Lattice Hydrodynamic Traffic Flow Model Considering On - Off Ramp Effect

An extended lattice hydrodynamic model of traffic flow is developed that incorporates on- and off-ramp effects and modified velocity adaptation dynamics near merging and diverging zones into the vehicle conservation equation. Linear stability analysis shows that on-ramp inflow destabilizes traffic by raising local density and lowering equilibrium velocity, while off-ramp outflow can either stabilize flow depending on its intensity, shorter relaxation times and stronger anticipation effects enhance overall stability. Nonlinear analysis using the reductive perturbation method yields a modified Korteweg-de Vries (mKdV) equation that describes the growth, saturation, and propagation of stop-and-go waves near ramp locations under critical conditions. Numerical simulations confirm that on-ramps act as congestion sources while off-ramps mitigate density accumulation and energy consumption analysis demonstrates that traffic instability is associated with higher acceleration/deceleration and increased energy dissipation, whereas stable flow minimizes energy use.

On-ramp and off-ramp effects; Linear and nonlinear stability; Stop-and-go waves; Traffic congestion; Numerical simulation

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