Keywords: 
• 交通流 /
• 激波 /
• 相变

Abstract: There often occurs tra?c accident or road construction in real tra?c, which leads to partial road closure. In this paper, we set up a tra?c 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, vmax denotes the maximum velocity of vehicle. Without loss of generality, we assume vmax 1=1 (corresponding to 27 km/h), where partial road is closed (for convenience, we define the road length as L1), vmax 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 ρcr1 =3/8 separates the LD phase from the SW phase, and ρcr2 =1/2 separates the SW phase from the HD phase. We also analyze the relationship between the average flux J and average densityρ. In the LD phase J = 43ρ, in the HD phase J =1?ρand J is 0.5 in the SW phase. We investigate the dependence of J onρ. 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 densityρcr1 is reached, and J corresponds to the SW phase (this time, J reaches the maximum value 0.5). One goal of tra?c-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 tra?c managers can control the car density in order to alleviate the tra?c congestion and enhance the capacity of existing infrastructure. After the second critical average densityρcr2 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. Si=i+4?8ρ, which is in agreement with simulations.