  We show how a fixed point based boundary-layer analysis technique can be used
to obtain the steady-state particle density profiles of driven exclusion
processes on two-lane systems with open boundaries. We have considered two
distinct two-lane systems. In the first, particles hop on the lanes in one
direction obeying exclusion principle and there is no exchange of particles
between the lanes. The hopping on one lane is affected by the particle
occupancies on the other, which thereby introduces an indirect interaction
among the lanes. Through a phase plane analysis of the boundary layer equation,
we show why the bulk density undergoes a sharp change as the interaction
between the lanes is increased. The second system involves one lane with driven
exclusion process and the other with biased diffusion of particles. In contrast
to the previous model, here there is a direct interaction between the lanes due
to particle exchange between them. In this model, we have looked at two
possible scenarios with constant (flat) and non-constant bulk profiles. The
fixed point based boundary layer method provides a new perspective on several
aspects including those related to maximal/minimal current phases,
possibilities of shocks under very restricted boundary conditions for the flat
profile but over a wide range of boundary conditions for the non-constant
profile.
