  We study the influence of a tunable dissipative environment on the dynamics
of Josephson junction arrays near the superconductor-insulator transition. The
experimental realization of the environment is a two dimensional electron gas
coupled capacitively to the array. This setup allows for the well-controlled
tuning of the dissipation by changing the resistance of the two dimensional
electron gas. The capacitive coupling cuts off the dissipation at low
frequencies. We determine the phase diagram and calculate the temperature and
dissipation dependence of the array conductivity. We find good agreement with
recent experimental results.
