An explicitly solvable kinetic model for vehicular traffic and associated macroscopic equations |
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Institution: | Institut für Techno- und Wirtschaftsmathematik (ITWM) 67663 Kaiserslautern, Germany;FB Mathematik, TU Darmstadt 64289 Darmstadt, Germany;Institut für Techno- und Wirtschaftsmathematik (ITWM) 67663 Kaiserslautern, Germany |
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Abstract: | In the present paper, a kinetic model for vehicular traffic is presented and investigated in detail. For this model, the stationary distributions can be determined explicitly. A derivation of associated macroscopic traffic flow equations from the kinetic equation is given. The coefficients appearing in these equations are identified from the solutions of the underlying stationary kinetic equation and are given explicitly. Moreover, numerical experiments and comparisons between different macroscopic models are presented. |
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