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The objective of this paper is to characterize and model the generated traffic in a real fiber network for voice and data transmission. The analyzed data has been provided by the cable operator Telecable Asturias, S.A.U., with more than 37,000 subscribers to the broadband access. A tool to monitor and analyze the traffic has been designed, and a model of the traffic generated in this fiber broadband access network is implemented, representing the usage that network subscribers make of the system. The traffic in each controller is obtained from the aggregation of the separated traffic streams originated by the user's applications. The most significant applications (ftp, http, p2p services, ...) have been processed. We demonstrate that this traffic is statistically self-similar, such behavior having serious implications for the design, control and analysis of high-speed networks. The results in these processes have been validated using the real data provided by the fiber network operator.