Joint Optimization of User Association and Resource Allocation for Load Balancing With Multi-Level Fairness

User association, the problem of assigning each user device to a suitable base station, is increasingly crucial as wireless networks become denser and serve more users with diverse service demands. The joint optimization of user association and resource allocation (UARA) is a fundamental issue for future wireless networks, as it plays a pivotal role in enhancing overall network performance, user fairness, and resource efficiency. Given the latency-sensitive nature of emerging network applications, network management favors algorithms that are simple and computationally efficient rather than complex centralized approaches. Thus, distributed pricing-based strategies have gained prominence in the UARA literature, demonstrating practicality and effectiveness across various objective functions, e.g., sum-rate, proportional fairness, max-min fairness, and alpha-fairness. While the alpha-fairness frameworks allow for flexible adjustments between efficiency and fairness via a single parameter α, existing works predominantly assume a homogeneous fairness context, assigning an identical α value to all users. Real-world networks, however, frequently require differentiated user prioritization due to varying application requirements and latency. To bridge this gap, we propose a novel heterogeneous alpha-fairness (HAF) objective function, assigning distinct α values to different users, thereby providing enhanced control over the balance between throughput, fairness, and latency across the network. We present a distributed, pricing-based optimization approach utilizing an auxiliary variable framework and provide analytical proof of its convergence to an ε-optimal solution, where the optimality gap ε decreases with the number of iterations.