Joint Optimization of User Association and Resource Allocation for Load Balancing With Heterogeneous Fairness

Abstract

The joint optimization of user association and resource allocation (UARA) is a fundamental challenge in modern wireless networks, essential for balancing performance, user fairness, and efficiency under growing service demands. Given the latency constraints of emerging applications, distributed pricing-based strategies have widely replaced complex centralized approaches. However, existing literature on <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-fairness predominantly assumes a homogeneous context, assigning an identical parameter <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> to all users. This rigidity fails to address the differentiated prioritization required by real-world networks with diverse application requirements. To bridge this gap, we propose a novel heterogeneous alpha-fairness (HAF) objective function. By assigning distinct <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> values to different users, our framework enables precise, user-specific control over the trade-off between throughput, fairness, and latency. We develop a distributed optimization algorithm utilizing an auxiliary variable framework and provide a rigorous analytical proof of its convergence to an <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-optimal solution. Furthermore, we theoretically show that the optimal solution satisfies a generalized fairness condition that reduces to Kelly’s proportional fairness when <inline-formula> <tex-math notation="LaTeX">$\alpha =1$ </tex-math></inline-formula> for all users. Numerical results demonstrate that the proposed HAF method significantly outperforms conventional homogeneous schemes, offering superior flexibility and performance across multiple criteria in heterogeneous network environments.