Expansion, compression and triangular shockwaves in traffic flow above critical point

We study the formation of shockwaves from an initial condition of the pulse form in supercritical flow of traffic by using the optimal velocity model. The jam with the pulse form propagates with changing the initial form. The wave velocity is derived numerically and analytically. The dependence of wave velocity on headway is clarified. When the headway is lower than the safety distance, the rear of initial pulse evolves to the expansion shockwave, while the front of initial pulse evolves to the compression shockwave if the headway is higher than the safety distance. The dependence of wave velocity on headway determines whether either expansion or compression waves evolve to the shockwave. After the rear of initial pulse collapses with the front, the wave evolves to the triangular shockwave. It is shown that the triangular shockwave is described by the Burgers equation.