Positive congestion effect on a totally asymmetric simple exclusion process with an adsorption lane

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 [(1×1)-, (2×1)-, and (2×2)-cluster cases]. We verify that the (2×2)-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 (2×1)-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 (2×2)-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.

Effect of self-deflection on a totally asymmetric simple exclusion process with functions of site assignments

This study proposes a model of a totally asymmetric simple exclusion process on a single-channel lane with functions of site assignments along the pit lane. The system model attempts to insert a new particle to the leftmost site at a certain probability by randomly selecting one of the empty sites in the pit lane, and reserving it for the particle. Thereafter, the particle is directed to stop at the site only once during its travel. Recently, the system was determined to show a self-deflection effect, in which the site usage distribution biases spontaneously toward the leftmost site, and the throughput becomes maximum when the site usage distribution is slightly biased to the rightmost site. Our exact analysis describes this deflection effect and show a good agreement with simulations.