A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine onedimensional maps. Based on the disaggregation of the temporal series generated, a valid explanation of the behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.