Abstract: We employ an efficient kinetic Monte Carlo (KMC) method to study traffic flow models on 1D and 2D lattices based on the exclusion principle and microscopic dynamics. This model implements stochastic rules for cars’ movement based on the configuration of the traffic ahead of each car. In Part 1), we compare two different look-ahead rules: one is based on the distance from the car under consideration to the car in front of it, the other one depends on the car density ahead.  In Part 2), we introduce a novel idea of multiple moves, which plays a key role in recovering the nonconcave flux in the macroscopic dynamics. In Part 3), we propose a look-ahead rule that depends on both the car density ahead and a generalized interaction function related to the distance between cars. For this case, we design an accelerated KMC method to reduce the computational complexity in the evaluation of the nonlocal transition rates. Our results show that the fluxes of the KMC simulations agree with the coarse-grained macroscopic averaged fluxes for the different look-ahead rules under various parameter settings. This talk includes the joint work with Cory Hauck, Changhui Tan and Ilya Timofeyev.