Two-lane totally asymmetric exclusion processes with particle creation and annihilation

This paper studies two-lane totally asymmetric simple exclusion processes (TASEP) coupled with particle creation and annihilation in one of the two lanes (lane 2). The dependence of the density profiles of both lanes on the lane-change rate Ω$\Omega$ is investigated. It is shown that with the increase of Ω$\Omega$, a complex behavior on both lanes occurs. Synchronization of the shocks in both lanes occurs when Ω$\Omega$ exceeds a threshold _Ωc≈10${\Omega }_c\approx 10$. A boundary layer is also observed at the left boundary as a finite-size effect. The situations arising from very large creation/annihilation rate and very small creation/annihilation rate are also investigated. The mean-field analysis is presented and it agrees well with Monte Carlo simulations.