Two-Channel Inhomogeneous TASEP with LK: A Model of Traffic Flow

Abstract

In recent years, the application of statistical mechanics to non-equilibrium systems has become a major research area. Asymmetric simple exclusion process (ASEP) plays an important role in non-equilibrium mechanics. This thesis focuses mainly on the dynamics of an asymmetrically coupled two-channel totally asymmetric simple exclusion process with Langmuir Kinetics in presence of a localized bottleneck in any one of the lanes. This model is suitable to study real world situations occurring on multi-lane highways when the flow in one of the lanes is disturbed due to an accident or on some ongoing construction work. We have adopted the hybrid-approach along with the numerical scheme to obtain steady-state phase diagrams and density profiles. We have explored the consequences of different parameters such as bottleneck strength, coupling strength and size of the system on the steady-state dynamics. It is observed that on varying the bottleneck transition rates the topology of the phase diagrams is influenced. Also, an increase in the order of coupling strength reduces the bottleneck effect. Our theoretical arguments are in well agreement with extensively performed Monte-Carlo simulations