Abstract: Due to the information interaction and feedback signals can be easily affected by stochastic noise, in this paper, the impact of stochastic noise on the convergence of the distributed network utility maximization algorithms was studied. The impact of stochastic noise on the distributed NUM algorithms was presented, and a sufficient condition under which the distributed NUM algorithms almost everywhere converge was provided and proved by modeling the stochastic noise as martingale and using martingale analysis method. Simulation experiments validate the conclusion of our theoretical analyses.