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@ARTICLE{Tordeux:171886,
      author       = {Tordeux, Antoine and Seyfried, Armin},
      title        = {{C}ollision-free non uniform dynamics within continuous
                      optimal velocity models},
      journal      = {Physical review / E},
      volume       = {90},
      number       = {4},
      issn         = {1539-3755},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {FZJ-2014-05442},
      pages        = {042812},
      year         = {2014},
      abstract     = {Optimal velocity (OV) car-following models give with few
                      parameters stable stop-and-go waves propagating like in
                      empirical data. Unfortunately, classical OV models locally
                      oscillate with vehicles colliding and moving backward. In
                      order to solve this problem, the models have to be completed
                      with additional parameters. This leads to an increase of the
                      complexity. In this paper, a new OV model with no additional
                      parameters is defined. For any value of the inputs, the
                      model is intrinsically asymmetric and collision-free. This
                      is achieved by using a first-order ordinary model with two
                      predecessors in interaction, instead of the usual inertial
                      delayed first-order or second-order models coupled with the
                      predecessor. The model has stable uniform solutions as well
                      as various stable stop-and-go patterns with bimodal
                      distribution of the speed. As observable in real data, the
                      modal speed values in congested states are not restricted to
                      the free flow speed and zero. They depend on the form of the
                      OV function. Properties of linear, concave, convex, or
                      sigmoid speed functions are explored with no limitation due
                      to collisions.},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {411 - Computational Science and Mathematical Methods
                      (POF2-411)},
      pid          = {G:(DE-HGF)POF2-411},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000344034000009},
      doi          = {10.1103/PhysRevE.90.042812},
      url          = {https://juser.fz-juelich.de/record/171886},
}