Two-Lane Lattice Hydrodynamic Modeling at Sag Sections With the Empirical Lane-Changing Rate.

Sag sections are freeway sections where the gradient varies significantly from top to bottom. Due to their special geometric characteristics, sag sections are often bottlenecks in motorway networks. However, we are still unclear about the underlying mechanisms of traffic congestion in the two-lane sag sections. Based on the actual lane change experience, a two-lane lattice traffic flow model at the sag sections considering the empirical lane change rate is proposed. The model is developed to reveal the evolutionary characteristics of traffic congestion at the sag section, and then to alleviate the traffic congestion problem at the sag section. In this paper, the empirical lane change rate is described as a function that depends on the road traffic density. First, the condition of traffic flow stability was obtained by analyzing the linear stability at sag sections when lane changes were allowed. The stability condition of traffic system show that lane change parameter and slope have important effects on the stability of traffic system. Then, the mKdV equation describing the phase transition of the traffic flow and its solution are obtained using nonlinear analysis. Finally, numerical simulations were performed. The results show that the increase of slope increases the traffic flow stability in uphill sections and the opposite in downhill sections. Moreover, the lane-change rate parameter can effectively increase the stability region and suppress traffic congestion.