In this paper, a new car-following model is presented, taking into account the anticipation of potential lane changing by the leading vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flow in the headway-sensitivity space, namely stable, metastable and unstable ones, are classified. Both the analytical and simu- lation results show that anxiety about lane changing does indeed have an influence on driving behavior and that a consideration of lane changing probability in the car-following model could stabilize traffic flows. The quantitative relationship between stability improvement and lane changing probability is also investigated.
Since ramps are an important composition of traffic systems and there often exist multi ramps in a tragic system, the number of ramps can have great effects on main road traffic and produce some complex phenomena. In this paper, we employ the model presented by Tang et al. [2009 Communications in Theoretical Physics 51（1） 71] to further study the effects of the number of on-ramps on the stability of traffic flow on a ring road. The numerical results show that this model can reproduce some complex tragic phenomena resulting from multi on-ramps on the ring road and the effects of the number of on-ramps on traffic flow, but the phenomena and the effects are both related to the initial density of the main road.
The macro modeling and the solution of traffic flow with road width were investigated.Firstly,a new macro model with the consideration of road width was proposed.Secondly,the effects of road width on uniform flow and small perturbation were studied.The analytical and numerical results show that widening (shrinking) road can enhance (reduce) the equilibrium speed and flow,and the increments (decrements) will increase with the absolute value of road width gradient.In addition,the numerical results illustrate that the new model can describe the effects of road width on the evolutions of uniform flow and small perturbation.
