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An explicitly solvable kinetic model for vehicular traffic and associated macroscopic equations. (English) Zbl 0994.90022

Summary: 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.

MSC:

90B20 Traffic problems in operations research
35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
90B06 Transportation, logistics and supply chain management
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