had been no intersection. For a signalized intersection, it is measured at the stop-line as the
vehicle enters the intersection. Among various types of delays, stopped delay is easy to derive and often used
as a performance indicator and will be discussed.
Vehicles are not uniformly coming to an intersection. i.e., they are not approaching the intersection at
constant time intervals. They come in a random manner. This makes the modeling of signalized intersection
delay complex. Most simple of the delay models is Webster's delay model. It assumes that the vehicles are
Page 4


Trac signal design-II
42.1 Overview
In the previous chapter, a simple design of cycle time was discussed. Here we will discuss how the cycle time is
divided in a phase. The performance evaluation of a signal is also discussed.
42.2 Green splitting
Green splitting or apportioning of green time is the proportioning of eective green time in each of the signal
phase. The green splitting is given by,
g
i
=

V
c
i
P
n
i=1
V
ci

 t
g
(42.1)
where V
c
i is the critical lane volume and t
g
is the total eective green time available in a cycle. This will be
cycle time minus the total lost time for all the phases. Therefore,
T
g
= C n:t
L
(42.2)
where C is the cycle time in seconds, n is the number of phases, and t
L
is the lost time per phase. If lost time
is dierent for dierent phases, then cycle time can be computed as follows.
T
g
= C
n
X
i=1
t
Li
(42.3)
where t
Li
is the lost time for phase i, n is the number of phases and C is the lost time in seconds. Actual
greentime can be now found out as,
G
i
= g
i
 y
i
+ t
Li
(42.4)
where G
i
is the actual green time, g
i
is the eective green time available, y
i
is the amber time, and L
i
is the
lost time for phase i.
Problem
The phase diagram with 
ow values of an intersection with two phases is shown in gure 42:1. The lost time
and yellow time for the rst phase is 2.5 and 3 seconds respectively. For the second phase the lost time and
yellow time are 3.5 and 4 seconds respectively. If the cycle time is 120 seconds, nd the green time allocated
for the two phases.
600
500
900
1000
Figure 42:1: Phase diagram for an intersection
                                          70.75
3
46.25
                                                          73.75 42.25 4
120
Figure 42:2: Timing diagram
Solution
 Critical lane volume for the rst phase, V
C1
= 1000 vph.
 Critical lane volume for the second phase, V
C2
= 600 vph.
 The sum of the critical lane volumes, V
C
= V
C1
+ V
C2
= 1000+600 = 1600 vph.
 Eective green time can be found out from equationas T
g
=120-(2.5-3.5)= 114 seconds.
 Green time for the rst phase, g
1
can be found out from equationas g
1
=
1000
1600
 114 = 71.25 seconds.
 Green time for the second phase, g
2
can be found out from equationas g
2
=
600
1600
 114= 42.75 seconds.
 Actual green time can be found out from equationThus actual green time for the rst phase, G
1
=
71.25-3+2.5 = 70.75 seconds.
 Actual green time for the second phase, G
2
= 42.75-3+2.5 = 42.25 seconds.
 The phase diagram is as shown in gure 42:2.
42.3 Pedestrian crossing requirements
Pedestrian crossing requirements can be taken care by two ways; by suitable phase design or by providing an
exclusive pedestrian phase. It is possible in some cases to allocate time for the pedestrians without providing
an exclusive phase for them. For example, consider an intersection in which the trac moves from north to
south and also from east to west. If we are providing a phase which allows the trac to 
ow only in north-south
direction, then the pedestrians can cross in east-west direction and vice-versa. However in some cases, it may
Time
Desired path Actual path
Distance
D
3
D
2
D
1
D
3
= Travel time delay
D
2
= Approach delay
D
1
= Stopped time delay
Figure 42:3: Illustration of delay measures
be necessary to provide an exclusive pedestrian phase. In such cases, the procedure involves computation of
time duration of allocation of pedestrian phase. Green time for pedestrian crossing G
p
can be found out by,
G
p
= t
s
+
dx
u
P
(42.5)
where G
p
is the minimum safe time required for the pedestrians to cross, often referred to as the \pedestrian
green time", t
s
is the start-up lost time, dx is the crossing distance in metres, and u
p
is the walking speed of
pedestrians which is about 15th percentile speed. The start-up lost time t
s
can be assumed as 4.7 seconds and
the walking speed can be assumed to be 1.2 m/s.
42.4 Performance measures
Performance measures are parameters used to evaluate the eectiveness of the design. There are many param-
eters involved to evaluate the eectiveness of the design and most common of these include delay, queuing, and
stops. Delay is a measure that most directly relates the driver's experience. It describes the amount of time
that is consumed while traversing the intersection. The gure 42:3 shows a plot of distance versus time for the
progress of one vehicle. The desired path of the vehicle as well as the actual progress of the vehicle is shown.
There are three types of delay as shown in the gure. They are stopped delay, approach delay and control delay.
Stopped time delay includes only the time at which the vehicle is actually stopped waiting at the red signal.
It starts when the vehicle reaches a full stop, and ends when the vehicle begins to accelerate. Approach delay
includes the stopped time as well as the time lost due to acceleration and deceleration. It is measured as the
time dierential between the actual path of the vehicle, and path had there been green signal. Control delay
is measured as the dierence between the time taken for crossing the intersection and time taken to traverse
the same section, had been no intersection. For a signalized intersection, it is measured at the stop-line as the
vehicle enters the intersection. Among various types of delays, stopped delay is easy to derive and often used
as a performance indicator and will be discussed.
Vehicles are not uniformly coming to an intersection. i.e., they are not approaching the intersection at
constant time intervals. They come in a random manner. This makes the modeling of signalized intersection
delay complex. Most simple of the delay models is Webster's delay model. It assumes that the vehicles are
                                              R
C
time
cumulative number of vehicles
g
i
V
i
S
Figure 42:4: Graph between time and cumulative number of vehicles at an intersection
arriving at a uniform rate. Plotting a graph with time along the x-axis and cumulative vehicles along the y-axis
we get a graph as shown in gure 42:4. The delay per cycle is shown as the area of the hatched portion in the
gure. Webster derived an expression for delay per cycle based on this, which is as follows.
d
i
=
C
2
[1
g i
C
]
2
1
V i
S
(42.6)
where g
i
is the eective green time, C is the cycle length, V
i
is the critical 
ow for that phase, and S is the
saturation 
ow.
Delay is the most frequently used parameter of eectiveness for intersections. Other measures like length of
queue at any given time (Q
T
) and number of stops are also useful. Length of queue is used to determine when
a given intersection will impede the discharge from an adjacent upstream intersection. The number of stops
made is an important input parameter in air quality models.

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