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@ARTICLE{Tordeux:842029,
      author       = {Tordeux, Antoine and Costeseque, Guillaume and Herty,
                      Michael and Seyfried, Armin},
      title        = {{F}rom {T}raffic and {P}edestrian {F}ollow-the-{L}eader
                      {M}odels with {R}eaction {T}ime to {F}irst {O}rder
                      {C}onvection-{D}iffusion {F}low {M}odels},
      journal      = {SIAM journal on applied mathematics},
      volume       = {78},
      number       = {1},
      issn         = {0036-1399},
      address      = {Philadelphia, Pa.},
      publisher    = {Soc.},
      reportid     = {FZJ-2018-00313},
      pages        = {63 - 79},
      year         = {2018},
      abstract     = {In this work, we derive first order continuum traffic flow
                      models from a microscopic delayed follow-the-leader model.
                      These are applicable in the context of vehicular traffic
                      flow as well as pedestrian traffic flow. The microscopic
                      model is based on an optimal velocity function and a
                      reaction time parameter. The corresponding macroscopic
                      formulations in Eulerian or Lagrangian coordinates result in
                      first order convection-diffusion equations. More precisely,
                      the convection is described by the optimal velocity while
                      the diffusion term depends on the reaction time. A linear
                      stability analysis for homogeneous solutions of both
                      continuous and discrete models is provided. The conditions
                      match those of the car-following model for specific values
                      of the space discretization. The behavior of the novel model
                      is illustrated thanks to numerical simulations. Transitions
                      to collision-free self-sustained stop-and-go dynamics are
                      obtained if the reaction time is sufficiently large. The
                      results show that the dynamics of the microscopic model can
                      be well captured by the macroscopic equations. For nonzero
                      reaction times we observe a scattered fundamental diagram.
                      The scattering width is compared to real pedestrian and road
                      traffic data.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000426747800004},
      doi          = {10.1137/16M110695X},
      url          = {https://juser.fz-juelich.de/record/842029},
}