We propose a new model for call arrival process on VoIP tandem networks under heavy traffic load condition. Based on empirical evidence, such call arrivals can be modeled as linear Gaussian processes, and we show that this approach can provide an intuitive and accurate representation for different traffic patterns. In addition, the Gaussian approximation allows finding explicit mathematical equations for the model parameters, and provides effective model validation and significance testing. The model is validated by using hundreds of millions of call records collected from a tandem network in the U.S. We use least-square estimation method to build the model and conduct goodness-of-fit tests to validate it. The result yields a coefficient of determination, R 2, of 0.9973 which shows 99.73% of the variability in the data is explained by the proposed model. The predictability of the model is demonstrated by its accuracy applied to another data set.