Analysis of the structural properties of the solutions to speed gradient traffic flow model

In this paper, we carry out an analysis of the structural properties of the solutions to the speed gradient (SG) traffic flow model. Under the condition that the relaxation effect can be neglected, it is shown that a 1-shock or a 1-rarefaction is associated with the first characteristic, but on the other hand, a contact discontinuity rather than a 2-shock or a 2-rarefaction is associated with the second characteristic. Since the existence of a 2-shock or 2-rarefaction violates the physical mechanism of the traffic flow, the SG model is more reasonable. If the relaxation effect cannot be neglected, it is somewhat difficult to carry out the analytical analysis and the numerical simulation results should be obtained.