Towards satisfying the requirements of International Mobile Telecommunications–Advanced, both the Institute of Electrical and Electronics Engineers (IEEE) and Third Generation Partnership Project (3GPP) introduced revolutionary wireless technologies, exploiting advanced technologies and architectures. Both IEEE's 802.16 (Worldwide Interoperability for Microwave Access (WiMAX)) and 3GPP's Long Term Evolution have been introduced to accommodate the increasing demand for mobile services and applications. To realize the true potential of these technologies, however, opportunistic frameworks for radio resource management must be designed to exploit the adaptive nature of mobile traffic. The utility optimized quality‐of‐service (QoS) framework proposed in this paper for the mobile WiMAX networks achieves this objective. To maintain support for QoS guarantees, the framework capitalizes on the adaptive nature of WiMAX traffic by individually linking connections with a utility function designed to both uphold the end users’ perceived performance and determine bandwidth allocations by a search tree maximization algorithm. In doing so, bandwidth utilization is maximized for all active connections, and blocking and dropping probabilities for new and handover calls, respectively, are minimized. The framework is evaluated through an extensive simulation model and is shown to outperform state‐of‐the‐art solutions. Copyright © 2014 John Wiley & Sons, Ltd.