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

Abstract

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, vmax rtial 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 ρcr 1= 3/8 separates the LD phase from the SW phase, and ρcr 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 ρcr 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 ρρcr 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. Si = i+4-8ρ, which is in agreement with simulations.