This paper proposes new utility-based fairness criteria for radio resource allocation in underlay cognitive radio networks based on harmonic mean concept. Then, joint rate and power allocation problem is considered for secondary users subject to the signal-to-interference-noise ratio and interference threshold constraints. It is shown that the proposed approach yields a better balance between throughput and fairness compared with conventional fairness criteria, namely maxmin and proportional fairness. Furthermore, in order to address the requirements of future wireless applications a cross-layer resource-allocation is proposed for heterogeneous traffic. A combination of streaming (which requires a maximum guaranteed average delay) and elastic traffic (with flexible rate requirements) is considered. The optimization problem allocates the available resources to the streaming users such that the quality-of-service constraints of the streaming users are satisfied. Through extensive simulations, the effect of streaming traffic on the total throughput of elastic users is investigated. Simulation results demonstrate the increase in throughput of elastic users achieved by decreasing number of streaming users.Copyright (c) 2012 John Wiley & Sons, Ltd.