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

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.

Hiroki Yamamoto, Shingo Ichiki, Daichi Yanagisawa, Katsuhiro Nishinari · 2021