Dynamic spectrum access (DSA) networks are composed of unprivileged users, called secondary users (SUs), that utilize the spectrum opportunities produced by the absence of co-located privileged primary users (PUs) via their cognitive capabilities. Providing a certain level of quality of service (QoS) to these users is a very challenging problem whilst providing protection to licensed PUs and contenting with nearby SUs. Even though centralized solutions may lead to better solutions in terms of network efficiency, the dynamic nature of DSA networks make the distributed solution approaches more attractive. In this paper, we present a fast, distributed, PU temporal-activity-estimation-aided spectrum assignment scheme for a multi-channel DSA system, including several multi-interface capable SUs with traffic demands at differentiated QoS levels. We first developed the proposed cognitive channel selection method, considering a simplified network having single channel and investigated its performance. Second, considering multi-channel environment, along with contending multi-SUs each of which can utilize multiple channels using their multi-interface property, we adopted the designed algorithm and coupled the proposed spectrum selection scheme with a distributed spectrum sharing mechanism that we devised to increase the overall network utility further. We modeled our scheme along with the network model using MATLAB (R) and evaluated its performance via several simulations. The extensive simulations validate the effectiveness of the proposed channel assignment scheme in terms of the Figure of Merit we defined, composed of the weighted sum of the throughput ratio values for packets of different QoS levels that successfully reached at the destination. The results also show the superior performance of the proposed scheme with respect to a native scheme that utilizes every spectrum opportunity in favor of the most demanding traffic flow. (C) 2017 Elsevier B.V. All rights reserved.