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Jitter is recognized as an important phenomenon that degrades the communication performance. Particularly, in real time services such as voice and video over the Internet, there is evidence that jitter departs from already proposed Laplacian models and that it has a heavy tail behavior. In this paper, we show that an Alpha-Stable jitter model is adequate, and that in some cases the Cauchy distribution provides a satisfactory approximation. Furthermore, this work shows how the jitter dispersion increases with the number of hops in the path, following a power law with scaling exponent dependent on the index of stability ¿. This allows us to predict the expected QoS in terms of the number of nodes and traffic parameters.