Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena

We summarize the findings of a large number of researches concerning the totally asymmetric simple exclusion process (TASEP) with complex lattice geometries. The TASEP has been recognized as a paradigm in modeling and analyzing non-equilibrium traffic systems. The paper surveys both the observed physical phenomena and several popular mean-field approaches used to analyze the extended TASEP models. Several interesting physical phenomena, such as phase separation, spontaneous symmetry breaking, and finite-size effect, have been identified and explained. The future investigations of the extended TASEP with complex lattice geometries are also introduced. This paper may help to obtain a better understanding of non-equilibrium systems.