Accelerated Kinetic Monte Carlo methods for general nonlocal traffic flow models

TL;DR

This paper introduces an accelerated kinetic Monte Carlo algorithm for simulating nonlocal traffic flow models, significantly improving computational efficiency while accurately capturing complex traffic dynamics.

Contribution

The paper develops a novel accelerated KMC method tailored for nonlocal traffic flow models with global interactions, enhancing simulation efficiency.

Findings

Accelerated KMC reduces computational complexity.

The method accurately reproduces fundamental traffic diagrams.

Numerical experiments demonstrate improved efficiency and accuracy.

Abstract

This paper presents a class of one-dimensional cellular automata (CA) models on traffic flows, featuring nonlocal look-ahead interactions. We develop kinetic Monte Carlo (KMC) algorithms to simulate the dynamics. The standard KMC method can be inefficient for models with global interactions. We design an accelerated KMC method to reduce the computational complexity in the evaluation of the nonlocal transition rates. We investigate several numerical experiments to demonstrate the efficiency of the accelerated algorithm, and obtain the fundamental diagrams of the dynamics under various parameter settings.