Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing

A new lattice hydrodynamic model is proposed by considering the interruption probability effect on traffic flow with passing and analyzed both theoretically and numerically. From linear and non-linear stability analysis, the effect of interruption probability on the phase diagram is investigated and the condition of existence for kink–antikink soliton solution of mKdV equation is derived. The stable region is enhanced with interruption probability and the jamming transition occurs from uniform flow to kink flow through chaotic flow for higher and intermediate values of non-interruption effect of passing. It is also observed that there exists conventional jamming transition between uniform flow and kink flow for lower values of non-interruption effect of passing. Numerical simulations are carried out and found in accordance with the theoretical findings which confirm that the effect of interruption probability plays an important role in stabilizing traffic flow when passing is allowed.