Stability Analysis of Lattice Model Considering the Honk Effect and Driver Heterogeneity
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摘要: 道路环境及密集交通流随机波动是交通扰动的诱因, 文中考虑道路环境中的汽车鸣笛效应和驾驶员异质性的影响, 提出鸣笛发生临界密度的概念, 建立了更符合实际的格子流体动力学模型, 并揭示非饱和交通状态下诱发交通流失稳的机理.在线性稳定性分析中利用扰动法得到了该模型的稳定性条件, 并基于还原微扰法对该模型的非线性稳定性问题进行研究, 通过求解mKDV方程获取的扭结-反扭结孤立波描述了在临界点附近密度波的传输规则.仿真结果表明, 考虑有鸣笛效应的新格子模型相比于Nagatani模型的稳定性更强, 而较大的临界密度对交通流稳定性存在消极影响; 与以往微观模型相比, 本文模型能解释鸣笛现象发生的自然条件, 即密度高且流量低的地方, 同时驾驶员特性也对交通流的稳定性存在着显著影响.Abstract: The road environment and traffic flow fluctuation are the incentive of traffic disturbance. This paper developed a new lattice model by introducing a concept of critical density by considering driver heterogeneity in the context of honk effect, and revealed the mechanism of inducing traffic flow instability. The stability condition of the lattice model is obtained by using the perturbation method in the linear stability analysis. The nonlinear stability of the proposed lattice model is studied through the reduced perturbation method, and the kink-antikink soliton solution by solving the mKDV equation describes the propagation discipline of density waves near the critical point. The simulation experiments verified that the stability of the modified lattice model is stronger than that of Nagatani model, while the large critical density has a negative effect on the stability of traffic flow. Compared to the previous microscopic models, the proposed model is able to explain the natural condition for honk occurrence, that is, high density and low flow area. In addition, the results show that the driver characteristic also has a significant impact on the stability of traffic flow.
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Key words:
- Traffic flow /
- lattice model /
- stability analysis /
- honk effect /
- driver heterogeneity /
- critical density
1) 本文责任编委 王鼎 -
图 1 对于不同的参数$p$下的车辆的灵敏度与密度相图$(\rho, a)$
Fig. 1 The phase diagram$(\rho, a)$of the sensitivity and the density under different values of parameter $p$
图 2 在不同参数权重$p$下新模型的密度时空演化图
Fig. 2 The space-time evolution of density for the new model under different values of parameter $p$
图 3 参数$q$对交通流稳定性的影响
Fig. 3 The influence of parameter $q$ on the traffic flow stability
图 4 临界密度$\rho_{{\rm lim}_{1}}$对交通流稳定性的影响
Fig. 4 The influence of critical density $\rho_{{\rm lim}_{1}}$ on the traffic flow stability
图 5 参数$c$对交通流稳定性的影响
Fig. 5 The influence of parameter $c$ on the traffic flow stability
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