  We study a circuit where a mesoscopic Josephson junction (JJ) is embedded in
an environment consisting of a large bias resistor and a normal metal -
superconductor tunnel junction (NIS). The effective Coulomb blockade of the JJ
can be controlled by the tunneling current through the NIS junction leading to
transistor-like characteristics. We show using phase correlation theory and
numerical simulations that substantial current gain with low current noise
($i_{n}\lesssim 1$ fA/$\sqrt{\text{Hz}}$) and noise temperature ($\lesssim $
0.1 K) can be achieved. Good agreement between our numerical simulations and
experimental results is obtained.
