Starting from a kinetic model it is derived a macroscopic traffic equation, whereby the appearing coefficients are identified from the homogeneous stationary solutions of the underlying kinetic equation. Macroscopic modeling of vehicular traffic started with the work of Lighthill and Whitham. They considered the continuity equation for the density p closing the equation by an equilibrium assumption on the mean velocity u. An additional momentum equation for u has been introduced by Payne and Whitham in analogy to fluid dynamics. Based on this work a kinetic model is introduced. The basic quantity in the kinetic approach is the single car distribution f(x, v) describing the density of cars at x with velocity v. The kinetic equation for the distribution function is obtained from considerations analogous to those in the kinetic theory of gases using a procedure similar to the formal derivation of Boltzmanns equation. The kinetic model is given by an evolution equation for the distribution function f.
An explicit kinetic model for traffic flow
2002
5 Seiten, 2 Bilder, 5 Quellen
Conference paper
English
Kinetic Model for Traffic Flow
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