In global gyrokinetic simulations it takes a long time for the turbulence to reach a quasisteady state, and quantitative predictions about the quasisteady state turbulence have been difficult to obtain computationally. In particular, global particle-in-cell gyrokinetic simulations have been inefficient for long simulations due to the accumulation of noise. It is demonstrated that a simple Krook operator can effectively control noise; it also introduces an unphysical dissipation, which damps the zonal flows and can significantly affect simulation results even when the relaxation time is very long. However, it is possible to project out the effects of the Krook operator on the zonal flows. This permits noise accumulation to be controlled while preserving the physics of interest; simulations are then run to determine the level of quasisteady state transport and the variation across the ensemble of turbulent dynamics. Convergence is demonstrated both in the number of computational particles and the unphysical relaxation time. © 2008 American Institute of Physics.