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Market analyst research studies predict significant mobile data traffic increase over the next 5 to 10 years. The mobile network operators have to be able to meet these capacity demands by upgrading and optimizing their existing networks in parallel with the deployment of new radio access technologies. This paper proposes a mathematical modeling framework for the mobile broadband traffic growth to be employed in mobile network evolution studies. We show that an "S-curve" model based on the Gompertz function can be appropriately parameterized and provides sufficient flexibility for predicting various traffic growth scenarios. We exemplify the use of the proposed traffic modeling approach with a network evolution case study in the generic setting of a dense urban European network deployment scenario in combination with assumptions on the target network key performance indicator and user equipment receiver capabilities.