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.

中文翻译：

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考虑异质交通流的坡度道路双车道网格水动力模型

在实际交通中，不仅有汽车，还有公交车、卡车等车辆。这些具有不同最高速度或安全车距或两者兼有的车辆不规则地穿插，形成异质的交通流。此外，现代汽车的最高速度几乎不受坡度的影响，因为汽车发动机和制动器很少以最大速度运行，而卡车的最高速度受到影响。考虑到各类车辆的性能五花八门，且车辆有时会在坡道上行驶，本文提出了一种考虑异构交通流的坡度道路双车道格子水动力模型。为了验证模型的合理性，首先进行线性稳定性分析，即 线性稳定性条件来源于线性稳定性理论，并据此绘制稳定性曲线。上述分析结果证明，本文研究的三个因素，即不同类型车辆的变道时间、坡度和混合，都对交通流的稳定性有显着影响。通过非线性分析方法推导出修正的Korteweg-de Vries（mKdV）方程，可以描述临界点附近交通密度波的传播特性。最后，对新模型进行了数值模拟，得到的数值模拟结果与理论值吻合较好。综上所述，增加变道率或上坡坡度可以提高车流稳定性。更，增加坡度会降低下坡的车流稳定性。最后，在不同类型车辆的异质交通流中，安全车头间距较大的车辆会导致交通流难以稳定，最高时速较大的车辆也是如此。