Energy-Based Proportional Fairness in Cooperative Edge Computing

By executing offloaded tasks from mobile users, edge computing augments mobile devices with computing/communications resources from edge nodes (ENs), thus enabling new services/applications (e.g., real-time gaming, virtual/augmented reality). However, despite being more resourceful than mobile devices, allocating ENs' computing/communications resources to a given favorable set of users (e.g., closer to edge nodes) may block other devices from their services. This is often the case for most existing task offloading and resource allocation approaches that only aim to maximize the network social welfare or minimize the total energy consumption but do not consider the computing/battery status of each mobile device. This work develops an energy-based proportionally fair task offloading and resource allocation framework for a multi-layer cooperative edge computing network to serve all user equipments (UEs) while considering both their service requirements and individual energy/battery levels. The resulting optimization involves both binary (offloading decisions) and continuous (resource allocation) variables. To tackle the NP-hard mixed integer optimization problem, we leverage the fact that the relaxed problem is convex and propose a distributed algorithm, namely the dynamic branch-and-bound Benders decomposition (DBBD). DBBD decomposes the original problem into a master problem (MP) for the offloading decisions and multiple subproblems (SPs) for resource allocation. To quickly eliminate inefficient offloading solutions, the MP is integrated with powerful Benders cuts exploiting the ENs' resource constraints. We then develop a dynamic branch-and-bound algorithm (DBB) to efficiently solve the MP considering the load balance among ENs. The SPs can either be solved for their closed-form solutions or be solved in parallel at ENs, thus reducing the complexity. The numerical results show that the DBBD returns the optimal solution in maximizing the proportional fairness among UEs. The DBBD has higher fairness indexes, i.e., Jain's index and min-max ratio, in comparison with the existing ones that minimize the total consumed energy.