Microscopic Car-Following Models Revisited: From Road Works to Fundamental Diagrams

We analyze the dynamics of the classical optimal velocity model for the case of road works. We introduce a new viewpoint, the so-called rotation solutions, which in case of an additional symmetry leads to Ponies-on-a-Merry-Go-Round-solutions (POMs) [D. G. Aronson, M. Golubitsky, and J. Mallet-Paret, Nonlinearity, 4 (1991), pp. 903-910]. This approach, which is also useful for the case without road works, opens the possibility of analytical and numerical bifurcation studies, which show a wide variety in the possible dynamics of this very simple model. In addition, we mimic different measurement approaches and recover the famous inverse Greek. structure in the fundamental diagram.