A lattice hydrodynamic model for on-ramp and off-ramp traffic flow considering non-equilibrium characteristics and heterogeneous mixed-flow speed delay

With the increasing complexity of urban expressway networks, traffic congestion at on-ramps and off-ramps has become a significant challenge, severely impacting urban mobility. To address the dynamic instability and traffic congestion caused by complex and variable merging and diverging traffic flows at these locations, propose a novel lattice hydrodynamic model, the Non-Equilibrium and Heterogeneous Mixed-Flow Model for On-Ramp and Off-Ramp Traffic Flow. First, the NEHM-OR/IR model divides the ramp road into three zones: no-impact area, merging-impact area, and diversion-impact area, analyzing the dynamic changes in traffic flow, density, and velocity in each zone. Second, it examines the non-equilibrium traffic flow characteristics of on-ramps and off-ramps based on speed limits and establishes the non-equilibrium conditions. Finally, the model innovatively integrates the effects of driving vigilance and heterogeneous mixed-flow speed delay in merging and diverging zones, considering both connected and non-connected vehicles, and derives the corresponding traffic flow conservation and motion equations. The linear stability analysis investigates the impact of on-ramp and off-ramp traffic flows on the stability of the overall traffic flow and provides the corresponding stability conditions. The linear stability analysis explores how on-ramp and off-ramp traffic flows affect overall traffic stability and derives the corresponding stability conditions. The numerical analysis shows that higher on-ramp flow causes congestion, while higher off-ramp flow improves stability. Increased on-ramp speed limits raise density and lower speeds, destabilizing traffic, whereas higher off-ramp speed limits decrease speeds and increase density after divergence. In composite ramp scenarios, higher connected vehicle penetration and commercial vehicle vigilance enhance stability, while increased heterogeneous mixed-flow speed delay and light passenger vehicle vigilance reduce stability. The results provide useful references for understanding and improving traffic flow at on-ramps and off-ramps.