Continuum Multimodal Traffic Dynamics Model Based on Kinematic Wave Theory

Modeling multimodal traffic dynamics and their interactions in a unified framework is critical for urban traffic planning and coordinated management. Nevertheless, continuous road traffic and discrete tramway traffic were often studied separately with distinct modeling paradigms, overlooking inter-modal interactions. We propose a continuum multimodal traffic dynamic model based on kinematic wave theory to capture the evolution of both traffic modes and their interactions within a consistent framework. The Lighthill–Whitham–Richards (LWR) model is adapted to tramway traffic and solved semi-analytically using the variational theory, consistent with road traffic modeling. Building on this, multimodal traffic dynamics are formulated for both separated and shared right-of-way (ROW) conditions. Numerical experiments are conducted to verify the effectiveness of the proposed model, evaluate the delay sensitivity to traffic demands, and assess the tramway traffic resilience to disturbances. Results indicate that the model accurately captures multimodal traffic dynamics under diverse conditions and demonstrates strong potential for urban traffic analysis and coordinated control.