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Application of Webster's Method to Optimizing Traffic Lights at the
Intersection of Bantul - Nasional III Street, Yogyakarta
Albert Hosea Santoso1, Hanifa Reygina Fajrin2, Prihantini3
1Department of Mathematics, Faculty of Mathematics and Science, Gadjah Mada University, 2Department of Mathematics, Faculty of Mathematics
and Science, Gadjah Mada University, 3Department of Mathematics Education, Faculty of Mathematics and Science, Yogyakarta State University
Sekip Utara Bulaksumur Yogyakarta 55281, Indonesia. Tel. +62-274-513339, Fax. +62-274-513339.
1Email: albert.h.s.@mail.ugm.ac.id 2Email: hanifareygina@mail.ugm.ac.id 3Email: titinprihantini4@gmail.com
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 Central Statistics Agency (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, If it applied in the field, it can reduce traffic congestion in The APILL intersection on Bantul - Nasional III Street Yogyakarta
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 crossStreets, 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 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 (pcu/h)
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 (pcu/ 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 saturation flow (y), is = Q / S
The measure of congestion is expressed as Ratio Phase, =
Where: S = Saturation flow (pcu/ h)
Q = Design flow (pcu/ h)
B. Determine the optimum cycle time
The factor needed to calculate the maximum cycle time (the optimum cycletime 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 =
Allowable lost time for the value of y in each direction:
, so 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 : = Actual green lights time (second)
= Green lights time cyclus (second)
k = Yellow lights time
Lt = lost time
RESULTS AND DISCUSSION
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:
i. 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 5.7
m
ii. The east part (coded: B) is Nasional III Street which has 2 lanes with 8 m wide entrance and exit lanes.
iii. 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
iv. 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 Jl. 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
24
Nasional III (East)
102
3
28
Bantul (South)
98
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. Non-conflicting through section A and C are grouped in a
single phase called phase I, and non-conflicting through section B and D are grouped in a single phase called phase II.
However there are permitted right turns in the traffic flow.
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
vehicles/times
06.00 - 07.00
8957
06.15 - 07.15
10848
06.30 - 07.30
12165
06.45 - 07.45
12734
07.00 - 08.00
12831
07.15 - 08.15
12498
07.30 - 08.30
11778
07.45 - 08.45
10848
08.00 - 09.00
9834
08.15 - 09.15
9144
08.30 - 09.30
9010
08.45 - 09.45
8545
09.00 - 10.00
8113
09.15 - 10.15
8178
09.30 - 10.30
7819
09.45 - 10.45
8148
10.00 - 11.00
8259
10.15 - 11.15
8058
10.30 - 11.30
7995
10.45 - 11.45
7889
11.00 - 12.00
7689
11.15 - 12.15
7597
11.30 - 12.30
7467
11.45 - 12.45
7545
12.00 - 13.00
7447
12.15 - 13.15
7629
12.30 - 13.30
7707
12.45 - 13.45
7822
13.00 - 14.00
8174
13.15 - 14.15
8433
13.30 - 14.30
8912
13.45 - 14.45
9009
14.00 - 15.00
9204
14.15 - 15.15
9437
14.30 - 15.30
9570
14.45 - 15.45
9812
15.00 - 16.00
9781
15.15 - 16.15
9730
15.30 - 16.30
9831
15.45 - 16.45
10061
16.00 - 17.00
10277
16.15 - 17.15
10423
16.30 - 17.30
10542
16.45 - 17.45
10571
17.00 - 18.00
10561
17.15 - 18.15
7966
17.30 - 18.30
5273
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
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
07.00-08.00
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
pce =1,0
pce = 1,3
pce = 0,2
vehicle
pcu
vehicle
pcu
vehicle
pcu
vehicles /
times
PCU /
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. Saturation flow 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
N =
= 0,203
E =
= 0,33
S =
= 0,416
W =
= 0,192
FR = ∑
= 0,416 + 0,33
= 0,746
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
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 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 98 seconds and 106
seconds, yellow is 3 seconds and green is equal to 32 seconds and 24 seconds. For Nasional III Street (East) and
Nasional III Street (West) the duration of red is 102 seconds and 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 (pcu), 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 (pcu), so that 603 pcu / 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 (pcu), 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 (pcu), 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 24 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 102 seconds. The red time for Bantul
(south) Street is 28 seconds, while the red time in the field is 98 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.
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
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. The new traffic light’s cycle time that we have found is more optimal than the traffic light’s cycle time in
the field. If we applied this result in the field, we can reduce traffic congestion in The APILL intersection on
Bantul - Nasional III Street Yogyakarta
ACKNOWLEDGEMENTS
We thank our colleagues from Gadjah Mada 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.
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