article · Transportmetrica B Transport Dynamics
Traffic streams containing diverse vehicle types often involve complex interactions, including varied speed choices and the violation of lane discipline. An extended second-order multi-class continuum model addresses these conditions by drawing on fluid dynamics concepts of moving obstacles. In this framework, slower vehicles are treated as moving obstacles that hinder faster traffic, leading to the introduction of a relative drag function within the velocity dynamics across three distinct vehicle classes. The mathematical formulation constitutes a hyperbolic conservation system that maintains the anisotropic nature of vehicular flow. A linear stability analysis provides the stability criterion for the system. Numerical evaluations using the Roe scheme indicate that this approach delivers a more realistic representation of heterogeneous traffic behaviour.
Accurately simulating mixed traffic where vehicles disregard lane boundaries and travel at varying speeds is difficult. Applying fluid dynamics principles to represent slower vehicles as obstacles helps create mathematical models that capture real-world congestion patterns more faithfully. This improved understanding aids in developing better mathematical tools for traffic management and infrastructure planning.
The model offers mathematical foundations for traffic simulation software and planning tools used by transport planners and traffic management software developers. Because the work is validated strictly through theoretical linear stability analysis and numerical schemes, it represents early-stage, foundational research. Substantial empirical calibration against physical roadway data and integration into commercial simulation suites would be necessary before real-world deployment.
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In heterogenous traffic flow the interaction between different vehicle classes play an important role. This article deals with the extension of second order multiclass traffic flow models to accommodate some violation of lane discipline and heterogeneous choice of speeds in a traffic stream. It proposes a continuum model for the interaction of different classes of vehicles in the traffic based on the concept of a moving obstacle from fluid dynamics. Using the assumption that the slow vehicles can be considered as moving obstacles to the fastest ones a relative drag function is introduced in the dynamics of the velocity of each respective classes. The proposed model considers three different vehicle classes and it is shown to express a hyperbolic conservation system which preserves the anisotropic nature of vehicles. A stability criterion of the model is obtained using the linear stability analysis. The performance of the model is evaluated using the Roe numerical scheme. The results show that the heterogeneous traffic behaviour with this new model is more realistic.
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DOI: 10.1080/21680566.2026.2723904
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