p–ISSN: 2723 - 6609 e-ISSN: 2745-5254
Vol. 5, No. 11, November 2024 http://jist.publikasiindonesia.id/
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4854
Modeling and Simulation of Vehicle Velocity-Density on Buah
Batu Road Using Second-Order Polynomial Regression
Rheyfan Syafdani1, Putu Harry Gunawan2*
Universitas Telkom Bandung, Indonesia
Email: [email protected]1, [email protected]2*
*Correspondence
ABSTRACT
Keywords: velocity,
density, velocity-density
function, second-order
polynomial regression,
lax-wendroff scheme.
The problem of traffic density is complex in the world of
land transportation, especially in urban areas, including
Bandung City. Buah Batu Road, one of the main roads in
Bandung City is 13 meters wide and 1.70 kilometers long,
connecting Bandung City and Bandung Regency. This study
examines the relationship between vehicle speed and traffic
density on Buah Batu Road, Bandung. Using the
macroscopic Lighthill-Whitham Richards (LWR) model,
Second Order Polynomial Regression, and Lax-Wendroff
scheme simulation. This study aims to obtain the speed-
density function for traffic. The introduction emphasizes the
importance of understanding traffic flow dynamics to reduce
congestion, especially in areas with significant vehicle
growth. The methodology used is direct observation of the
Buah Batu Road section with an observed length of 18
meters, with data collected through cellphone camera
recordings at various times. These observation data provide
insight into vehicle density and speed under various
conditions.
Introduction
The problem of traffic density is complex in the world of land transportation,
especially in urban areas, including Bandung City. (Nugroho Julianto, 2010). Congestion
generally occurs at road intersections, especially during rush hour, namely in the morning
when employees go to work, or children go to school and in the evening when they come
home. (Triwibisono & Aurachman, 2020). With rapid population growth, data from 2020
shows that there were 1.2 million two-wheeled vehicles in Bandung City and 536
thousand four-wheeled vehicles (Dewi, Badruzzaman, Fajar, Suhaedi, & Harahap, 2020).
The problem of congestion has become a major challenge for the quality of life of citizens,
not only disrupting travel delays, but also increasing the risk of traffic accidents,
damaging air quality due to vehicle emissions, and disrupting community productivity.
Traffic flow characteristic types are generally categorized into three models,
namely Macroscopic, Microscopic, and Mesoscopic (van Wageningen-Kessels, van Lint,
Vuik, & Hoogendoorn, 2015). The macroscopic model views traffic as a continuous fluid
Vol. 5, No. 11, November 2024 http://jist.publikasiindonesia.id/
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4854
Modeling and Simulation of Vehicle Velocity-Density on Buah
Batu Road Using Second-Order Polynomial Regression
Rheyfan Syafdani1, Putu Harry Gunawan2*
Universitas Telkom Bandung, Indonesia
Email: [email protected]1, [email protected]2*
*Correspondence
ABSTRACT
Keywords: velocity,
density, velocity-density
function, second-order
polynomial regression,
lax-wendroff scheme.
The problem of traffic density is complex in the world of
land transportation, especially in urban areas, including
Bandung City. Buah Batu Road, one of the main roads in
Bandung City is 13 meters wide and 1.70 kilometers long,
connecting Bandung City and Bandung Regency. This study
examines the relationship between vehicle speed and traffic
density on Buah Batu Road, Bandung. Using the
macroscopic Lighthill-Whitham Richards (LWR) model,
Second Order Polynomial Regression, and Lax-Wendroff
scheme simulation. This study aims to obtain the speed-
density function for traffic. The introduction emphasizes the
importance of understanding traffic flow dynamics to reduce
congestion, especially in areas with significant vehicle
growth. The methodology used is direct observation of the
Buah Batu Road section with an observed length of 18
meters, with data collected through cellphone camera
recordings at various times. These observation data provide
insight into vehicle density and speed under various
conditions.
Introduction
The problem of traffic density is complex in the world of land transportation,
especially in urban areas, including Bandung City. (Nugroho Julianto, 2010). Congestion
generally occurs at road intersections, especially during rush hour, namely in the morning
when employees go to work, or children go to school and in the evening when they come
home. (Triwibisono & Aurachman, 2020). With rapid population growth, data from 2020
shows that there were 1.2 million two-wheeled vehicles in Bandung City and 536
thousand four-wheeled vehicles (Dewi, Badruzzaman, Fajar, Suhaedi, & Harahap, 2020).
The problem of congestion has become a major challenge for the quality of life of citizens,
not only disrupting travel delays, but also increasing the risk of traffic accidents,
damaging air quality due to vehicle emissions, and disrupting community productivity.
Traffic flow characteristic types are generally categorized into three models,
namely Macroscopic, Microscopic, and Mesoscopic (van Wageningen-Kessels, van Lint,
Vuik, & Hoogendoorn, 2015). The macroscopic model views traffic as a continuous fluid
Modeling and Simulation of Vehicle Velocity-Density on Buah Batu Road Using
Second-Order Polynomial Regression
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4855
flow and analyzes variables such as speed, density, and traffic flow. Then, the
Microscopic model is a model that observes individual vehicle behavior and interactions
between vehicles, which focuses more on analyzing acceleration, deceleration, and
distance between vehicles. Then, the Mesoscopic model is a model that combines the
Macroscopic and Microscopic approaches (J. Popping, 2013).
Buah Batu Road is 13 meters wide and 1.70 kilometers long, connecting Bandung
City and Bandung Regency. It is located near several important locations, such as toll
roads, food places, and other entertainment centers. (Duddy Studyana et al., 2020), and
make this road frequently passed. With the high volume of existing vehicles, Buah Batu
Road also faces a tough challenge in maintaining smooth traffic and avoiding congestion
that has the potential to harm mobility on Buah Batu Road. (Fadriani & Pirmansyah,
2022).
Fig. 1. Illustration of Conditions on Buah Batu Road
An illustration of traffic congestion can be seen in Fig. 1. This journal will observe
the relationship between speed and traffic flow density. The speed function depends on
the speed of the vehicle. Therefore, the second-order polynomial regression function
approximates the speed function from the observed data. The speed function is obtained
from the relationship between the average velocity of vehicles. (v) and density (ρ)In
traffic flow.
This study analyses and simulates a traffic flow model based on the velocity-density
function obtained from observation data. The structure of this journal is arranged as
follows, Introduction introduces the research topic, Methods discusses the macroscopic
model of traffic flow and the application of Second Order Polynomial Regression, Results
and Discussion present the results and discussion of the methods used, and finally
Conclusion presents the conclusions of this study.
Method
Traffic Flow Model
Traffic flow analysis involves the movement of vehicles in a road network, which
involves complex interactions between vehicles, drivers, and road infrastructure. This
study uses the Lighthill-Whitham-Richards (LWR) macroscopic model, which is the
Second-Order Polynomial Regression
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4855
flow and analyzes variables such as speed, density, and traffic flow. Then, the
Microscopic model is a model that observes individual vehicle behavior and interactions
between vehicles, which focuses more on analyzing acceleration, deceleration, and
distance between vehicles. Then, the Mesoscopic model is a model that combines the
Macroscopic and Microscopic approaches (J. Popping, 2013).
Buah Batu Road is 13 meters wide and 1.70 kilometers long, connecting Bandung
City and Bandung Regency. It is located near several important locations, such as toll
roads, food places, and other entertainment centers. (Duddy Studyana et al., 2020), and
make this road frequently passed. With the high volume of existing vehicles, Buah Batu
Road also faces a tough challenge in maintaining smooth traffic and avoiding congestion
that has the potential to harm mobility on Buah Batu Road. (Fadriani & Pirmansyah,
2022).
Fig. 1. Illustration of Conditions on Buah Batu Road
An illustration of traffic congestion can be seen in Fig. 1. This journal will observe
the relationship between speed and traffic flow density. The speed function depends on
the speed of the vehicle. Therefore, the second-order polynomial regression function
approximates the speed function from the observed data. The speed function is obtained
from the relationship between the average velocity of vehicles. (v) and density (ρ)In
traffic flow.
This study analyses and simulates a traffic flow model based on the velocity-density
function obtained from observation data. The structure of this journal is arranged as
follows, Introduction introduces the research topic, Methods discusses the macroscopic
model of traffic flow and the application of Second Order Polynomial Regression, Results
and Discussion present the results and discussion of the methods used, and finally
Conclusion presents the conclusions of this study.
Method
Traffic Flow Model
Traffic flow analysis involves the movement of vehicles in a road network, which
involves complex interactions between vehicles, drivers, and road infrastructure. This
study uses the Lighthill-Whitham-Richards (LWR) macroscopic model, which is the
Rheyfan Syafdani, Putu Harry Gunawan
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4856
basis of traffic flow theory. The Lighthill-Whitham-Richards (LWR) model examines
important characteristics such as vehicle density, speed, and travel time. This model is
based on the continuity equation and assumes a balanced relationship between speed and
density. The continuity equation ensures that the number of vehicles in a given area
remains constant over time (Wong & Wong, 2002).
The equation form of the Lighthill-Whitham-Richards (LWR) model is presented
as follows. (Vikram, Chakroborty, & Mittal, 2013):
𝜕𝜌
𝜕𝑡 + 𝜕𝑞
𝜕𝑥 = 0 (1)
By replacing 𝜕𝑞 with 𝜌𝑈(𝜌)In this equation, we get (Harry Gunawan, 2014),
(Gunawan & Siahaan, 2017):
𝜕𝜌
𝜕𝑡 + 𝜕(𝜌𝑈(𝜌))
𝜕𝑥 = 0 (2)
In equation 2, 𝜌represents the vehicle density, indicating how this density changes
over time. The variable 𝑡refers to vehicle travel time, which describes changes in density
over some time. The term 𝜌𝑈(𝜌)signifies the velocity function dependent on vehicle
density, meaning the average velocity of vehicles varies according to traffic density. The
variable 𝑥Is the positional variable, indicating spatial changes along the road network. In
simulating a traffic flow model, it is first necessary to define the velocity function. This
paper uses second-order polynomial regression to estimate the velocity function based on
observed data.
Polynomial Regression
Polynomial regression is a statistical analysis method used to model the relationship
between independent variables. 𝑥 and dependent variable 𝑦 using polynomials of degree
𝑛 (Liu & Deng, 2021). This method involves fitting a polynomial curve to the data, which
allows for a more accurate estimation of complex relationships between variables than
simple linear regression. The result is a polynomial function that minimizes the error
between predicted values and observed data. This paper will use second-order polynomial
regression to obtain a velocity function based on observed data. The independent variable
used in this function is density, while the dependent variable is velocity.
The following is the general form of the Polynomial Regression equation.
(Ostertagová, 2012).:
𝑦 = 𝛽0 + 𝛽1𝑥 + 𝛽2𝑥2 + 𝛽3𝑥3 + . . . + 𝛽𝑛𝓍𝑛 + 𝜖 (3)
Because this journal will use second-order polynomial regression, the equation used is:
= 𝛽0 + 𝛽1𝓍 + 𝛽2𝓍2 + 𝜖 (4)
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4856
basis of traffic flow theory. The Lighthill-Whitham-Richards (LWR) model examines
important characteristics such as vehicle density, speed, and travel time. This model is
based on the continuity equation and assumes a balanced relationship between speed and
density. The continuity equation ensures that the number of vehicles in a given area
remains constant over time (Wong & Wong, 2002).
The equation form of the Lighthill-Whitham-Richards (LWR) model is presented
as follows. (Vikram, Chakroborty, & Mittal, 2013):
𝜕𝜌
𝜕𝑡 + 𝜕𝑞
𝜕𝑥 = 0 (1)
By replacing 𝜕𝑞 with 𝜌𝑈(𝜌)In this equation, we get (Harry Gunawan, 2014),
(Gunawan & Siahaan, 2017):
𝜕𝜌
𝜕𝑡 + 𝜕(𝜌𝑈(𝜌))
𝜕𝑥 = 0 (2)
In equation 2, 𝜌represents the vehicle density, indicating how this density changes
over time. The variable 𝑡refers to vehicle travel time, which describes changes in density
over some time. The term 𝜌𝑈(𝜌)signifies the velocity function dependent on vehicle
density, meaning the average velocity of vehicles varies according to traffic density. The
variable 𝑥Is the positional variable, indicating spatial changes along the road network. In
simulating a traffic flow model, it is first necessary to define the velocity function. This
paper uses second-order polynomial regression to estimate the velocity function based on
observed data.
Polynomial Regression
Polynomial regression is a statistical analysis method used to model the relationship
between independent variables. 𝑥 and dependent variable 𝑦 using polynomials of degree
𝑛 (Liu & Deng, 2021). This method involves fitting a polynomial curve to the data, which
allows for a more accurate estimation of complex relationships between variables than
simple linear regression. The result is a polynomial function that minimizes the error
between predicted values and observed data. This paper will use second-order polynomial
regression to obtain a velocity function based on observed data. The independent variable
used in this function is density, while the dependent variable is velocity.
The following is the general form of the Polynomial Regression equation.
(Ostertagová, 2012).:
𝑦 = 𝛽0 + 𝛽1𝑥 + 𝛽2𝑥2 + 𝛽3𝑥3 + . . . + 𝛽𝑛𝓍𝑛 + 𝜖 (3)
Because this journal will use second-order polynomial regression, the equation used is:
= 𝛽0 + 𝛽1𝓍 + 𝛽2𝓍2 + 𝜖 (4)
Modeling and Simulation of Vehicle Velocity-Density on Buah Batu Road Using
Second-Order Polynomial Regression
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4857
In equation 4 𝑦 is the dependent variable, 𝑥 is an independent variable, 𝛽0Is an
intercept, 𝛽1Is the linear coefficient, 𝛽2 is the quadratic coefficient, and 𝜖Is the error term.
This model captures the non-linear relationship between 𝑥 and 𝑦.
Results and Discussion
In this Journal, data collection was conducted through direct observation on Buah
Batu Road, Bandung, West Java, Indonesia. The length of the observed road section was
18 meters. Data were collected from one direction of the road, specifically the road
section marked in Fig. 2. This Journal considers 4 motorcycles in the observation which
is equivalent to 1 car, and one truck or bus is equivalent to 2 cars.
Fig. 2 Location of the Dataset was Taken
Data collection was carried out over several days at different and random times, by
recording traffic conditions using a tripod-mounted camera in video form. After obtaining
the data, the data was preprocessed by converting the video into numeric data which was
then entered into Excel format to facilitate data collection and made into .csv format.
Furthermore, Fig. 3 provides a location where the recording camera was positioned for
data collection.
Second-Order Polynomial Regression
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4857
In equation 4 𝑦 is the dependent variable, 𝑥 is an independent variable, 𝛽0Is an
intercept, 𝛽1Is the linear coefficient, 𝛽2 is the quadratic coefficient, and 𝜖Is the error term.
This model captures the non-linear relationship between 𝑥 and 𝑦.
Results and Discussion
In this Journal, data collection was conducted through direct observation on Buah
Batu Road, Bandung, West Java, Indonesia. The length of the observed road section was
18 meters. Data were collected from one direction of the road, specifically the road
section marked in Fig. 2. This Journal considers 4 motorcycles in the observation which
is equivalent to 1 car, and one truck or bus is equivalent to 2 cars.
Fig. 2 Location of the Dataset was Taken
Data collection was carried out over several days at different and random times, by
recording traffic conditions using a tripod-mounted camera in video form. After obtaining
the data, the data was preprocessed by converting the video into numeric data which was
then entered into Excel format to facilitate data collection and made into .csv format.
Furthermore, Fig. 3 provides a location where the recording camera was positioned for
data collection.
Rheyfan Syafdani, Putu Harry Gunawan
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4858
Fig. 3 Plan of the observation site
Approximation of Velocity Function
Table 1
Buah Batu Road Traffic Flow Dataset
No T-In T-Out ∆t Speed Density
1 00:29 00:39 10 1.80 0.55
2 00:32 00:55 23 0.78 0.41
3 00:33 00:45 12 1.50 0.48
4 00:36 01:00 24 0.75 0.48
5 00:36 00:48 12 1.50 0.48
… … … … … …
500 07:47 07:50 3 6.00 0.03
The main purpose of data observation is to obtain the speed function by collecting
data on traffic flow density, and vehicle speeds encountered in the observation location.
In total, 500 data have been collected. This data set is detailed in Table 1. The next step
involves calculating the speed and density functions with the collected data. The
calculation equations used are as follows:
𝜌 = 𝑉
𝑉𝑚𝑎𝑥
, 𝑣 = 𝐿
∆𝑡 (5)
Where 𝜌Is the density, 𝑣 is velocity, 𝑉Is the volume of vehicles, 𝑉𝑚𝑎𝑥Is the
maximum volume that can be accommodated in the domain, 𝐿 represents the length of
the studied road domain, and ∆𝑡Is the travel time. The results of the velocity function
using second-order polynomial regression can be seen in Fig. 4.
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4858
Fig. 3 Plan of the observation site
Approximation of Velocity Function
Table 1
Buah Batu Road Traffic Flow Dataset
No T-In T-Out ∆t Speed Density
1 00:29 00:39 10 1.80 0.55
2 00:32 00:55 23 0.78 0.41
3 00:33 00:45 12 1.50 0.48
4 00:36 01:00 24 0.75 0.48
5 00:36 00:48 12 1.50 0.48
… … … … … …
500 07:47 07:50 3 6.00 0.03
The main purpose of data observation is to obtain the speed function by collecting
data on traffic flow density, and vehicle speeds encountered in the observation location.
In total, 500 data have been collected. This data set is detailed in Table 1. The next step
involves calculating the speed and density functions with the collected data. The
calculation equations used are as follows:
𝜌 = 𝑉
𝑉𝑚𝑎𝑥
, 𝑣 = 𝐿
∆𝑡 (5)
Where 𝜌Is the density, 𝑣 is velocity, 𝑉Is the volume of vehicles, 𝑉𝑚𝑎𝑥Is the
maximum volume that can be accommodated in the domain, 𝐿 represents the length of
the studied road domain, and ∆𝑡Is the travel time. The results of the velocity function
using second-order polynomial regression can be seen in Fig. 4.
Modeling and Simulation of Vehicle Velocity-Density on Buah Batu Road Using
Second-Order Polynomial Regression
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4859
Figure 4 Second Order polynomial Regression Dataset Model Result
Fig. 4., shows a gradual decrease in vehicle speeds as density increases. The red
line shows a less pronounced but similar trend, with speeds decreasing significantly at
first, then slowing down, and increasing slightly at very high densities. Fig. 4. highlights
how density has a significant impact on traffic flow and vehicle speeds. As a result, the
speed function obtained by following equation 5 is:
𝑣(𝜌) = −12.995𝜌 + 4.819
With coefficient ρ negative value of the speed function indicates that increasing
density consistently decreases vehicle speed, indicating that vehicles tend to move slower
in dense traffic conditions. The intercept of the function represents the initial vehicle
speed as density approaches zero, with an estimated maximum speed of about 4.819.
The second-order polynomial regression used in this analysis captures the non-
linear relationship between density and vehicle speed, with the regression curve showing
a sharper decrease in speed at higher densities. This reflects that as traffic becomes denser,
vehicle speeds can significantly reduce. This analysis provides strong evidence that
increasing traffic density is directly correlated with decreasing vehicle speeds.
Numerical Simulation
The traffic flow simulation used is the Lax-Wendroff simulation for vehicle density
along the Buah Batu road. Initialization is carried out on a road length of 100 units with
101 discrete points. The initial density is set at 0.45. The characteristic speed is calculated
based on the previously determined polynomial coefficients for both conditions, and the
simulation runs for 300-time steps with a time interval of 0.01 units.
Second-Order Polynomial Regression
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4859
Figure 4 Second Order polynomial Regression Dataset Model Result
Fig. 4., shows a gradual decrease in vehicle speeds as density increases. The red
line shows a less pronounced but similar trend, with speeds decreasing significantly at
first, then slowing down, and increasing slightly at very high densities. Fig. 4. highlights
how density has a significant impact on traffic flow and vehicle speeds. As a result, the
speed function obtained by following equation 5 is:
𝑣(𝜌) = −12.995𝜌 + 4.819
With coefficient ρ negative value of the speed function indicates that increasing
density consistently decreases vehicle speed, indicating that vehicles tend to move slower
in dense traffic conditions. The intercept of the function represents the initial vehicle
speed as density approaches zero, with an estimated maximum speed of about 4.819.
The second-order polynomial regression used in this analysis captures the non-
linear relationship between density and vehicle speed, with the regression curve showing
a sharper decrease in speed at higher densities. This reflects that as traffic becomes denser,
vehicle speeds can significantly reduce. This analysis provides strong evidence that
increasing traffic density is directly correlated with decreasing vehicle speeds.
Numerical Simulation
The traffic flow simulation used is the Lax-Wendroff simulation for vehicle density
along the Buah Batu road. Initialization is carried out on a road length of 100 units with
101 discrete points. The initial density is set at 0.45. The characteristic speed is calculated
based on the previously determined polynomial coefficients for both conditions, and the
simulation runs for 300-time steps with a time interval of 0.01 units.
Rheyfan Syafdani, Putu Harry Gunawan
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4860
Figure 5 Traffic flow simulation with the Lax-Wendroff scheme after Smoothing
The Lax-Wendroff scheme is a numerical method for solving hyperbolic
conservation laws in one-dimensional space, particularly useful in traffic flow modeling.
This conservative scheme ensures the conservation of traffic density over time by
applying a second-order Taylor series expansion. The resulting equations model the
evolution of traffic density. (𝜌)Er discrete time intervals, adjusting the density based on
the flow rate and the difference between adjacent points. This method effectively handles
non-linearity and discontinuity, making it robust to simulate realistic traffic scenarios.
(Babbar & Chandrashekar, 2024).
The simulation results are shown in Fig. 5., which illustrates the initial density
distribution (blue dashed line) and the final density distribution after simulation (orange
line). A Gaussian filter is applied to the simulation results to produce a more precise graph
by reducing noise and smoothing the data. From the simulation results, significant
fluctuations occur at the initial road length of 40 to around 50, indicating instability of
traffic flow.
The results of the simulation analysis show that increasing density consistently
causes a decrease in vehicle speed. The velocity function for this condition is 𝑣(𝜌) =
−12.995𝜌 + 4.819. The intercept indicates the initial speed of vehicles when the density
is close to zero, with a maximum speed of about 4,819. The negative coefficient proves
that increasing density reduces speed, indicating slower movement in high-density traffic.
This underlies the use of second-order polynomial regression in capturing the non-
linearity between density and velocity.
Conclusion
The conclusion of this study shows that the Second Order Polynomial Regression
method with numerical simulation using the Lax-Wendroff scheme is effective in
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4860
Figure 5 Traffic flow simulation with the Lax-Wendroff scheme after Smoothing
The Lax-Wendroff scheme is a numerical method for solving hyperbolic
conservation laws in one-dimensional space, particularly useful in traffic flow modeling.
This conservative scheme ensures the conservation of traffic density over time by
applying a second-order Taylor series expansion. The resulting equations model the
evolution of traffic density. (𝜌)Er discrete time intervals, adjusting the density based on
the flow rate and the difference between adjacent points. This method effectively handles
non-linearity and discontinuity, making it robust to simulate realistic traffic scenarios.
(Babbar & Chandrashekar, 2024).
The simulation results are shown in Fig. 5., which illustrates the initial density
distribution (blue dashed line) and the final density distribution after simulation (orange
line). A Gaussian filter is applied to the simulation results to produce a more precise graph
by reducing noise and smoothing the data. From the simulation results, significant
fluctuations occur at the initial road length of 40 to around 50, indicating instability of
traffic flow.
The results of the simulation analysis show that increasing density consistently
causes a decrease in vehicle speed. The velocity function for this condition is 𝑣(𝜌) =
−12.995𝜌 + 4.819. The intercept indicates the initial speed of vehicles when the density
is close to zero, with a maximum speed of about 4,819. The negative coefficient proves
that increasing density reduces speed, indicating slower movement in high-density traffic.
This underlies the use of second-order polynomial regression in capturing the non-
linearity between density and velocity.
Conclusion
The conclusion of this study shows that the Second Order Polynomial Regression
method with numerical simulation using the Lax-Wendroff scheme is effective in
Modeling and Simulation of Vehicle Velocity-Density on Buah Batu Road Using
Second-Order Polynomial Regression
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4861
modeling the relationship between vehicle speed (𝑣) with density (𝜌)n the traffic flow of
Buah Batu Road. The results of the analysis show that vehicle speed decreases with
increasing traffic density. The results of the speed function are as follows, 𝑣(𝜌) =
−12.995𝜌 + 4.819. The negative coefficient of the function indicates that increasing
density decreases vehicle speed, and reveals that the density distribution shows significant
fluctuations when vehicle congestion occurs.
These findings have important implications for traffic planning and management.
Implementing new management strategies can help create more stable and efficient traffic
flows, improving safety and comfort for road users. Future research can focus on
developing more sophisticated models that incorporate various obstacles and dynamic
traffic conditions. For example, incorporating real-world traffic data and adaptive traffic
signal control systems can improve the accuracy and applicability of the model.
Additionally, extending the model to include variations in driver behavior, road
conditions, and weather effects can provide a more comprehensive understanding of
traffic patterns.
Second-Order Polynomial Regression
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4861
modeling the relationship between vehicle speed (𝑣) with density (𝜌)n the traffic flow of
Buah Batu Road. The results of the analysis show that vehicle speed decreases with
increasing traffic density. The results of the speed function are as follows, 𝑣(𝜌) =
−12.995𝜌 + 4.819. The negative coefficient of the function indicates that increasing
density decreases vehicle speed, and reveals that the density distribution shows significant
fluctuations when vehicle congestion occurs.
These findings have important implications for traffic planning and management.
Implementing new management strategies can help create more stable and efficient traffic
flows, improving safety and comfort for road users. Future research can focus on
developing more sophisticated models that incorporate various obstacles and dynamic
traffic conditions. For example, incorporating real-world traffic data and adaptive traffic
signal control systems can improve the accuracy and applicability of the model.
Additionally, extending the model to include variations in driver behavior, road
conditions, and weather effects can provide a more comprehensive understanding of
traffic patterns.
Rheyfan Syafdani, Putu Harry Gunawan
Indonesian Journal of Social Technology, Vol. 5, No. 11, November 2024 4862
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preserving Lax-Wendroff Flux Reconstruction for hyperbolic conservation laws
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