Mechanism analysis of traffic congestion at sag section of the tunnel

Sag sections are segments of the expressway where the slope changes greatly from downward to upward. In the expressway networks, sag sections are usually the bottleneck of traffic. Sag sections have become an important inducement of traffic congestion for its special geometric characteristics. However, the intrinsic mechanism of traffic congestion on sag sections is still unclear, especially the congestion in the tunnels. To describe the traffic flow of different road conditions, a dynamic optimal velocity function is proposed. Then, coupled with the proposed function, a new lattice hydrodynamic model is developed to reveal the influence of sag on the stability of traffic flow in the tunnel. The linear stability condition is further obtained to analyze the potential effects of sag on the dynamics of traffic flow. The modified Korteweg-de Vrie (mKdV) equation is also derived by using perturbation theory, and the corresponding kink-antikink soliton solution is obtained. Finally, the evolution process of traffic flow during the sag section is demonstrated by numerical simulation. It is suggested that the downhill section sag worse the stability of traffic flow, while the uphill section could stabilize the traffic flow, which is consistent with the theoretical analysis well. In addition, we also study the evolution laws of density waves under different disturbances in the metastable region.