A novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow

In the actual traffic, there are not only cars, but also buses, trucks and other vehicles. These vehicles with different maximum speeds or security headway or both are interspersed irregularly to form a heterogeneous traffic flow. In addition, most of the maximum speed of modern cars is hardly affected by gradients due to the fact that the car engine and brakes are rarely operated at their max while the maximum speed of trucks is affected. Considering that the performance of various types of vehicles is multifarious and the vehicles sometimes drive on the road with slopes, a novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow is proposed in this paper. In order to verify the rationality of the model, the linear stability analysis is carried out first, that is, the linear stability conditions are derived from the linear stability theory and the stability curve is drawn accordingly. The results of the above analysis prove that the three factors studied in this paper, namely, time lane change, slope and mixing of different types of vehicles, all have a significant influence on the stability of traffic flow. The modified Korteweg-de Vries (mKdV) equation is deduced by the nonlinear analysis method, which can describe the propagation characteristics of the traffic density waves near the critical point. Last but not least, the numerical simulation for new model is conducted and the numerical simulation results obtained are in good agreement with theoretical ones. In summary, increasing the lane changing rate or the slope on the uphill can improve the traffic flow stability. What is more, increasing the slope can lower the traffic flow stability on the downhill. Finally, in the heterogeneous traffic flow of different types of vehicles, the vehicles with larger security headway will make traffic flow difficult to stabilize, as do the vehicles with larger maximum speed.