Inspired by the phenomenologies of an open totally asymmetric simple exclusion process (TASEP) with Langmuir kinetics (Lk) and finite resources that dynamically control the entry and exit rates of the TASEP lane, we study the stationary densities and phase transitions in a TASEP with Lk connected to both ends of a particle reservoir. The resulting phase diagrams in the plane of the control parameters are significantly different from those in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model is closely related to a TASEP coupled with Lk on a ring with a point defect, but admits more phases than the latter. Phenomenological implications of our results are discussed.

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• Hopping transport
• Nonequilibrium statistical mechanics
• Nonequilibrium lattice models
• Asymmetric simple exclusion process
• Coarse graining
• Mean field theory
• Monte Carlo methods