Sun, XY; Zhu, JF, Study of the shock wave induced by closing partial road in traffic flow, ACTA PHYSICA SINICA, 64(11), JUN 2015.

摘要：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) denotes the maximum velocity of vehicle. Without loss of generality, we assume v(max 1) = 1 (corresponding to 27 km/h), where partial road is closed (for convenience, we define the road length as L-1), v(max 2) = 2 (corresponding to 54 km/h) in the section of normal road (we define the road length as L-2). In our simulations, let L-1 = L-2 = 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 rho(cr1) = 3/8 separates the LD phase from the SW phase, and rho(cr2) = 1/2 separates the SW phase from the HD phase. We also analyze the relationship between the average flux J and average density rho. In the LD phase J = 4/3 rho, in the HD phase J = 1 - rho and J is 0.5 in the SW phase. We investigate the dependence of J on rho. It is shown that with the increase of rho, 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 rho(cr1) 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 < rho < 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 rho(cr2) 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 - 8 rho, which is in agreement with simulations.