Biased Dynamics of Langmuir Kinetics and Coupling on Exclusion Process

In traffic flow, flyovers play a vital role in reducing traffic congestion, advancing commute timing, and helping to prevent collision scenarios. Inspired by the real-life applications of flyover, we model a coupled two-lane transport system where the lanes are divided into three segments in which the particle lane switching mechanism executes only in the middle segment of the lane, and particle inclusion and expulsion kinetics are performed in first and last segment of the lane to embody the infrastructure of flyover. The nature of the system characteristics is analyzed for diverse values of particle inclusion, expulsion, and coupling rates through graphical diagrams of phase planes, density profiles, shock dynamics, and phase transitions. The time-invariant behavior of the system is inspected numerically by utilizing the well-known method of mean-field theory, and it is discovered that the biased dynamics of particle inclusion, expulsion, and fully asymmetric coupling condition yield the phase diagram to disclose more unanticipated mixed stationary phases. Besides, the system experiences the fruitful novel incident of the double shock phase when the possibility of particle inclusion occurs relatively higher than the expulsion event. Also, it is noticed that the system experiences the fascinating phenomenon of shock propagation by traveling in either vertical/horizontal direction in the shock region of the phase diagram under the symmetric coupling circumstance, such as the position of the shock suddenly transits from the right to left segment without crossing the middle segment. The calculated numerical results are in good agreement with Monte Carlo simulation.