Interactions of waves in the speed-gradient traffic flow model

In this paper, we use the speed-gradient (SG) model proposed by Jiang et al. [Transportation Research Part B, 36 (2002) 405–419] to study the initial value problem of traffic flow. The evolution of multi-traffic waves is examined through setting piecewise continuous initial density. Numerical results show that distinct shocks and smooth transition layers appear instantaneously for some initial densities, and the shock front is smoothed by the smooth transition layer ahead of or behind it if, in the initial density, the length of shock section or the length of lower-density section before the shock is very short. We thus verify that the SG model can satisfyingly reproduce the evolution of multi-traffic waves with various initial densities.