FORECASTING ROAD TRAFFIC CAPACITY USING MATHEMATICAL MODELING OF TRAFFIC FLOW DYNAMICS
DOI:
https://doi.org/10.51699/15fms907Keywords:
Road Traffic Capacity, Traffic Flow Dynamics, Traffic Capacity Forecasting, Mathematical Modeling, Traffic Density, Traffic Flow Theory, Congestion Analysis, Transportation Engineering, Intelligent Transportation Systems (ITS), Traffic Simulation, Urban Traffic Management, Roadway Performance Evaluation, Nonlinear Traffic Models, Transportation Planning, Traffic OptimizationAbstract
The rapid growth of urbanization, motorization, and transportation demand has significantly increased the complexity of traffic management in modern cities. Accurate forecasting of road traffic capacity has therefore become a crucial task for transportation engineers, urban planners, and policymakers seeking to improve mobility, reduce congestion, and optimize infrastructure utilization. This study presents a mathematical modeling framework for predicting road traffic capacity based on fundamental traffic flow dynamics. The proposed approach employs the classical relationship between traffic flow, traffic density, and average vehicle speed and integrates an exponential speed–density function to describe nonlinear traffic behavior under varying congestion conditions. The mathematical model enables the determination of critical traffic density and maximum traffic throughput through analytical optimization of the flow–density relationship. Numerical simulations were conducted using a wide range of traffic density values to evaluate the model’s predictive performance and investigate congestion formation mechanisms. The simulation results demonstrate that traffic flow increases with density up to a critical threshold, beyond which traffic instability and congestion effects emerge, causing a reduction in operational efficiency. Furthermore, the model successfully reproduces the nonlinear characteristics of real traffic systems and provides physically interpretable estimates of roadway capacity. The findings indicate that the proposed modeling approach can serve as an effective tool for short-term and medium-term traffic forecasting, transportation planning, and intelligent transportation system applications. The model is computationally efficient, analytically transparent, and easily adaptable to various road network conditions. In addition, the framework creates opportunities for integration with real-time traffic monitoring technologies, sensor networks, and artificial intelligence algorithms. The proposed methodology contributes to the advancement of data-driven traffic management strategies and provides a practical foundation for improving road network performance, reducing congestion, and supporting sustainable urban transportation development.
References
B. D. Greenshields, “A study of traffic capacity,” in Highway Research Board Proceedings, 1935.
A. D. May, Traffic Flow Fundamentals. Englewood Cliffs, NJ, USA: Prentice Hall, 1990.
M. Treiber and A. Kesting, Traffic Flow Dynamics. Berlin, Germany: Springer, 2013.
M. Papageorgiou et al., “Review of road traffic control strategies,” Proceedings of the IEEE, 2003.
B. S. Kerner, The Physics of Traffic. Berlin, Germany: Springer, 2004.
M. J. Lighthill and G. B. Whitham, “On kinematic waves II: A theory of traffic flow on long crowded roads,” Proceedings of the Royal Society A, vol. 229, no. 1178, pp. 317–345, 1955.
P. I. Richards, “Shock waves on the highway,” Operations Research, vol. 4, no. 1, pp. 42–51, 1956.
C. F. Daganzo, “The cell transmission model: A dynamic representation of highway traffic,” Transportation Research Part B, vol. 28, no. 4, pp. 269–287, 1994.
G. F. Newell, “A simplified car-following theory,” Transportation Research Part B, vol. 36, no. 3, pp. 195–205, 2002.
D. Helbing, “Traffic and related self-driven many-particle systems,” Reviews of Modern Physics, vol. 73, no. 4, pp. 1067–1141, 2001.
M. Treiber and A. Kesting, Traffic Flow Dynamics: Data, Models and Simulation. Berlin, Germany: Springer, 2013.
S. P. Hoogendoorn and P. H. L. Bovy, “State-of-the-art of vehicular traffic flow modelling,” Proceedings of the Institution of Mechanical Engineers, vol. 215, no. 4, pp. 283–303, 2001.
H. M. Zhang, “A non-equilibrium traffic model,” Transportation Research Part B, vol. 36, no. 3, pp. 275–290, 2002.
B. S. Kerner, Introduction to Modern Traffic Flow Theory and Control. Berlin, Germany: Springer, 2009.
M. Papageorgiou and A. Kotsialos, “Freeway ramp metering: An overview,” IEEE Transactions on Intelligent Transportation Systems, vol. 3, no. 4, pp. 271–281, 2002.
