  We study a totally asymmetric simple exclusion process equipped with Langmuir
kinetics with boundaries connected to a common reservoir. The total number of
particles in the system is conserved and controlled by filling factor $\mu$.
Additionally, crowding of reservoir is taken into account which regulates the
entry and exit of particles from both boundary as well as bulk. In the
framework of mean-field approximation, we express the density profiles in terms
of Lambert-W functions and obtain phase diagrams in $\alpha-\beta$ parameter
space.
  Further, we elucidate the variation of phase diagram with respect to filling
factor and Langmuir kinetics. In particular, the topology of the phase diagram
is found to change in the vicinity of $\mu=1$. Moreover, the interplay between
reservoir crowding and Langmuir kinetics develops a novel feature in the form
of back-and-forth transition. The theoretical phase boundaries and density
profiles are validated through extensive Monte Carlo simulations.% We performed
Monte Carlo simulations to validate our theoretical findings.
