Author(s)

TianYi Chen^1*, Cheng Cui²

Affiliation(s)

¹School of Economics and Management, Nanjing Forestry University, Nanjing 210037, Jiangsu, China.

²School of Science, Nanjing Forestry University, Nanjing 210037, Jiangsu, China.

Corresponding Author

TianYi Chen

ABSTRACT

Accurate estimation of traffic flow is crucial for urban traffic management and control, particularly when only main road monitoring data is available and feeder road data is missing. This study addresses the challenge of inferring feeder road traffic flow from main road data by developing a series of regression models tailored to different road structures and traffic conditions. For a Y-shaped basic road network, both linear and piecewise linear regression models were established, achieving perfect fitting of the main road traffic flow. In multi-branch scenarios that account for delays and cyclical fluctuations, an integrated model comprising constant, piecewise linear, and periodic functions was proposed, achieving a goodness of fit of 0.9722. Under traffic signal control conditions, a composite model including piecewise functions and periodic components was developed, effectively addressing traffic interruptions caused by signals, with a goodness of fit of 0.9642. In noisy data environments, a robust regression framework with adaptive weighting was introduced, maintaining high accuracy despite noise interference. The results indicate that the proposed models can effectively reconstruct feeder road traffic patterns, offering excellent interpretability and robustness. This provides a reliable data foundation for signal timing optimization and congestion management, offering practical solutions for traffic flow estimation in certain observed road networks.

KEYWORDS

Linear regression model; Least squares method; Iterative optimization; Nonlinear regression model

CITE THIS PAPER

TianYi Chen, Cheng Cui. Relationship between traffic flow and time based on regression models. World Journal of Engineering Research. 2025, 3(5): 15-22. DOI: https://doi.org/10.61784/wjer3056.

REFERENCES

[1] Sayed S A, Abdel-Hamid Y, Hefny H A. Artificial intelligence-based traffic flow prediction: a comprehensive review. Journal of Electrical Systems and Information Technology, 2023, 10(1): 13.

[2] Kashyap A A, Raviraj S, Devarakonda A, et al. Traffic flow prediction models - a review of deep learning techniques. Cogent Engineering, 2022, 9(1): 2010510.

[3] Razali N A M, Shamsaimon N, Ishak K K, et al. Gap, techniques and evaluation: traffic flow prediction using machine learning and deep learning. Journal of Big Data, 2021, 8(1): 152.

[4] Chen J, Zheng L, Hu Y, et al. Traffic flow matrix-based graph neural network with attention mechanism for traffic flow prediction. Information Fusion, 2024, 104: 102146.

[5] Ji J, Wang J, Huang C, et al. Spatio-temporal self-supervised learning for traffic flow prediction. In: Proceedings of the AAAI Conference on Artificial Intelligence, 2023, 37(4): 4356-4364.

[6] Bao Y, Huang J, Shen Q, et al. Spatial-temporal complex graph convolution network for traffic flow prediction. Engineering Applications of Artificial Intelligence, 2023, 121: 106044.

[7] Wang H, Zhang R, Cheng X, et al. Hierarchical traffic flow prediction based on spatial-temporal graph convolutional network. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(9): 16137-16147.

[8] Shu W, Cai K, Xiong N N. A short-term traffic flow prediction model based on an improved gate recurrent unit neural network. IEEE Transactions on Intelligent Transportation Systems, 2021, 23(9): 16654-16665.

[9] Navarro-Espinoza A, López-Bonilla O R, García-Guerrero E E, et al. Traffic flow prediction for smart traffic lights using machine learning algorithms. Technologies, 2022, 10(1): 5.

[10] Cao S, Wu L, Wu J, et al. A spatio-temporal sequence-to-sequence network for traffic flow prediction. Information Sciences, 2022, 610: 185-203.