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

Multilane 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 x 1)-, (2 x 1)-, and (2 x 2)-cluster cases]. We verify that the (2 x 2)-cluster mean-field analysis reproduces the differences between the two directional flows and approximates well the results of computer simulations for some cases. We observe that (2 x 1)-cluster mean-field analyses are already good approximations of the simulation results for unidirectional flows; on the other hand, the accuracy of the approximations much improves by (2 x 2)-cluster one for bidirectional flows. We explain the phenomena in a qualitative manner by a simple analysis of correlations. We expect these findings to give informative suggestions for actual traffic systems.

Automated summary

This paper proposes a two-lane model with interactions between the lanes and investigates both bidirectional and unidirectional flows. Theoretical expressions for the global density of the system in the steady state are obtained through mean-field analyses, and it is found that the (2 x 2)-cluster mean-field analysis approximates the simulation results well. The phenomena are explained qualitatively through a simple analysis of correlations. These findings provide informative suggestions for actual traffic systems.