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The primary aim of this paper is to present new models for objective, nonintrusive, prediction of voice quality for IP networks and to illustrate their application to voice quality monitoring and playout buffer control in VoIP networks. The contributions of the paper are threefold. First, we present a new methodology for developing perceptually accurate models for nonintrusive prediction of voice quality which avoids time-consuming subjective tests. The methodology is generic and as such it has wide applicability in multimedia applications. Second, based on the new methodology, we present efficient regression models for predicting conversational voice quality nonintrusively for four modern codecs (G.729, G.723.1, AMR and iLBC). Third, we illustrate the usefulness of the models in two main applications - voice quality prediction for real Internet VoIP traces and perceived quality-driven playout buffer optimization. For voice quality prediction, the results show that the models have accuracy close to the combined ITU PESQ/E-model method using real Internet traces (correlation coefficient over 0.98). For playout buffer optimization, the proposed buffer algorithm provides an optimum voice quality when compared to five other buffer algorithms for all the traces considered