Phase transition of a new lattice hydrodynamic model with consideration of on-ramp and off-ramp

- A new traffic lattice hydrodynamic model is proposed by firstly considering the on-ramp and off-ramp.
- Linear stability analysis is conducted to reveal the impact of on-ramp and off-ramp on traffic stability.
- Nonlinear reductive perturbation method is used to uncover traffic jamming transition characteristics.
- The on-ramp can worsen the traffic stability of the main road but off-ramp is positive in stabilizing the traffic flow of the main road.

A new traffic lattice hydrodynamic model with consideration of on-ramp and off-ramp is proposed in this paper. The influence of on-ramp and off-ramp on the stability of the main road is uncovered by theoretical analysis and computer simulation. Through linear stability theory, the neutral stability condition of the new model is obtained and the results show that the unstable region in the phase diagram is enlarged by considering the on-ramp effect but shrunk with consideration of the off-ramp effect. The mKdV equation near the critical point is derived via nonlinear reductive perturbation method and the occurrence of traffic jamming transition can be described by the kink-antikink soliton solution of the mKdV equation. From the simulation results of space-time evolution of traffic density waves, it is shown that the on-ramp can worsen the traffic stability of the main road but off-ramp is positive in stabilizing the traffic flow of the main road.