Analyses of shock waves and jams in traffic flow

In this paper, we study the certain qualitative properties of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. We discussed the travelling wave solution for our model and find out the condition for the shock wave. Shock and rarefaction waves are obtained from the new model and are consistent with the diverse nonlinear dynamical phenomena observed in a real traffic flow. However, our model for large values of anisotropic parameter removes the discontinuity as pointed out by Berg et al (2000 Phys. Rev. E 61 1056). The nonlinear theory of the cluster effect in a traffic flow i.e., the effect of appearance of a region of high density and low average velocity of vehicles in an initially homogeneous flow, is also discussed. It is shown that an appearance of a localized perturbation of finite amplitude in the stable homogeneous flow can lead to a self-formation of a local cluster of vehicles. It is also been observed that the cluster effect from our model shows a good agreement with the results of Kerner and Konhauser (1994 Phys. Rev. E 50 54) and Jiang et al (2002 Trans. Res. B 36 405).