A novel lattice traffic flow model on a curved road

Due to the existence of curved roads in real traffic situation, a novel lattice traffic flow model on a curved road is proposed by taking the effect of friction coefficient and radius into account. The stability condition is obtained by using linear stability theory. The result shows that the traffic flow becomes stable with the decrease of friction coefficient and radius of the curved road. Using nonlinear analysis method, the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equation are derived to describe soliton waves and the kink-antikink waves in the meta-stable region and unstable region, respectively. Numerical simulations are carried out and the results are consistent with the theoretical results.