Simulation Model to Reduce the Traffic Jams with a Stochastic
Program
M. ALI MUSRI S
Universitas Pembinaan Masyarakat Indonesia (UPMI)
Jl. Teladan No.15, Teladan Barat, Medan
INDONESIA
SITI FATIMAH
Universitas Potensi Utama
Jl. KL Yos Sudarso Km 6,5 No 3A, Tanjung Mulia, Medan
INDONESIA
SAIFUL ANWAR MATONDANG
Universitas Islam Sumatera Utara
Jl. Sisingamangaraja No.Kelurahan, Teladan Barat, Medan
INDONESIA
Abstract: Traffic congestion needs a simulation model to reduce its effects on traffics jams and pollution. The
traffic cessation caused by the large number of vehicles exceeding the capacity of the road users. This study
applied a stochastic program to the traffic congestion; it causes most of the working hours to be spent on roads
that indirectly place a negative impact on economic growth. It also causes serious air pollution that will worsen
the overall environmental condition. Data obtained show the factors causing traffic congestion in the city of
Medan and with approach the stochastic program model used to solve this problem. Data indicated that there
are four factors causing traffic congestion in Medan, which are non-growth of road, economic growth,
population growth, and increase of motor vehicle.Population factor; the existence of good population growth
caused by natural and migration growth. It concludes that the traffic jams are due to the socio-economic
factors; namely the development of community business activities. Also socio-cultural factors; the existence of
changes in the pattern of life and public order due to outside influences, communication, and information
systems.
Key-Words: Stochastic program, traffic congestion, population growth, road length
Received: March 22, 2021. Revised: November 7, 2021. Accepted: December 5, 2021. Published: January 7, 2022.
1 Introduction
Traffic Jam is one of the important issues in public
spaces, it makes the congestion the number of
vehicles exceeding the capacity of the road users.
The negative impact of traffic congestion also
causes most of the working hours to be spent on
roads that indirectly gives a negative impact on
economic growth. It also causes air pollution that
will worsen the overall environmental condition.
Therefore, it is hoped that by reducing traffic
congestion, the city can play a very important role in
people's lives by ensuring a healthy environment
that is free from pollution [1].
Traffic congestion continues to be a major problem
in cities around the world, especially in developing
countries which result in major delays, increased
fuel wastage and monetary losses. Due to the poor
road network, the general result of many developing
countries is the presence of small, critical areas that
are common to congestion with poor traffic
management around this area is potentially resulting
in long traffic congestion. Weak traffic management
is the main reason for worldwide traffic congestion
[2]. For example, traffic congestion in Medan City
is getting more and more chaotic. The absence of a
clear spatial layout concept for the city of Medan as
along-term transportation network plan results from
the poor development of Medan City.
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DOI: 10.37394/232015.2022.18.5
M. Ali Musri S, Siti Fatimah,
Saiful Anwar Matondang
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Two main categories cause traffic congestion: (a)
micro-level factors (eg. relating to on-road traffic)
and (b) macro-level factors associated with overall
demand for road users. Traffic congestion is
triggered at the micro-level (eg. on the road) and
driven at the macro level by factors that contribute
to the occurrence of traffic congestion. Micro-level
factors, for example, many people and goods want
to move at the same time means too many vehicles
for limited road space. Many trips may be delayed
by irregular but frequent events, such as accidents,
vehicle damage, false traffic signals, special events
such as mass social gatherings, political
demonstrations, adverse weather conditions, etc.,
which are contributing to various traffic problems.
On the other hand, macro-level factors such as land
use, income levels, car ownership trends,
infrastructure investment, regional economic
dynamics, etc. can also cause congestion [3].
Traffic congestion arises when a highway approach
system is concerned with vehicle capacity, resulting
in many negative impacts from fuel disposal and
increasing exhaust emissions. Several studies have
modelled the situation in urban areas and the
economic values associated with excessive fuel
consumption and time wasted in traffic. While this
is a considerable economic loss, there are several
externals of unspecified congestion, including the
public health impact of excess air pollutant
emissions during the period of congestion [4].
2 Method
This research applied the Stochastic Program to
make a simulation model to reduce the traffic jam in
Medan Municipal of North Sumatra, Indonesia.
Based on the incorporation of uncertainty into the
constraints and objective function of a mathematical
program would result in a stochastic program [8].
This Stochastic program was used as a form of a
stochastic model that may reduce traffic congestion
in Medan City. The Stochastic programming refers
to a mathematical program that can be linear,
mixed, nonlinear, but by displaying stochastic
elements in the data. Many mathematical problems
have been used to determine a feasible model of
settlement when the problem arises uncertainty.
Many optimization issues contain uncertainty [5].
Some cases of these problems contain a random
process or some unknown information. The
incorporation of this uncertainty into the constraints
and objective functions of a mathematical program
produces a stochastic program. It can therefore be
stated that as:
1. In a deterministic math program, data
(coefficients) are known (certain)
numbers.
2. In the stochastic program, the data
(coefficient) is an unknown number
(uncertain) presented as an opportunity
distribution.
Stochastic programs are proposed to replace
deterministic models, where unknown coefficients
and parameters are random [6]. The general term of
Stochastic Program can be expressed as follows:
s.t
Where , and are discreet random variables
( is assumed to be deterministic) which its
probability distribution is known.
3 Problem Solution
The result of the analysis shows that 4 factors
dominate the cause of traffic congestion in Medan;
lack of road area, economic growth, population
growth, an increasing number of vehicles.
Thus, its relation to the stochastic program model:
1 1 2 2 3 3 4 4
1
min
n
Tjj
j
f x c x c x c x c x c x c x
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Note :
1
x
= Lack of road area
2
x
= Economic growth
3
x
= Population growth
4
x
= Increasing number of vehicles
Then, for each factor coefficients are obtained
as
1 2 3 4
0,67; 0,78; 0,86; 0,73c c c c
. So
that, the general form of a stochastic program can be
written as:
1 1 2 2 3 3 4 4
1
min
n
Tjj
j
f x c x c x c x c x c x c x
1 2 3 4
1
min 0,67 0,78 0,86 0,73
n
Tjj
j
f x c x c x x x x x
In this model, the listed constant value of 0.67 can
be interpreted that the variable width of the road that
does not grow (
1
x
) positive effect on traffic
congestion in the city of Medan. When the width of
the road does not increase has increased by one unit,
then the traffic jam in Medan City will also increase
by 0.67 units.
In this model, the value of the listed constants is
0.78. In this model, the listed constant value of 0.78
can be interpreted that the variable of economic
growth (
2
x
) has a positive effect on traffic
congestion in Medan. As economic growth
increases by one unit, traffic congestion in Medan
would increase toward 0.78 unit. In this model, the
listed constant value of 0.86 can be interpreted that
the variable increase in population (
3
x
) has a
positive effect on traffic congestion in Medan. As
the population grows by an increase of one unit,
traffic congestion in Medan could reach 0.86 unit. In
this model, the listed constant value of 0.73 can be
interpreted that the variable increase in the number
of motor vehicles (
4
x
) positively affect the traffic
congestion in the city of Medan. As the number of
motor vehicles increases by one unit, traffic
congestion in Medan will also increase by 0.73
units.
3.1 The Solution to Traffic Congestion in Medan
Several steps can be taken to solve the traffic
congestion problem that must be formulated in a
comprehensive plan. Here are some alternative
solutions to reduce traffic congestion in Medan City,
namely:
1. Increase the capacity
a) Widen the road
b) Transform the traffic circulation into a
one-way street
c) Reduce the conflict in the cross-section
by limiting a certain traffic flow
2. Reduce the number of private vehicles and
encouraged to use of public transportation
3. Provide a place to people who want to sell
things that can prevent them to sell on the
side of the road
4. Prohibit vehicles to park on the side of the
road
5. Restriction on the number of vehicles
6. Increase the load capacity
7. Implement appropriate and effective traffic
management.
8. Provide better public transportation which is
professionally managed
9. Partiality to public transportation
3.2 Population Growth
The population is an important element in economic
activity as well as an effort to build an economy
because the population provides manpower, experts,
heads of companies of entrepreneurs in creating
economic activities [7]. Based on that, the
population of Medan citizen for 6 years is shown in
table 1 below.
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Table 1. Population Density of Medan City by
District 2010-2016
No.
Districts
Large
(Km2)
Populati
on
Populatio
n density
(/Km2)
1.
Medan
Tuntunga
n
20,68
84.775
4.099
2.
Medan
Johor
14,58
130.414
8.945
3.
Medan
Amplas
11,19
121.362
10.846
4.
Medan
Denai
9,05
145.677
16.097
5.
Medan
Area
5,52
98.955
17.927
6.
Medan
Kota
5,27
74.406
14.119
7.
Medan
Maimun
2,98
40.624
13.097
8.
Medan
Polonia
9,01
55.369
6.145
9.
Medan
Baru
5,84
40.519
6.938
10.
Medan
Selayang
12,81
104.454
8.154
11.
Medan
Sunggal
15,44
115.687
7.493
12.
Medan
Helvetia
13,16
149.806
11.383
13.
Medan
Petisah
6,82
63.33
9.097
14.
Medan
Barat
5,33
72.620
13.625
15.
Medan
Timur
7,76
111.369
14.352
16.
Medan
Perjuanga
n
4,09
95.790
23.421
17.
Medan
Tembung
7,99
137.062
17.154
18.
Medan
Deli
20,84
178.147
8.548
19.
Medan
Labuan
36,67
116.357
3.625
20.
Medan
Marelan
23,82
156.394
6.566
21.
Medan
Belawan
26,25
98.020
3.734
Amount
265,10
2.191.14
0
8.265,33
As the population keeps growing, the population
density increases from 7,913people/Km2in 2010 to
8,265.33 people/Km2pada in 2016. The population
density is relatively high, concerning where the
available land area is relatively limited. This
situation can certainly lead to an imbalance between
the carrying capacity and the capacity of existing
environments. The largest number of residents in
Deli District is followed by Marelan and Helvetia.
The lowest number of population is in Medan Baru,
Medan Maimun and Medan Polonia. The highest
population density is in Medan Perjuangan, Medan
Area, and Medan Tembung. Meanwhile, the lowest
population density is in Medan Labuhan Sub-district
with 3,173 people/Km2.
3.3 City Growth
According to Levy et al [4], a city is a residential
area with a relatively large population, a high-
intensity workplace of the population and a place of
public service. City growth refers to the notion of
quantity, which in this case is indicated by the
number of factors of production used by the city's
economic system. The greater the production means
an increasing demand.
City growth is a physical change of the city as a
result of urban social development.
3 factors influence the growth of the city:
a. Population factor; the existence of good
population growth caused by natural and
migration growth
b. Socio-economic factors; namely the
development of community business
activities
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c. Socio-cultural factors; the existence of
changes in the pattern of life and public
order due to outside influences,
communication, and information systems.
3.4 The Approaching of a Stochastic Program to
Prevent the Traffic Congestion in Medan
Many management planning and operational issues
that contain uncertainty are discussed and resolved
via stochastic programs., for example, the problem
of traffic congestion in Medan. This problem is
related to knowing what factors are causing traffic
jam in Medan (eg. population growth, economic
growth, unevenness of shopping centres). So that
the formulation of the problem is to determine the
factors causing traffic congestion in Medan and how
the stochastic program model used to solve traffic
congestion problems.
4 Conclusion
Data interpretation gives two conclusions;
1. Simulation of Stochastic Program has four
factors which cause the traffic congestion in Medan
Municipal are: the lack of road area, economic
growth, population growth, and the increase of
private vehicles. Thus, to reduce the traffic
congestion in Medan, the government needs to
manage the road professionally and with full of
responsibility. Then, for economic growth, the
government needs to put more efforts to provide
efficient public transportation facilities. For
population growth, the government needs to
socialize the people about the significance of small
and efficient families.
2. For controlling the growth of private vehicles the
regulation to limit the economic usage of cars is
untill 10 yeras. The Policy to make limitation is
expected to reduce the number of vehicles which are
responsible for the traffic congestion.
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