We study a stochastic lattice particle system with exclusion principle. A kinetic equation and its diffusion limit are formally derived from the Monte Carlo dynamics. This derivation is investigated analytically and numerically and compared with the classical hydrodynamic limit of the stochastic exclusion process. Numerical results are presented for different values of jump probabilities

We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters. In particular, we focus on 1-to-1, 2-to-1 and 1-to-2 junctions. Based on an upwind type numerical scheme, we prove the maximum principle and the existence of weak solutions on networks. We also investigate the limiting behavior of the proposed models when the nonlocal influence tends to infinity. Numerical examples show the difference between the proposed coupling conditions and a comparison to the Lighthill-Whitham-Richards network model.