部分道路关闭引起的交通激波特性研究

本文根据实际交通中经常遇到的交通事故或部分道路施工等情况, 建立了部分道路关闭的交通流模型. 采用平均场理论分析和确定性NS元胞自动机规则分别对模型进行解析和数值模拟, 结果表明, 系统存在三种稳定的物理状态:低密度相、激波相和高密度相, 并找到了系统发生相变的临界密度. 理论分析和数值模拟能很好地符合.

Study of the shock wave induced by closing partial road in traffic flow

There often occurs traffic accident or road construction in real traffic, which leads to partial road closure. In this paper, we set up a traffic model for the partial road closure. According to the Nagel-Schreckenberg (NS) cellular automata update rules, the road can be separated into cells with the same length of 7.5 m. L = 4000 (corresponding to 30 km) is set to the road length in the simulations. For a larger system size, our simulations show that the results are the same with those presented in the following. In our model, v_max rtial road is closed (for convenience, we define the road length as L₁), v_{max 2}= 2 (corresponding to 54 km/h) in the section of normal road (we define the road length as L₂). In our simulations, let L₁= L₂ = 2000. We would like to mention that changing these parameter values does not have a qualitative influence on the simulation results. The simulation results demonstrate that three stationary phases exist, that is, low density (LD), high density (HD) and shock wave (SW). Two critical average densities are found:the critical point ρ_{cr 1}= 3/8 separates the LD phase from the SW phase, and ρ_{cr 2}= 1/2 separates the SW phase from the HD phase. We also analyze the relationship between the average flux J and average density ρ. In the LD phase J = 4/3ρ, in the HD phase J= 1 -ρ and J is 0.5 in the SW phase. We investigate the dependence of J on ρ. It is shown that with the increase of ρ, J first increases, at this stage J corresponds to the LD phase. Then J remains to be a constant 0.5 when the critical average density ρ_{cr 1} is reached, and J corresponds to the SW phase (this time,J reaches the maximum value 0.5). One goal of traffic-management strategies is to maximize the flow. We find that the optimal choice of the average density is 3/8 < ρ< 1/2 in the present model. Similar road situation often occurs in everyday life, so the traffic managers can control the car density in order to alleviate the traffic congestion and enhance the capacity of existing infrastructure. After the second critical average density ρ_{cr 2} is reached, J decreases with the increase of average density, which corresponds to the HD phase. We also obtain the relationship between the shock wave position and the average density by theoretical calculations, i.e. S_i = i+4-8ρ, which is in agreement with simulations.