Kinetic Monte Carlo simulations of 1D and 2D traffic flows: Nonlocal models with generalized look-ahead rules

Abstract

This paper presents a study on traffic flow models in one-dimensional (1D) and two-dimensional (2D) lattices. The models incorporate generalized look-ahead rules that consider nonlocal slow-down effects. The proposed cellular automata (CA) models use stochastic rules to determine the movement of cars based on the traffic configuration ahead of each car. Specifically, a look-ahead rule is used that considers both the car density ahead and a generalized interaction function based on the distance between cars. The CA models are simulated using an efficient kinetic Monte Carlo (KMC) algorithm. The numerical results in 1D demonstrate that the flows from the KMC simulations align with the macroscopic averaged fluxes for the look-ahead rule, across various parameter settings. In the 2D results, a sharp phase transition is observed from freely flowing traffic to global jamming, depending on the initial density of cars.