On a class of new nonlocal traffic flow models with look-ahead rules

TL;DR

This paper introduces a new class of 1D nonlocal traffic flow models with look-ahead rules that incorporate nonlocal effects and asymmetries, using cellular automata and stochastic processes to better capture complex traffic dynamics.

Contribution

The paper develops novel nonlocal cellular automata models with multiple moves and derives their macroscopic dynamics, advancing traffic modeling with look-ahead rules.

Findings

Fluxes from simulations match macroscopic predictions.

Nonlocal look-ahead rules improve traffic flow representation.

Multiple moves are key to capturing non-concave flux behavior.

Abstract

This paper presents a new class of one-dimensional (1D) traffic models with look-ahead rules that take into account of two effects: nonlocal slow-down effect and right-skewed non-concave asymmetry in the fundamental diagram. The proposed 1D cellular automata (CA) models with the Arrhenius type look-ahead interactions implement stochastic rules for cars' movement following the configuration of the traffic ahead of each car. In particular, we take 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. Both rules feature a novel idea of multiple moves, which plays a key role in recovering the non-concave flux in the macroscopic dynamics. Through a semi-discrete mesoscopic stochastic process, we derive the coarse-grained macroscopic dynamics of the CA model. We also design a numerical scheme to simulate the proposed CA models with an efficient list-based kinetic Monte Carlo (KMC) algorithm. 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.