Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics

TL;DR

This paper introduces a two-lane TASEP model with extended Langmuir kinetics, analyzing bidirectional and unidirectional flows, and provides theoretical and simulation results to understand complex traffic dynamics.

Contribution

It develops a novel two-lane TASEP model with state-dependent rates and offers a comprehensive mean-field analysis validated by simulations.

Findings

4-cluster mean-field closely matches simulation results

Differences between bidirectional and unidirectional flows are reproduced

The model enhances understanding of traffic flow dynamics

Abstract

Multi-lane totally asymmetric simple exclusion processes with interactions between the lanes have recently been investigated actively. This paper proposes a two-lane model with extended Langmuir kinetics on a periodic lattice. Both bidirectional and unidirectional flows are investigated. In our model, the hopping, attachment, and detachment rates vary depending on the state of the corresponding site in the other lane. We obtain a theoretical expression for the global density of the system in the steady state from three kinds of mean-field analyses (1-, 2-, and 4-cluster cases). We verify that the 4-cluster mean-field analysis approximates well the results of computer simulations for the two directional flows and reproduces the differences between them. We expect these findings to contribute to a deeper understanding of the dynamic features of actual traffic systems.