\input zb-basic
\input zb-ioport
\iteman{io-port 02139983}
\itemau{Filliger, Roger}
\itemti{Discrete derivation of Ruijgrok and Wu's nonlinear two-velocity Boltzmann model with an application to traffic-flow modelling.}
\itemso{Multiscale Model. Simul. 2, No. 3, 440-451 (2004).}
\itemab
The behaviour of a complex system of coupled elementary cells can be described by following the analogy of the kinetic theory of diluted gases. On the microscopic level, the space-discrete equations of the RW-model [{\it Th. W. Ruijgrok} and {\it T. T. Wu}, ``A completely solvable model of the nonlinear Boltzmann equation'', Phys. A 113, No. 3, 401--416 (1982; MR 84a:76031)] are recognized as the nonlinear master equations of interacting Markov processes on a one-dimensional lattice. Using a variant of the Trotter--Kato approximation theory [{\it T. G. Kurtz}, J. Funct. Anal. 3, 354--375 (1969; Zbl 0174.18401)], a space-continuous RW-model can be derived. The derivation shows the main kinetic features of the equations, which are, besides the migration term, a reaction and a collision mechanism of mass action type.  The application within traffic theory is considered. Together with the above kinetic features and a convergence scheme, a micro-, meso-macro link for the popular macroscopic traffic model of {\it M. J. Lighthill} and {\it G. B. Whitham} [Proc. R. Soc. Lond., Ser. A 229, 317--345 (1955; Zbl 0064.20906)] is established.
\itemrv{Franz Selig (Wien)}
\itemcc{}
\itemut{Boltzmann equation; semigroup approximation; micro-macro link; traffic flow}
\itemli{doi:10.1137/030600412}
\end