In this work, we propose a resource allocation algorithm for the LTE downlink that makes use of an adaptive multifractal envelope process and a minimum service curve. The proposed scheduling algorithm aims to improve some network parameters while guaranteeing a maximum delay to the user by considering the following information: backlog, channel condition and user traffic behavior. In order to estimate the maximum network delay, we propose an adaptive minimum service curve for the LTE network that can be used for admission control purposes in the resource allocation algorithm. The performance of the proposed scheduling algorithm is compared to those of several scheduling schemes known in the literature through computational simulations of the LTE downlink. In order to develop a new adaptive envelope process and to precisely describe network flows, we propose an adaptive algorithm to estimate the parameters of the Multifractal Wavelet Model (MWM).The proposed envelope process is compared to the main traffic model based envelope processes known in the literature. Simulations of the LTE downlink considering AMC (Adaptive Modulation and Coding) are carried out showing the efficiency of the proposed resource allocation approach that considers adaptive estimation of network traffic parameters.