Prediction of Traffic Flow Time Series Data on Jakarta-Cikampek Toll Road Using a Chaotic Approach and Local Linear Approximation Method

Yessy  Yusnita; Nur Hamiza  Adenan; Angelalia Roza

doi:10.24191/jaeds.v6i1.166

Authors

Yessy Yusnita Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Perak, Malaysia.
Nur Hamiza Adenan Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Perak, Malaysia.
Angelalia Roza Faculty of Engineering, Institut Teknologi Padang, Padang, Indonesia.

DOI:

https://doi.org/10.24191/jaeds.v6i1.166

Keywords:

Traffic Flow Forecasting, Chaos Approach, Local Linear Approximation Method, Time Series Analysis, Jakarta–Cikampek Toll Road

Abstract

The Jakarta–Cikampek Toll Road is widely recognised as a critical corridor linking Jakarta with major industrial centres and expanding residential areas in West Java. Traffic along this route is frequently dense and exhibits noticeable fluctuations over time. At certain periods, these variations reveal nonlinear patterns shaped not only by commuter movements and freight transport but also by broader economic activity. This study focuses on short-term traffic forecasting by modelling traffic flow as a nonlinear dynamical system rather than a purely stochastic process. A chaos-based framework is applied to the traffic flow time series through two main stages: first, the presence of chaotic behaviour is examined using the 0–1 test; second, short-term forecasting is performed using the Local Linear Approximation Method (LLAM), which utilises neighbouring trajectories in phase space. Hourly traffic flow data recorded over seven consecutive days are analysed, with 144 observations used for training and 24 for testing. The 0–1 test confirms the existence of chaotic dynamics within the series. During the forecasting stage, LLAM demonstrates reasonable agreement with observed traffic flow, achieving a Pearson correlation coefficient (r) of 0.8964, a Mean Absolute Error (MAE) of 159.41 vehicles per hour, and a Root Mean Squared Error (RMSE) of 203.42 vehicles per hour. These findings indicate that chaos-based modelling provides a dependable approach for short-term traffic forecasting. Beyond predictive accuracy, the framework offers practical value by supporting quicker operational responses, improved congestion management, and more effective short-term planning in dynamic toll-road environments.

Downloads

Download data is not yet available.

References

J. D. Wang and C. O. N. Susanto, “Traffic Flow Prediction with Heterogeneous Data Using a Hybrid CNN-LSTM Model,” Comput. Mater. Contin., vol. 76, no. 3, pp. 3097–3112, 2023, doi:10.32604/cmc. 2023.040914.

BPS, “Land Transportation Statistics,” Indonesia, 2024.

T. Lanori and B. H. Supriyanto, “Problems of the Impact of Modernization of Indonesia’s Public Transportation Equipment System,” Int. J. Soc. Sci., vol. 2, no. 5, pp. 2163–2176, 2023, doi:10.53625/ijss.v2i5.4929.

R. Pamuji and F. S. Widyatami, “Traffic Management and Engineering Works for Halim LRT-HSR Integration Station in Jakarta-Cikampek Toll Road Segment Km. 1+280 to 1+420,” J. Tek. Sipil, vol. 18, no. 1, pp. 87–105, 2022, doi:10.28932/jts.v18i1.4382.

F. Zukhruf, A. Maulana, T. S. Nugroho, O. Purwanti, and S. Ananda, “Traffic Impact Analysis Due to Disruption During Major Events using Micro-Simulation Model,” J. Jalan Jemb., vol. 41, no. 2, pp. 123–133, 2024, doi:https://doi.org/10.58499/jatan.v41i2.1219.

Zhang et al, “Short-term Traffic Flow Prediction: A Method of MEA-LSTM Model Based on Chaotic Characteristics Analysis,” J. Sustain. Built Environ., vol. 1, no. 1, pp. 1–13, 2024, doi:https://doi.org/10.70731/yk3fpz22.

G. Li, H. Deng, and H. Yang, “Traffic Flow Prediction Model Based on Improved Variational Mode Decomposition and Error Correction,” Alexandria Eng. J., vol. 76, pp. 361–389, 2023, doi:10.1016/j.aej.2023.06.008.

Zhou et al., “Variational Graph Neural Networks for Road Traffic Prediction in Intelligent Transportation Systems,” IEEE Trans. Ind. Informatics, vol. 17, no. 4, pp. 2802–2812, 2021, doi:10.1109/TII.2020.3009280.

A. Carianni and A. Gemma, “Overview of Traffic Flow Forecasting Techniques,” IEEE Open J. Intell. Transp. Syst., vol. 6, no. June, pp. 848–882, 2025, doi:10.1109/OJITS.2025.3580802.

Y. Yusnita, N. H. Adenan, and A. Roza, “Applications of the Chaos Approach on Transportation Systems – A Review,” Malaysian J. Sci. Adv. Technol., vol. 5, no. 4, pp. 251–259, 2025, doi:https://doi.org/10.56532/mjsat.v5i4.557.

A. Mashuri, N. H. Adenan, N. S. Abd Karim, W. T. Siew, and Z. Zeng, “Application of Chaos Theory in Different Fields - A Literature Review,” J. Sci. Math. Lett., vol. 12, no. 1, pp. 92–101, Jan. 2024, doi:10.37134/jsml.vol12.1.11.2024.

B. Naheliya, P. Redhu, and K. Kumar, “Chaotic Gravitational Search Algorithm and Long Short Term Memory Model for Traffic Flow Prediction,” Futur. Trends Contemp. Math. Appl. Vol. 3 B. 3, vol. 3, pp. 19–29, 2024, doi:10.58532/v3bfcm3p2ch1.

N. H. Zakaria, N. H. Adenan, N. Suriya, A. Karim, and A. Mashuri, “Prediction of Water Level Time Series Data for Dam at Selangor using Chaotic Approach and Local Linear Approximation Method,” J. Sci. Math. Lett., vol. 9, no. 2021, pp. 10–17, 2021, doi:https://doi.org/10.37134/jsml.vol9.sp.2.2021.

B. & Ramadevi and K. Bingi, “Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review,” Symmetry MDPI, vol. 14, no. 955, pp. 1–43, 2022, doi:https://doi.org/10.3390/sym14050955.

Y. Zhuang and G. Valley, “Horizon Forcing : Improving the Recurrent Forecasting of Chaotic Systems,” ACM Trans. Intell. Syst. Technol., vol. 16, no. 5, pp. 1–23, 2025, doi:10.1145/3718090.

S. Ali, S. Bogarra, M. N. Riaz, P. P. Phyo, D. Flynn, and A. Taha, “Applied Sciences From Time-Series to Hybrid Models: Advancements in Short-Term Load Forecasting Embracing Smart Grid Paradigm,” MDPI Appl. Sci., vol. 14, no. 4442, pp. 1–46, 2024, doi:https://www.mdpi.com/2076-3417/14/11/4442.

Ruslan et al, “Prediction Modelling Through Chaotic Approach on Ozone (O3) Pollutant Time Series in Shah Alam City,” ASM Sci. J., vol. 17, 2020, doi:10.32802/asmscj.2022.1159.

Adenan et al, “Traffic Flow Prediction in Urban Area Using Inverse Approach of Chaos Theory,” Civ. Eng. Archit., vol. 9, no. 4, pp. 1277–1282, 2021, doi:10.13189/cea. 2021.090429.

Alias et al, “Predicting Carbon Monoxide Time Series Between Different Settlement Areas in Malaysia Through Chaotic Approach,” J. Sci. Math. Lett., vol. 9, no. 2021, pp. 55–62, 2021.

H. S. Gafel and S. Rashid, “Enhanced Evolutionary Approach for Solving Fractional Difference Recurrent Neural Network Systems: A comprehensive Review and State of the Art in View of Time-Scale Analysis,” AIMS Math., vol. 8, no. August, pp. 30731–30759, 2023, doi:https://www.aimspress.com/journal/Math AIMS.

C. Skokos, G. A. Gottwald, and J. Laskar, "Chaos Detection and Predictability", vol. 100, no. 2. 2010.

G. A. Gottwald and I. Melbourne, “A Test for A Conjecture on the Nature of Attractors for Smooth Dynamical Systems,” Chaos, vol. 24, no. 024403, pp. 1–10, 2014, doi:10.1063/1.4868984.

S. Wallot and D. Mønster, “Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab,” Front. Psychol., vol. 9, no. September, pp. 1–10, 2018, doi:10.3389/fpsyg. 2018.01679.

L. Cao, “Practical Method for Determining the Minimum Embedding Dimension of A Scalar Time Series,” Phys. D Nonlinear Phenom., vol. 110, no. 1–2, pp. 43–50, 1997, doi:10.1016/S0167-2789(97)00118-8.

S. Raubitzek and T. Neubauer, “Taming the Chaos in Neural Network Time Series Predictions,” 2021, doi:https://doi.org/10.3390/e23111424.