  Biomolecular processes are typically modeled using chemical reaction networks
coupled to infinitely large chemical reservoirs. A difference in chemical
potential between these reservoirs can drive the system into a non-equilibrium
steady state (NESS). In reality, these processes take place in finite systems
containing a finite number of molecules. In such systems, a NESS can be reached
with the help of an externally driven pump for which we introduce a simple
model. Crucial parameters are the pumping rate and the finite size of the
chemical reservoir. We apply this model to a simple biochemical oscillator, the
Brusselator, and quantify the performance using the number of coherent
oscillations. As a surprising result, we find that higher precision can be
achieved with finite-size reservoirs even though the corresponding current
fluctuations are larger than in the ideal infinite case.
