Effect of optimal estimation of flux difference information on the lattice traffic flow model

• A new lattice model considering the optimal estimation flux difference information has been developed.
• The linear stable condition of the new model is derived.
• The mKdV equation is obtained and solved to describe the traffic jamming transitions.
• The results show that the new consideration can improve the stability of traffic flow.

In this paper, a new lattice model is proposed by considering the optimal estimation of flux difference information. The effect of this new consideration upon the stability of traffic flow is examined through linear stability analysis. Furthermore, a modified Korteweg–de Vries (mKdV) equation near the critical point is constructed and solved by means of nonlinear analysis method, and thus the propagation behavior of traffic jam can be described by the kink–antikink soliton solution of the mKdV equation. Numerical simulation is carried out under periodical condition with results in good agreement with theoretical analysis, therefore, it is verified that the new consideration can enhance the stability of traffic systems and suppress the emergence of traffic jams effectively.