Flow difference effect in the lattice hydrodynamic model

In this paper, a new lattice hydrodynamic model based onNagatani's model [Nagatani T 1998 Physica A 261 599] ispresented by introducing the flow difference effect. The stabilitycondition for the new model is obtained by using the linearstability theory. The result shows that considering the flowdifference effect leads to stabilization of the system comparedwith the original lattice hydrodynamic model. The jammingtransitions among the freely moving phase, the coexisting phase, andthe uniform congested phase are studied by nonlinear analysis.The modified KdV equation near the critical point is derived todescribe the traffic jam, and kink--antikink soliton solutionsrelated to the traffic density waves are obtained. The simulationresults are consistent with the theoretical analysis for the newmodel.