  We study an open system composed of two parallel totally asymmetric simple
exclusion processes with particle attachment and detachment in the bulk. The
particles are allowed to change their lane from lane-A to lane-B, but not
conversely. We investigate the steady-state behavior of the system using
boundary layer analysis on continuum mean-field equations to provide the phase
diagram. The structure of the phase diagram is quite complex and provides a
complete insight about the steady-state dynamics. We examine two kinds of
transitions in the phase plane: bulk transitions and surface transitions,
qualitatively as well as quantitatively. The dynamics of shock formation,
localization and their dependence on the system parameters and boundary rates
have been investigated. We also justify the non-existence of downward shock in
both the lanes using fixed point theory. Further, we examine the effect of
increasing lane-changing rate on the steady-state dynamics and observe that the
number of steady-state phases reduces with increase in lane-changing rate. Our
theoretical results are supported with extensive Monte-Carlo simulation
results.
