Content uploaded by Prihantini - Titin
Author content
All content in this area was uploaded by Prihantini - Titin on Jan 25, 2021
Content may be subject to copyright.
PROC. INTERNAT. CONF. SCI. ENGIN. ISSN 2597-5250
Volume 3, April 2020 | Pages: 347-352 E-ISSN 2598-232X
Application of Webster's Method to Optimizing Traffic Lights at the
Intersection of Bantul - Nasional III Street, Yogyakarta
Prihantini1,*, Albert Hosea Santoso2,**, Hanifa Reygina Fajrin2,***
1Department of Mathematics Education, Faculty of Mathematics and Science, Yogyakarta State University
2Department of Mathematics, Faculty of Mathematics and Science, Gadjah Mada University
Email: titinprihantini4@gmail.com*, albert.h.s.@mail.ugm.ac.id**, hanifareygina@mail.ugm.ac.id***
Abstract. Indonesia is a developing country with the fourth largest population in the world. Population in one of the provinces in
Indonesia, namely Yogyakarta Special Region. Based on data from the Badan Pusat Statistik (BPS), the Special Region of Yogyakarta
reached 3.8 million people in 2018. Of this number, almost one third (1.2 million people) are residents of Sleman. While the region with
the next largest population is Bantul with 1 million inhabitants. Increasing population causes the need to move and other needs, as well as
activities in the education, office and trade sectors also increase. This increase will also affect transportation by increasing the number of
vehicles, but this increase is not in line with the existing traffic light updates. As a result, the capacity of the street section has decreased
and caused congestion, for example at the APILL intersection on Bantul-Nasional III Street, Yogyakarta. This shows that the existing
traffic light settings are not optimal. Therefore, it is necessary to evaluate the duration of the traffic lights to minimize congestion. This
research was conducted to analyze the traffic light system at the APILL intersection on Bantul-Nasional III Street, Yogyakarta using the
Webster method. The results of calculations using this method obtained results for the Bantul Street (north), the duration of the green light
30 seconds, yellow 3 seconds and red 28 seconds. For Nasional III Street (East), the duration of the green light is 24 seconds, yellow is 3
seconds and red is 34 seconds. For Bantul Street (south), the duration of the green light is 30 seconds, yellow is 3 seconds and red is 28
seconds. For Nasional III Street (West), the duration of the green light is 24 seconds, yellow is 3 seconds and red is 34 seconds. These
results look more optimal than those on the field today.
Keywords: Traffic Performance, Webster Methode, Traffic Lights, Traffic Congestion, Optimization
INTRODUCTION
Transportation in general and traffic in particular is a
phenomenon that is seen everyday in human life. The
higher the level of movement of citizens of a city, the
higher the level of travel. If this increase in travel is not
followed by an increase in adequate transportation
infrastructure, there will be an imbalance between
demand and supply which will eventually lead to an
unevenness in mobility in the form of congestion. Traffic
congestion in a city or a place now is no longer a strange
thing that can occur in a segment or cross streets,
congestion arises because of conflicting movements that
come in each direction of the intersection and to reduce
this conflict many controls are carried out to optimize
the intersection with use traffic lights.
Traffic is a condition with a regulation using traffic
lights installed at an intersection in order to regulate the
flow of traffic. The regulation of traffic flow at an
intersection is basically intended for how the movement
of vehicles in each group of vehicle movements can
move alternately so that they do not interfere with each
other. There are various types of controls using traffic
lights where this consideration is very dependent on the
situation and intersection conditions such as volume,
intersection geometry, and so on.
Adaptive and synchronous traffic control systems
have been used in many developed countries. With the
adaptive traffic control system, the duration of red and
green is adjusted to the density of vehicle arrivals. With
this system, it is expected that the duration of vehicle
waiting times from all directions tends to be the same
and will not exceed one cycle. In other words there are
no vehicles that experience red cues twice. There is a
synchronous traffic control system to reduce the travel
time of the main Street. Arrangements are synchronized
with each other so that most of the vehicles on the main
Street don't wait too long for green cues.
Synchronous traffic control is used to reduce the
duration of vehicles waiting on the main street. The
synchronization process in synchronous traffic settings is
quite complicated. Determination of the time and
duration of the green involves many parameters, such as:
the green time the main direction of the next traffic
control, the speed and acceleration of the vehicle, as well
as the vehicle travel time from one traffic setting to
another traffic setting. Calculation of green time must
also be supported by sensors of the presence of vehicles
on the main Street which is quite a lot. To keep in sync,
a synchronous traffic regulator cannot be adaptive.
An increase in the density of vehicle arrivals from a
direction can increase the duration of a vehicle's waiting
time in that direction to get a green light signal. In this
study, the authors make the concept of adaptive
synchronous traffic control systems. The system is not
synchronized with other traffic regulators, but with the
348 PROC. INTERNAT. CONF. SCI. ENGIN. 3: 347-352, April 2020
collapse of the vehicle arrival density data from the main
direction. With this system, although there are changes
in the density of vehicle arrivals from several directions,
it is expected that the duration of the vehicle waiting
time can be made at a minimum, especially for the main
directions. This research is expected to be a solution to
minimize traffic congestion.
MATERIALS AND METHODS
1. Traffic Light Characteristics.
Traffic lights are auxiliary devices with lights mounted
on function with lights mounted on the lane for the
purpose of installing a traffic flow. Traffic flow settings
at the time of movement of traffic for the movement of
vehicles in each group movement can be alternately
unrelated. There are various kinds of arrangements using
traffic lights where this consideration is very dependent
on the discussion and adjustment of existing conditions
such as volume, geometry, intersections and so forth.
Geometry and traffic conditions will affect the capacity
and performance of traffic on the planning. Therefore,
planning must be able to decide according to the needs
of each group according to needs.
The traffic light system uses the following types of
lights:
a. Green lights (green); is a vehicle that gets the signal
must move forward.
b. Yellow lights (yellow); is a vehicle that receives
compensation to make a decision to apply the next
traffic lights (green or red lights).
c. Red light (red); is a vehicle that gets to stop before
the stop line.
Please note that with the new traffic light regulations
for vehicles that turn left as long as they are not set, the
vehicles that are allowed to turn the road continue.
Repaired with various lights this applies to set the traffic
lights on time.
2. Traffic conditions and movements
Obtained four forms, basic traffic is traffic at the time
of traffic
a. Dive
Diverging is the event separating a vehicle from one
current to another lane.
b. Merge
The event of the joining of vehicles moving on
several compilation roads joins at one point of
storage, and is also present when the vehicle makes a
shopping and joining movement.
c. Weave
Weaving is a meeting of two or more traffic flows
that run in the same direction along a path on a
highway without the help of traffic signs.
d. Crossing
Crossing events between vehicle flows from one lane
to an intersection usually depend on such conditions
which will lead to conflicts on road changes.
3. Webster's method
Webster's method is a method used to determine the time
of a traffic light that has been developed by F.V.
Webster. To determine the time to turn on the traffic
lights can be done the following steps.
A. Determine the saturation current
Table 1. Saturation current at junction (Webster method)
Street Width (m)
Street Length (smp/j)
3.05
1850
3.35
1875
3.65
1900
3.95
1950
4.25
2075
4.60
2250
4.90
2475
5.20
2700
Source, Diktat Lecture 9 RLL, ITP teaching staff
If the width (l) exceeds this, then the saturation
current = l x 525 (smp/ h)
Specifically for good intersections (free vision, etc.)
the number is added by 20%, and for bad intersections
(inclines, insufficient views, etc.) these figures should be
reduced by 15%.
The ratio of normal current to saturated current (y), is
= Q / S
The measure of congestion is expressed as Ratio
Phase, =
Where: S = saturated current (smp/ h)
Q = real current (smp/ h)
B. Determine the optimum cycle time
The factor needed to calculate the maximum cycle time
(the optimum cycle time setting) is the lost time (L),
which is the length of time for a full cycle when there is
no vehicle. This is done not only all red lights time and
red lights time / red / yellow but also as the preparation
time of the road (starting-up) and preparation for the stop
(tailing-off) that occurs when the color change of the
lamp. Wasted time is calculated by the formula:
Lt = 2n + R
n = Number of phases
R = Time of all red and red lights time / red / yellow (2
+ 3 = 5 second)
Lt = Can also be defined as the number of periods of
green lights time reduced by one second per green.
By road research laboratories in the UK, providing
optimum cycle time () is
PRIHANTINI et al. – Application of Webster's Method to Optimizing Traffic Lights … 349
=
Allowable lost time for the value of y in each direction:
sehingga g1 =
g2 =
Description:
FR = Phase Ratio
q = Vehicle flow (vehicle/hours)
g = Green lights time period (second)
Table 2. Cycle length limit table
Number of Phase
Recommended cycle lenght
2
40 - 80 second
3
50 - 100 second
4
80 – 130 second
Actual green lights time
= + −
Where:
= Green lights time aktual (second)
= Green lights time siklus (second)
k = Yellow lights time
Lt = lost time
Nasional III Street (West) and Nasional III Street
(East). Geometric description of the four-way
intersection can be seen in the image below.
Figure 1. Street Junction.
In Figure 1, it has the following information:
1) The north section (coded: A) is Bantul Street which
has 2 lanes, with an entrance width of 5.8 m and an
exit lane of 5.7m
2) The east part (coded: B) is Nasional III Street which
has 2 lanes with 8 m wide entrance and exit lanes.
3) The southern part (coded: C) is Bantul Street has 2
lanes with an entrance width of 5.2 m and an exit of
5.6 m
4) The west part (coded: D) is National III Street which
has 2 lanes with a width of 8 m in and out lanes.
The old traffic light cycle data at intersection four
Bantul-Nasional III Street, Yogyakarta.
Table 3. Long cycle of traffic lights.
Street Width (m)
Red
(second)
Yellow
(second)
Green
(second)
Bantul (North)
106
3
32
Nasional III (East)
103
3
28
Bantul (South)
106
3
32
Nasional III Street
(West)
103
3
28
Traffic volume data is obtained by citing the research
we found. In that study, researchers conducted a survey
and recorded all types of vehicles that crossed the
intersection. Hourly traffic volume at 15-minute
intervals, which are then converted from hourly vehicles
to per-hour passenger car units.
Retrieval of traffic flow data is carried out for one
day, namely Wednesday, March 15, 2017 at 06: 00-18:
30 which can be seen in the following table.
Table 4. Data of vehicles per times.
Interval
Total
Interval
Total
vehicles/times
vehicles/times
06.00 - 07.00
8957
12.00 - 13.00
7447
06.15 - 07.15
10848
12.15 - 13.15
7629
06.30 - 07.30
12165
12.30 - 13.30
7707
06.45 - 07.45
12734
12.45 - 13.45
7822
07.00 - 08.00
12831
13.00 - 14.00
8174
07.15 - 08.15
12498
13.15 - 14.15
8433
07.30 - 08.30
11778
13.30 - 14.30
8912
07.45 - 08.45
10848
13.45 - 14.45
9009
08.00 - 09.00
9834
14.00 - 15.00
9204
08.15 - 09.15
9144
14.15 - 15.15
9437
08.30 - 09.30
9010
14.30 - 15.30
9570
08.45 - 09.45
8545
14.45 - 15.45
9812
09.00 - 10.00
8113
15.00 - 16.00
9781
09.15 - 10.15
8178
15.15 - 16.15
9730
09.30 - 10.30
7819
15.30 - 16.30
9831
09.45 - 10.45
8148
15.45 - 16.45
10061
10.00 - 11.00
8259
16.00 - 17.00
10277
10.15 - 11.15
8058
16.15 - 17.15
10423
10.30 - 11.30
7995
16.30 - 17.30
10542
10.45 - 11.45
7889
16.45 - 17.45
10571
11.00 - 12.00
7689
17.00 - 18.00
10561
11.15 - 12.15
7597
17.15 - 18.15
7966
11.30 - 12.30
7467
17.30 - 18.30
5273
11.45 - 12.45
7545
350 PROC. INTERNAT. CONF. SCI. ENGIN. 3: 347-352, April 2020
Based on the data above, it can be seen that the Peak
Hour Volume is at 07: 00-08: 00 with details that can be
seen in the following table:
Table 5. Peak Hour Volume
INTERVAL
STREET
HV
LV
MC
UM
07.00-08.00
A to B (LEFT)
7
40
260
2
A to C (STRAIGHT)
9
124
912
20
A to D (RIGHT)
0
67
617
3
Total
16
231
1789
25
B to C (LEFT)
1
32
875
22
B to D (STRAIGHT)
94
505
1938
6
B to A (RIGHT)
11
66
423
1
Total
106
603
3236
29
C to D (LEFT)
2
61
340
10
C to A (STRAIGHT)
15
196
2800
30
C to B (RIGHT)
11
109
973
9
Total
28
366
4113
49
D to A (LEFT)
1
26
19
1
D to B (STRAIGHT)
61
274
1141
4
D to C (RIGHT)
10
55
637
11
Total
72
355
1797
16
Table 5. Traffic Volume of APILL intersection.
Street
Segment
Code
LV
HV
MC
Emp =1,0
Emp = 1,3
Emp = 0,2
vehicle
smp
vehicle
smp
vehicle
smp
vehicles
/ times
Smp
/
times
A
231
231
16
20
1789
357
608
B
603
603
106
137
3236
647
3945
1387
C
366
366
28
36
4113
822
4507
1224
D
355
355
72
93
1797
359
2224
807
Description:
(LV) = Light Vehicle
(HV) = Heavy Vehicle
(MC) = Motorcycle
(UM) = Unmotorycle or non-motorized vehicles
Next, the optimum cycle time will be determined
()
=
a. Yellow lights time (R)= 3 second
b. Saturated current at each intersection
For north direction = 5,7 × 525 = 2992,5
For east direction = 8 x 525 = 4200
For south direction = 5,6 x 525 = 2940
For west direction = 8 x 525 = 4200
c. Determine the value of y
=
= 0,203
t =
= 0,33
s =
= 0,416
b =
= 0,192
FR = ∑
= 0,416 + 0,33
= 0,746
d. d. Determine lost time ( Lt)
Lt = 2n + R
= 2(2) + 3
= 7
So the optimum cycle time is:
=
=
=
= 61 second
Total cycle time of the maximum Green lights
= 0−
= 61 – 7
= 54 second
Green lights time
Phase I =
=
= 30 second
Phase II =
=
= 24 second
Red lights time
Phase I = 0−Green lights time−Yellow lights time
= 61 – 30 - 3
= 28 second
Phase II = 0−Green lights time−Yellow lights time
= 61 – 24 - 3
= 34 second
PRIHANTINI et al. – Application of Webster's Method to Optimizing Traffic Lights … 351
Table 6. Cycle time of traffic lights.
Direction
Green
Yellow
Red
North
30
3
28
East
24
3
34
South
30
3
28
West
24
3
34
Based on the results previously described, a
discussion was made about the application of the
Webster Method in traffic lights at four intersections of
Bantul (north), Bantul (south), National III (West) and
National III (East) Streets. The discussion included the
intersection geometry data, vehicle volume, optimum
cycle time, green time and red time.
The geometry of the intersection of the four Streets of
Bantul (north), Bantul Street (south), Nasional III Street
(West) and Nasional III Street (East) has a median of
streets, where the inflow and outflow are not in the same
lane. Based on Table 4.1, the traffic cycle data at APILL
intersection on Bantul - Nasional III Street Yogyakarta
uses 2 phases, where for Bantul Street (south) and Bantul
Street (north) the duration of red is 106 seconds, yellow
is 3 seconds and green is equal to 32 seconds. For
Nasional III Street (East) and Nasional III Street (West)
the duration of red is 103 seconds, yellow is 3 seconds
and green is 28 seconds
The APILL intersection on Bantul-Nasional III Street
Yogyakarta is an intersection that often occurs in traffic,
this is caused by the high volume of vehicles. The peak
traffic volume of 12.5 hours of observation is obtained at
07.00-08.00 WIB. The peak traffic volume on the Bantul
Street (north) with the number of light vehicles is 231
vehicles / hour, heavy vehicles is 16 vehicles / hour and
motorbikes is 1789 vehicles / hour, all types of vehicles
are converted to passenger car units (junior high school),
so 231 pcu/hour for light vehicles, 20 pcu / hour for
heavy vehicles and 357 for motorbikes, so that peak hour
volume of 608 pcu/hour is obtained.
The volume of peak traffic on Nasional III Street
(East) with the number of light vehicles is 603 vehicles /
hour, heavy vehicles is 106 vehicles/hour and
motorbikes is 3236 vehicles/hour, all types of vehicles
are converted into passenger car units (junior high
school), so that 603smp/hour is obtained for light
vehicles, 137 pcu/hour for heavy vehicles and 647 for
motorbikes, so that peak hour volume is 1387 pcu / hour.
The peak traffic volume on the Bantul Street (south)
with the number of light vehicles is 366 vehicles / hour,
heavy vehicles is 28 vehicles/hour and motorbikes are
4113 vehicles/hour, all types of vehicles are converted to
passenger car units (junior high school), so 366 pcu /
hour for light vehicles, 36 pcu/hour for heavy vehicles
and 822 for motorbikes, so that peak hour volume is
1224 pcu/hour.
The peak traffic volume on Nasional III Street (West)
with the number of light vehicles is 355 vehicles / hour,
heavy vehicles is 72 vehicles / hour and motorbikes is
1797 vehicles / hour, all types of vehicles are converted
into passenger car units (junior high school), so that 355
pcu / hour is obtained for light vehicles, 93 pcu / hour for
heavy vehicles and 359 for motorbikes, so a peak hour
volume of 807 pcu / hour is obtained.
The optimum cycle time at the intersection of four is
61 seconds, this looks more optimal, compared to the
optimum cycle time in the field of 133 seconds.
The maximum number of green time cycles is
obtained by subtracting the optimal cycle time from the
lost time (Lt), so that the maximum number of green
time cycles is 54 seconds.
The green time for each phase is obtained by
multiplying phase each phase by the maximum number
of time cycles, divided by the phase ratio, so that the
green time for the Bantul (north) Street is 30 while the
green time in the field is 32 seconds. The green time for
Nasional III Street (East) is 24 seconds, while the green
time in the field is 28 seconds. The green time for the
Bantul (south) Street is 30 seconds, while the green time
on the field is 32 seconds and the green time for
Nasional III Street (West) is 24 seconds, while the green
time on the field is 28 seconds. This looks more efficient
than the green time on the ground.
The red time for each phase is obtained by
subtracting the optimum cycle time between green time
and yellow time, so that it is obtained
The red time for the Bantul Street (north) is 28 while
the red time in the field is 106 seconds. The red time for
Nasional III Street (East) is 34 seconds, while the red
time on the field is 103 seconds. The red time for Bantul
(south) Street is 28 seconds, while the red time in the
field is 106 seconds and the red time for Nasional III
Street (West) is 34 seconds, while the red time in the
field is 103 seconds. This looks more efficient than the
red time on the ground.
RESULTS AND DISCUSSION
The conclusion that can be drawn based on the research
objectives is how to adjust the duration of the traffic
lights using the Webster method obtained results for the
Bantul Street (north), the duration of the green light 30
seconds, yellow 3 seconds and red 28 seconds. For
Nasional III Street (East), the duration of the green light
24 second, yellow 3 second and red 34 second. For
Bantul Street (south), ), the duration of the green light
30 second, yellow 3 second and red 28 second. For
Nasional III Street (West), ), the duration of the green
light 24 second, yellow 3 second and red 34 second.
CONCLUSION
The results of calculations using this method obtained
results for the Bantul Street (north), the duration of the
352 PROC. INTERNAT. CONF. SCI. ENGIN. 3: 347-352, April 2020
green light 30 seconds, yellow 3 seconds and red 28
seconds. For Nasional III Street (East), the duration of
the green light is 24 seconds, yellow is 3 seconds and red
is 34 seconds. For Bantul Street (south), the duration of
the green light is 30 seconds, yellow is 3 seconds and red
is 28 seconds. For Nasional III Street (West), the
duration of the green light is 24 seconds, yellow is 3
seconds and red is 34 seconds. These results look more
optimal than those on the field today. The suggestion in
this study is for the next researcher to use a compatible
graph at the intersection of Bantul - Nasional III Street
Yogyakarta, by adding the assumptions and variables
used.
ACKNOWLEDGEMENTS
We thank our colleagues from Gadjah Mada University
and Yogyakarta State University for providing insights
and expertise that greatly assisted this research.our
completion of this project could not have been
accomplished without the support of each other.
REFERENCES
Badan Pusat Statistik. 2010. Penduduk Indonesia Menurut
Provinsi dan Kab/Kota SP 2010. BPS, Badan Pusat Statistik,
Jakarta
Fitria, Binti Tsamrotul. 2015. Penurunan Model Traffic Flow
Berdasarkan Hukum - Hukum Kesetimbangan. [Dissertation].
Maulana Malik Ibrahim Islamic State University, Malang
[Indonesian]
Miftahurrahmah. 2016. Aplikasi Teori Graf dalam Pengaturan
Lampu Lalu Lintas. [Dissertation]. Alauddin Makassar Islamic
State University, Makassar [Indonesian]
Pambudi, Adi Widya. 2017. Kinerja Simpang Bersinyal Jalan
Bantul, Ringroad Selatan, Yogyakarta. [Dissertation].
Muhammadiyah Yogyakarta University, Yogyakarta
[Indonesian]
