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Volume 13
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Article

Traffic Characterization Based on Driver Reaction

by
Zawar Hussain Khan
1,*,
Khurram S. Khattak
2,
Ahmed B. Altamimi
1,
Thomas Aaron Gulliver
3,
Alaa Chabir
1 and
Shah Hussain
4
1
Department of Computer Engineering, College of Computer Science and Engineering, University of Háil, Háil 55476, Saudi Arabia
2
Department of Computer Systems Engineering, University of Engineering and Technology, Peshawar 25000, Pakistan
3
Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 1700, STN CSC, Victoria, BC V8W 2Y2, Canada
4
Department of Mathematics, College of Science, University of Háil, Háil 55476, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(16), 2616; https://doi.org/10.3390/math13162616
Submission received: 7 June 2025 / Revised: 6 August 2025 / Accepted: 12 August 2025 / Published: 15 August 2025
(This article belongs to the Section E: Applied Mathematics)
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Abstract

A macroscopic model for nonhomogeneous traffic is introduced that incorporates relaxation time and lateral time headway, and accounts for driver reaction time. Driver reaction is based on models of real-world nonhomogeneous traffic flow in Pakistan and Iran. A lateral time headway model is obtained using lane change data to characterize traffic during lane changes. The performance of the proposed model is compared with the well-known Payne–Whitham (PW) model on a 3000 m circular road using the FORCE numerical scheme. The results show that the initial multi-cluster density distribution evolves more realistically and accurately with the proposed model. Thus, it can be used to aid in traffic congestion mitigation for on-ramps and off-ramps.
Keywords: macroscopic model; relaxation time; lateral time headway; regression; FORCE scheme; multi-cluster density distribution; nonhomogeneous traffic macroscopic model; relaxation time; lateral time headway; regression; FORCE scheme; multi-cluster density distribution; nonhomogeneous traffic

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MDPI and ACS Style

Khan, Z.H.; Khattak, K.S.; Altamimi, A.B.; Gulliver, T.A.; Chabir, A.; Hussain, S. Traffic Characterization Based on Driver Reaction. Mathematics 2025, 13, 2616. https://doi.org/10.3390/math13162616

AMA Style

Khan ZH, Khattak KS, Altamimi AB, Gulliver TA, Chabir A, Hussain S. Traffic Characterization Based on Driver Reaction. Mathematics. 2025; 13(16):2616. https://doi.org/10.3390/math13162616

Chicago/Turabian Style

Khan, Zawar Hussain, Khurram S. Khattak, Ahmed B. Altamimi, Thomas Aaron Gulliver, Alaa Chabir, and Shah Hussain. 2025. "Traffic Characterization Based on Driver Reaction" Mathematics 13, no. 16: 2616. https://doi.org/10.3390/math13162616

APA Style

Khan, Z. H., Khattak, K. S., Altamimi, A. B., Gulliver, T. A., Chabir, A., & Hussain, S. (2025). Traffic Characterization Based on Driver Reaction. Mathematics, 13(16), 2616. https://doi.org/10.3390/math13162616

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